PROBABILISTIC MODELING OF CONDITION-BASED...
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PROBABILISTIC MODELING OF CONDITION-BASED MAINTENANCE STRATEGIES AND QUANTIFICATION OF ITS BENEFITS FOR AIRLINERS By SRIRAM PATTABHIRAMAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012
Transcript of PROBABILISTIC MODELING OF CONDITION-BASED...
PROBABILISTIC MODELING OF CONDITION-BASED MAINTENANCESTRATEGIES AND QUANTIFICATION OF ITS BENEFITS FOR AIRLINERS
By
SRIRAM PATTABHIRAMAN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2012
c© 2012 Sriram Pattabhiraman
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To my loving parents, Pattabhiraman and Usha, and to my beloved sister, Harini
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ACKNOWLEDGMENTS
First and foremost, I would like to thank my advisors, Dr. Nam Ho Kim and Dr.
Raphael Haftka, for giving this opportunity to pursue a doctorate degree. My sincere
thanks for the motivation, and all the comments and suggestions on all aspects of
research, you provided during my entire length of study. The experiences with you did
shape me to become a better person. I am highly indebted to you for that.
I would like to thank my committee members, Dr. Nagaraj Arakere, and Dr. Panos
Pardalos, for their continued support and valued suggestions on my work. A special
thanks for Dr. Pardalos for agreeing to be on my committee on such a short notice.
I would like to thank all my past and present lab mates and friends, Shriram, Matt,
Alex, Diane, Anirban, Felipe, Taiki, Chanyoung, Saad, Kyle, Jinuk, Jinsang, Jian Li, for
their much valued support during a course of my study. Your valuable comments during
the group meetings helped hone my inter-personal and presentation skills.
I would like to thank Dr. Christian Gogu and Dr. Christian Bes, at the Universite de
Paul Sabatier, Toulouse, France, for the internship opportunity. I would like to thank them
for the valuable insight into my research and for all the logistics help during my time in
France.
Life in Gainesville would have been incomplete, if not for my beloved friends. For
those endless discussion on football, music, and practically everything under the sun,
for making me feel completely at home in an alien land, for making my life, practically
void of dull moments, I am thankful to all my friends, and in particular, to the esteemed
members of JFJ group and rev. Sanagam, The.
To my parents and sister, for their continued support during every significant
moment in my life, right from my birth. A simple thanks will never do justice to what you
all mean to me.
I would also like to thank NASA and Air Force for the financial assistance during the
course of my study.
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
CHAPTER
1 INTRODUCTION AND LITERATURE REVIEW . . . . . . . . . . . . . . . . . . 13
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2.1 Damage Tolerance Design . . . . . . . . . . . . . . . . . . . . . . . 151.2.2 Scheduled Maintenance . . . . . . . . . . . . . . . . . . . . . . . . 171.2.3 Condition-based Maintenance . . . . . . . . . . . . . . . . . . . . . 201.2.4 Structural Health Monitoring . . . . . . . . . . . . . . . . . . . . . . 22
1.3 Research Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 METHODOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.2 Corrective Maintenance Procedure . . . . . . . . . . . . . . . . . . . . . . 26
2.2.1 Scheduled Maintenance . . . . . . . . . . . . . . . . . . . . . . . . 282.2.2 Condition-based Maintenance Procedure . . . . . . . . . . . . . . 29
2.3 Modeling Damage Growth and Inspection Process . . . . . . . . . . . . . 312.3.1 Fatigue Damage Growth due to Fuselage Pressurization . . . . . . 322.3.2 Inspection Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3 COMPARING SCHEDULED MAINTENANCE ANDCONDITION BASED MAINTENANCE . . . . . . . . . . . . . . . . . . . . . . . 37
3.1 Damage Growth Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 373.2 Comparison Between Maintenance Processes . . . . . . . . . . . . . . . 383.3 Weight Savings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.1 Minimum Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . 423.3.2 Effect of Varying Thickness . . . . . . . . . . . . . . . . . . . . . . 43
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 SKIPPING UNWANTED PREVENTIVE MAINTENANCE USING CBM . . . . . 48
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Maintenance Strategies to Skip Unnecessary Structural Airframe
Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
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4.2.1 Sched-SHM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2.2 Condition based Maintenance Procedure - skip (CBM-skip) . . . . 51
4.3 Comparison Between Different Maintenance Processes . . . . . . . . . . 514.4 Cost Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.5 Effect of Parameters Affecting CBM-skip on Maintenance Cost . . . . . . 584.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 MAINTENANCE PREDICTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.2 Maintenance Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.3 Choosing Optimal Value of (m, C) . . . . . . . . . . . . . . . . . . . . . . 655.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6 EFFECT OF DAMAGE QUANTIFICATION ERROR OF ONBOARDSHM SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.1 Classifying Management Error Arising from Damage Quantification Error 706.1.1 Condition-based Maintenance . . . . . . . . . . . . . . . . . . . . . 716.1.2 Constant Ratio between Detected and Actual Crack Size . . . . . . 716.1.3 Constant Difference between Detected and Actual Crack Size . . . 75
6.2 Countering Damage Quantification Error . . . . . . . . . . . . . . . . . . . 766.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
APPENDIX
A IDENTIFYING PARAMETERS FOR PARIS LAW . . . . . . . . . . . . . . . . . 81
B COST MODEL FOR SHORT RANGE AIRPLANE (A320) . . . . . . . . . . . . 83
C DIRECT INTEGRATION PROCEDURE . . . . . . . . . . . . . . . . . . . . . . 85
D IDENTIFYING ANOMALIES IN A FLEET OF AIRPLANES . . . . . . . . . . . . 87
D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87D.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87D.3 Error Quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90D.4 Modeling Lemon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
D.4.1 Modeling Lemon by Initial Crack Size . . . . . . . . . . . . . . . . . 91D.4.2 Modeling Lemon by Pressure Differential . . . . . . . . . . . . . . . 92
D.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
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LIST OF TABLES
Table page
3-1 Parameters of damage growth model and inspection model and their values . . 37
3-2 Parameters of CBM processes and the constraints set to determine them . . . 38
3-3 Comparing scheduled and condition-based maintenance on reliability andcriteria contributing to lifecycle cost with same replacement threshold (= 12mm)for both maintenance strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3-4 Comparing the best and worst case costs of CBM with the cost of scheduledmaintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3-5 Dimensions and material properties of fuselage cylinder . . . . . . . . . . . . . 43
3-6 Cost and weight savings from the original fuselage design, to the fuel + maintenancecost of scheduled maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4-1 Comparison of different maintenance processes on the number of maintenancetrips, percentage of panels replaced per airplane, and probability of fatiguefailure of a single panel until the end of life . . . . . . . . . . . . . . . . . . . . . 53
4-2 Comparing the best and worst case costs of different CBM processes withthe cost for scheduled maintenance . . . . . . . . . . . . . . . . . . . . . . . . 57
4-3 Lifetime Fuel cost (based on $/gal) for scheduled maintenance and CBM, fordifferent cases of fuselage mass increase due to on-board sensors and actuators.Fuel cost based on $126.1 / barrel [1] . . . . . . . . . . . . . . . . . . . . . . . 57
6-1 Effect of threshold for requesting maintenance on the number of maintenancetrips, percentage of panels replaced, and the probability of failure of a paneluntil the end of life of a A320 airplane, with a life of 60,000 flight cycles . . . . . 72
6-2 Management error resulting from damage quantification error for various combinationsof threshold for requesting maintenance, amaint and the COV of damage quantification(DQ) error when a constant ratio is maintained between the detected and actualcrack sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6-3 Management error resulting from damage quantification error for various combinationsof threshold for requesting maintenance, amaint and the COV of damage quantification(DQ) error when a constant difference is maintained between the detectedand actual crack sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6-4 Management error resulting from considering detected crack size (aDet) tobe of a value greater than that quantified (aQuant) by on-board SHM system,when threshold for requesting maintenance, amaint = 70mm and the COV ofdamage quantification (DQ) error = 10% when a constant ratio is maintainedbetween the detected and actual crack sizes . . . . . . . . . . . . . . . . . . . 77
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B-1 Airplane parameters affecting cost . . . . . . . . . . . . . . . . . . . . . . . . . 84
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LIST OF FIGURES
Figure page
2-1 The effect of inspection and replacement process on crack length distributions 28
2-2 Example of the scheduled maintenance process . . . . . . . . . . . . . . . . . 29
2-3 Flowchart of maintenance scheduling and assessment procedure for SHMbased inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2-4 Possible region of Paris model parameters . . . . . . . . . . . . . . . . . . . . 34
3-1 Change in cost from that of cost at thickness = 2mm, for various contributorsfor lifecycle cost, for change in fuselage thickness to maintain same level ofprobability of failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3-2 Comparing variation of fuel + maintenance cost for CBM with fuselage thickness,with fuel + maintenance cost for scheduled maintenance at fuselage thickness= 2mm, for different cases of weight increase due to onboard SHM equipment 45
4-1 Flowchart of the Sched-SHM maintenance process . . . . . . . . . . . . . . . . 50
4-2 Flowchart depicting maintenance scheduling and assessment procedure forCBM-skip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4-3 Fraction of airplanes undergoing structural airframe maintenance (i.e. repair)at each scheduled maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4-4 Effect of parameters, ath−skip and arep on the no. of structural airframe maintenancetrips, the no. of unscheduled maintenance trips, and the percentage of panelsreplaced for CBM-skip maintenance strategy . . . . . . . . . . . . . . . . . . . 59
4-5 The effect of the parameters, ath−skip and arep, on the maintenance cost, as afunction of parameters, kSHM and kuns h, and panel replacement cost for CBM-skipmaintenance strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4-6 Pareto front constructed based on parameters affecting maintenance cost . . . 61
5-1 Prediction plot considering the extremities and mean values of joint distributionof (m, C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5-2 Ideal prediction plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5-3 Prediction plots when (m, C) were optimized considering rms of the area differenceuntil the nth maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5-4 Optimal values of (m, C) for cases considered in Figure 5-3 . . . . . . . . . . . 67
5-5 Prediction plot when optimal values of (m, C) until end of a scheduled maintenanceis used to predict the maintenance for the next scheduled maintenance . . . . 67
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5-6 Plot of errors in the prediction plot . . . . . . . . . . . . . . . . . . . . . . . . . 68
6-1 Explaining the effect of damage quantification error . . . . . . . . . . . . . . . . 73
A-1 Comparing the sensitivity of inspection interval for optimal set of parametersand the trend observed in reality . . . . . . . . . . . . . . . . . . . . . . . . . . 82
C-1 Regions of (C,m) for N = 50,000 and a0 = 1mm . . . . . . . . . . . . . . . . . . 86
D-1 Explaining Hierarchical clustering and different ways to compute distance betweenclusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
D-2 Variation of Type I and II errors with maintenance assessments, for variouscases of immediate history considered to classify a lemon . . . . . . . . . . . . 92
D-3 Variation of Type I and II errors with maintenance assessments, for variouscases of immediate history considered to classify a lemon based on differencein pressure differential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
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Abstract of dissertation Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of theRequirements for the Degree of Doctor of Philosophy
PROBABILISTIC MODELING OF CONDITION-BASED MAINTENANCESTRATEGIES AND QUANTIFICATION OF ITS BENEFITS FOR AIRLINERS
By
Sriram Pattabhiraman
May 2012
Chair: Dr. Nam Ho KimCochair: Dr. Raphael T. HaftkaMajor: Mechanical Engineering
Airplane fuselage structures are designed with the concept of damage tolerance,
wherein small damage are allowed to remain on the airplane, and damage that
otherwise affect the safety of the structure are repaired. The damage critical to the
safety of the fuselage are repaired by scheduling maintenance at pre-determined
intervals.
Scheduling maintenance is an interesting trade-off between damage tolerance and
cost. Tolerance of larger damage would require less frequent maintenance and hence,
a lower cost, to maintain a certain level of reliability. Alternatively, condition-based
maintenance techniques have been developed using on-board sensors, which track
damage continuously and request maintenance only when the damage size crosses
a particular threshold. This effects a tolerance of larger damage than scheduled
maintenance, leading to savings in cost. This work quantifies the savings of condition-based
maintenance over scheduled maintenance. The work also quantifies converting the cost
savings into weight savings.
Structural health monitoring will need time to be able to establish itself as a
stand-alone system for maintenance, due to concerns on its diagnosis accuracy and
reliability. This work also investigates the effect of synchronizing structural health
monitoring system with scheduled maintenance. This work uses on-board SHM
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equipment skip structural airframe maintenance (a subsect of scheduled maintenance),
whenever deemed unnecessary while maintain a desired level of safety of structure.
The work will also predict the necessary maintenance for a fleet of airplanes, based
on the current damage status of the airplanes. The work also analyses the possibility
of false alarm, wherein maintenance is being requested with no critical damage on the
airplane. The work use SHM as a tool to identify lemons in a fleet of airplanes. Lemons
are those airplanes that would warrant more maintenance trips than the average
behavior of the fleet.
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CHAPTER 1INTRODUCTION AND LITERATURE REVIEW
1.1 Introduction
Traditionally, aircraft structures have been designed using the concept of damage
tolerance, in which the structure is designed to withstand small cracks, and large cracks
are repaired through scheduled inspections and maintenance. This concept turns out to
be more cost-effective than safe-life design, wherein the structure is designed so that it
doesn’t fail until the end of its life. The concept is cost-effective than safe-life because
airplanes designed based on the latter would be much heavier, and thus, more costly.
In damage tolerance design, it is important to inspect a structure regularly so that all
damage that can possibly threaten the safety can be repaired.
Selecting inspection interval for scheduled inspections depend on size of tolerated
damage and lifecycle cost. To maintain the same level of safety of structure, frequent
inspections may allow toleration of a larger crack. But, frequent inspections would cause
a higher lifecycle cost. Similarly, less frequent inspections leads to lower lifecycle cost,
but tolerates only a small crack size to remain on the structure. But the tolerance of
small crack is limited by the inspection capability. The schedule of maintenance is often
optimized on the cost while maintaining a desired level of reliability.
Alternative to scheduled maintenance, there is ongoing research on condition-based
maintenance. In this approach, damage is continuously monitored, and maintenance is
requested when the damage size crosses a certain threshold. Continuous monitoring
tolerates a much larger crack to remain on the structure, thereby leading to a lower
lifecycle cost. But, there could be substantial cost involved in installing a condition-based
maintenance system, causing higher lifecycle cost. But on-going research work
suggests condition-based maintenance to be cost efficient([2],[3]). A condition-based
maintenance system could be optimized to match a certain level of reliability of a system
or for cost.
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Recently, structural health monitoring (SHM) systems have become available using
on-board sensors and actuators. These systems can perform damage assessment as
frequently as needed, and they could be a good tool for condition-based maintenance.
Hence, inspection by structural health monitoring would warrant a higher damage
tolerance than scheduled maintenance, but could monitor damage more frequently and
in less time than non-destructive inspection. They may have a significant installation
cost, but once installed, the operational cost is quite negligible. Condition-based
maintenance using structural health monitoring could be a valid candidate for savings in
lifecycle cost of an airplane.
Savings in lifecycle cost of an airplane could be traded against savings on the
weight of the airplane, while maintaining the same level of reliability of the airplane
structure. A thinner airplane structure would warrant a faster crack growth and hence,
would cause more maintenance trips, thereby causing an increase in lifecycle cost.
But thinner airplane decreases the fuel cost spent to fly the airplane. The effect of
condition-based maintenance by structural health monitoring system on the weight and
lifecycle cost trade-off is an interesting possibility to look at.
On-board structural health monitoring equipment has some un-resolved issues to
function as a stand-alone device for inspection purpose. There are concerns on the
reliability of the on-board SHM system, and also on the accuracy of its diagnosis. These
concerns must be ironed out before the SHM system is made a part of maintenance
schedule. There is a high possibility of SHM system integrated with traditional scheduled
maintenance, complementing it, before condition-based maintenance scheme is
accepted into the design of maintenance schedule.
Once the condition-based maintenance scheme is integrated with the existing
maintenance scheme, condition-based maintenance could be used as a tool to predict
the time of next structural airframe maintenance (a subset of scheduled maintenance).
Condition-based maintenance could also be used as a tool to identify lemons in a
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fleet of airplanes. Lemons, are those airplanes that require more structural airframe
maintenance than the rest of the fleet.
1.2 Background
1.2.1 Damage Tolerance Design
Structures are traditionally designed with a concept of safe-life. Safe-life design
methodology relies on the use of safety factors on load and material properties to
prevent failure until the end of life of the structure. Safe-life design methodology was
later replaced by fail-safe design methodology wherein a structure may fail before its
end of life, and inspection and maintenance techniques are used to repair the structure
before it fails. Mcbreaty [4] compared safe-life and fail-safe methodology on airframe
design and concluded that the safe-life method is generally inadequate while fail-safe
method is practical and sound. Kennethb [5] concluded that fail-safe design reduced
weight and cost on US Armys LHX, as compared to safe-life design while reducing the
probability of catastrophic failure.
Designing structures using fail-safe methodology is very well addressed in literature.
David [6] presented the general approach to a fail-safe problem, and the various existing
method, and their shortcomings. Queslati and Sankar [7] used fail-safe methodology
to design active and passive suspension on tractor and semitrailer model. Breese and
Gordaninejad [8] used fail-safe methodology on mountain bicycle damper to maintain
minimum required damping capacity in case of electronic systems failure.
For structural applications, Sun et al. [9] solved a fail-safe optimal design problem
for a three member truss under stress, buckling for multiple loading conditions. Moses
[10] used reliability analysis to design trusses based on the failure of the weakest link.
In metallic structures involving fatigue, fail-safe design is used with the concept
of damage tolerance. An established way is to allow small damage to remain on the
structure and replace / repair the damage, only when it grows large enough to affect
the reliability of the structure. This approach is termed as damage tolerance. Broek
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[11] described the damage tolerance requirements applicable to commercial airplanes,
ships, offshore structures and nuclear pressure vessels and Rudd [12] presented the
analytical and experimental damage tolerance requirements for aircraft structures.
Designing structures with the concept of damage tolerance to prevent fatigue
failure is very well addressed in literature. Lind [13] gave an introduction on the
damage tolerance concept. He defined damage tolerance approach as a reciprocal
of vulnerability of the structure, i.e a damage tolerant structure will not be vulnerable to
unforseen future damage. Margery [14] advocated the use of probabilistic methodology
for damage tolerance methods. Lazzeri [15] compared safe life and probabilistic damage
tolerant approaches on the risk of failure and costs for aircraft structural design. Alam
and Jenkins [16] realized the concept of damage tolerance by performing a finite
element analysis (static and dynamic) of a spider web.
In general, damage tolerance analysis is used to determine the effect of cracks on
the strength of a structure and crack growth as a function of time. Broek [17] computed
the remaining life of a ten member structure in structural bending. He noted the tolerable
flaw sizes for different aluminium alloys. Toor [18] summarized different methodologies
to find the residual strength of a structure. He also summarized the various crack growth
laws used in practice. Swift [19] predicted the residual strength of damaged, stiffened
fuselage panels of DC-10, based on matrix force solution on an idealized structure.
The concept of damage tolerance is prevalent in various applications. Graves and
Lagace [20] assessed damage tolerance approach to prevent fracture of pressurized
graphite / epoxy cylinders. Russell et al. [21] discussed various methodologies for
damage tolerance design with specific focus on the fail-safety of composite sandwich
structures. OBrien [22] ensured the damage tolerance design of composite off-axis
plies by predicting the de-lamination growth in the structure. Hayman [23] discussed
damage tolerance design and corrective measures to prevent failure for a naval ship. He
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considered damage present in sandwich structures to have fiber reinforced plastic face
sheets.
For application of concept of damage tolerance to metallic structures, Lazzeri
and Mariani [24] presented different methodologies of damage tolerance, currently in
practice, for helicopter industry. Zerbst et al. [25] gave a brief overview of applications
based on damage tolerance approach in the railway industry. They also mentioned
issues on using damage tolerance approaches for axles, wheels and rails. Mistree
et al. [26] used damage tolerance approaches to design offshore structures. Chamis
[27] used damage tolerance analysis for turbine engine components. He propagated
uncertainty in material properties using computational methods to evaluate the reliability
and remaining useful life of the structure.
For metallic aircraft structures, Zhang and Li [28] used damage tolerance approach
to prevent fatigue failure with a skin crack under a broken stinger. Salgado and Aliabadi
[29] used damage tolerance concept for design of stiffened panels. They also used
dual boundary element method for crack propagation analysis. Alibad et al. [30] also
used dual boundary element method for crack propagation analysis in stiffened fuselage
to analyze effect of membrane and out of plane bending loads. Their work focuses
on damage tolerance approach on metallic fuselage of an airplane, to prevent fatigue
failure. This dissertation focus on damage tolerance approach to prevent fatigue failure
in fuselage of airplane, caused due to excessive damage propagation.
1.2.2 Scheduled Maintenance
Fatigue failure on metallic fuselage panel is caused by excessive damage
propagation. In the damage tolerance approach, small cracks are allowed to remain on
the airplane, while large cracks, that may affect the safety of the airplane are repaired.
The repair of the large cracks is done by maintenance. During maintenance, the
airplane is taken off service and sent to hangar, wherein the corrective maintenance
actions are performed. Eastin and Mowery [31] examined the damage tolerance design
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requirements for large transportation airplanes in the last 30 years with respect to
operational life and damage tolerance threshold. Since these maintenance procedures
are scheduled at pre-determined times to prevent fatigue failure of airplanes, it is termed
as scheduled maintenance.
Maintenance is usually scheduled to prevent failure of a system. Sherif and Smith
[32] reviewed various optimal maintenance scheduling methodology currently used
in literature for systems subjected to failure. Wang [33] presented a survey of various
maintenance policies involving single unit and multi unit deteriorating systems. Bea
[34] summarized a series of technological developments in maintenance to better the
integrity and durability of large crude-oil carriers. Styart and Lin [35] demonstrated a
methodology for probabilistic damage tolerance based maintenance scheduling for
composite structures based on a theory of optimal statistical decisions.
Scheduling maintenance very often will guarantee a high level of safety, but could
be very expensive. Breen [36] reviewed various methodologies for designing structural
maintenance schedule, in practice in United States military and commercial airplanes
and also noted the differences in the methodologies with Royal Australian Air force
airplanes. The optimal maintenance schedule for a system usually involves minimizing
cost while maintaining the desired level of safety. Maintenance is scheduled usually with
emphasis on both safety and cost.
Baek et al. [37] optimized inspection schedule for end beam of uncovered freight
train (brake) to maintain a desired level of safety. Manning et al. [38] optimized the
inspection schedule to maintain a certain level of reliability when the crack growth is
governed by stochastic models. Yang et al. [39] developed an optimum maintenance
schedule for deteriorating bridge structures in probabilistic framework with the objective
of minimizing life-cycle maintenance cost. Oke and Charles-Owabe [40] optimized the
scheduled maintenance schedule, while considering a period- dependent cost function
for the maintenance. Jing et al. [41] optimized maintenance cost for non-periodic
18
inspection interval when the inspection is imperfect. Brot [42] used probabilistic
simulations to minimize fatigue failures with special emphasis on the relative merits of
multiple inspections over a terminating action. Okasha and Frangnopol [43] used genetic
algorithm to solve multi-objective optimization problem involving system reliability,
redundancy and lifecycle cost to schedule structural maintenance.
In airplane, maintenance is scheduled to maintain the airworthiness of the airplane
in service. Airworthiness is a term to describe whether an aircraft has been certified
by national aviation authority, suitable for a safe flight. Akdeniz [44] discussed need
for structural maintenance program to check the airworthiness of airplanes. Ahmadi et
al. [45] described trends in aircraft maintenance in the past 50 years. Hagemaier [46]
stated that in addition to corrosion assessment, repair assessment and service bulletin
compliance programs for the structural safety of the aging aircraft, the aircraft is also
protected by manufacturer’s extended airframe fatigue testing programs and industries’
advancement in non-destructive inspection technology.
There is a lot of work in literature on scheduling the optimum inspection interval
for airplanes, using damage tolerance approach. Goranson [47] noted the various
challenges in scheduling maintenance using damage tolerance approach, considering
the uncertainty in damage detection and the various types of fatigue that affect the
airworthiness of the airplane. Singh and Koenke [48] optimized the inspection schedule
with a tradeoff between safety and maintenance cost and placed emphasis on the
inspection techniques and their importance in damage tolerance design. Nechval et al.
[49] used damage tolerance approach to focus on the inspection scheme of a fatigued
multi-state system (MSS) with decreasing intervals of inspections. Kale and Haftka [50]
used damage tolerance approach to have a trade-off between weight and inspection
cost for aircraft structures subject to fatigue damage growth.
Advancement in the damage tolerance approach for scheduling maintenance
for airplanes involves incorporating real time degradation of the structure into aircraft
19
design. Simpson and Brooks [51] provided processes for incorporating degradation
aspects of aircraft into existing infrastructure of aircraft system design, manufacturing
and maintenance. They also discussed the effect of these structural integrity processes
on cost and safety. Tsai et al. [52] optimized inspection interval considering the effect of
mechanical service, repair and replacement during a particular maintenance operation.
Repair restores the degraded strength partly, while replacement is set to recover the
component to its original condition. The inspection interval is optimized on availability
maximization.
Incidentally, Grimsley et al. [53] noted that a great deal of progress has been made
in probabilistic damage tolerance approach for aircraft structures so that the future
work is more focused on the savings in cost rather than on safety. A different type of
maintenance process, termed condition-based maintenance is gaining in popularity over
scheduled maintenance as the former is found to be more economical (Starr [54] than
the latter.
1.2.3 Condition-based Maintenance
Condition-based maintenance, as the name suggests, has a tool that requests
maintenance when a particular condition is satisfied. Jardine et al. [55] summarized
the recent developments in diagnostics and prognostics of mechanical systems
implementing condition-based maintenance with emphasis on models, algorithms
and maintenance decision making.
Condition-based maintenance technique tracks a continuously deteriorating system
and request maintenance when the deterioration level crosses a pre-determined
threshold. Different approaches have been considered in the literature to model the
deterioration and decision processes. Dieulle et al. [56] used a maintenance scheduling
function to choose the next inspection and maintenance time for a continuously
deteriorating system. Marseguerra et al. [57] used genetic algorithm for a multi-component
system for determining the optimal degradation level beyond which maintenance has
20
to be performed. Chen and Trivedi [58] used a semi-Markov decision process for the
maintenance policy optimization of condition-based maintenance schedule. Ghasemi
et al. [59] used proportional hazards model to represent the system’s degradation and
Markov decision process to model optimal maintenance schedule.
Castainer et al. [60] considered a condition-based maintenance policy for a two-unit
deteriorating system. Each unit is subject to gradual deterioration and is monitored
by sequential non-periodic inspections. Chen and Trivedi [61] derived closed form
expressions of system availability when the device undergoes both deterioration as
well as Poisson type failures. These closed form solutions enabled them to find faster
algorithms to determine the optimal inspection schedule.
Work has also been done in literature to model condition-based maintenance with
emphasis on minimizing cost. Grail et al. [62] modeled condition-based maintenance
process schedule, analytically, for a stochastically and continuously deteriorating single
unit system, with an objective to minimize cost per unit time. Hontelez et al. [63] found
the optimum maintenance policy with cost for continuously deteriorating process, by
formulating the decision process as a discrete Markov decision problem.
Condition-based maintenance was found to lead to savings in cost over scheduled
maintenance. Beral and Speckman [2] observe the advantage of condition based
maintenance using SHM over preventative / scheduled maintenance on various factors
including lifecycle cost and weight of airplane. Boller [3] observed that using SHM for
condition-based maintenance would lead to lower downtime and inspection costs. This
dissertation focuses on quantifying advantages of condition-based maintenance over
scheduled maintenance to prevent fatigue failure in fuselage panels of commercial
airplanes.
In practical situations, for condition-based maintenance technique is used to monitor
the current damage state of a structure, and request maintenance if the structure has
21
deteriorated considerably. Section 1.2.4 describes a technique used to monitor the
current damage of a structure, structural health monitoring.
1.2.4 Structural Health Monitoring
Structural health monitoring is a tool for condition-based maintenance. This
technique analyzes the current damage state of a structure. Boller et al. [64] provided a
background of physical and mathematical models for a huge gamut of applications from
civil infrastructure to management, on the subject of structural health monitoring. Boller
and Biemans [65] presented various techniques that could be used for structural health
monitoring purposes and they also provided methods to validate a structural health
monitoring system. Johnson et al. [66] defined the first attempt at benchmark problem
for comparing different structural health monitoring techniques. They defined a 12 DOF
shear building model as that benchmark problem.
Different types of structural health monitoring system have been researched in
literature. Boller [67] presented different means of monitoring and subsequent life
management for aged airplanes. Giurgiutiu et al. [68] tested E/M impedance method
for near field damage detection and wave propagation methods for far field damage
detection, on simple geometry specimens with seeded cracks. Friswell and Penny
[69] demonstrated that for structural health monitoring using low frequency vibration,
to detect cracks on beam structures. Ihn and Chang [70] used pitch catch method
and imaging method using piezoelectric actuator / sensor to characterize damage
on aluminum plate and stiffened composite plate. Galea et al. [71] used patch in-situ
systems to monitor the damage in composite structures. Sohn et al. [72] used statistical
pattern recognition technique to monitor structural condition of a boat. Zhang et al. [73]
detected damage away from a sensor location using Transmittance Function Monitoring
that use vibration measurements of peizoceramic patches to detect damage. Rose
[74] used ultrasonic guided waves for structural health monitoring purposes. They have
an ability to inspect hidden structures under water, coatings, insulations and concrete.
22
Sekine et al. [75] used fiber Bragg grafting to identify location and shapes of crack in
aircraft panels. Vanik et al. [76] presented a Bayesian probabilistic methodology for
structural health monitoring. They updated the model parameters and probability of
damage for each substructure on a regular basis.
Structural health monitoring techniques also differ on the material used for
monitoring damage on a structure. Mufti [77] used fibre reinforced polymers and
integrated fibre optic sensing technologies to monitor structures, constructed in Canada.
Kang et al. [78] used carbon nano-tube polymer material to form piezoelectric strain
sensor for structural health monitoring applications. Baker et al. [79] embedded optical
fibre sensors for structural health monitoring for adhesively bonded composite repairs
to Australian military aircraft. Boller and Al [80] reviewed existing load monitoring
systems with particular focus on piezoelectric sensors for monitoring impact loads. In
this dissertation, any type of aforementioned on-board diagnostics technique could be
used. It is necessary for them to detect and characterize damage on fuselage panel of
airplane.
Structural health monitoring is considered as an important tool for monitoring
damage in various applications. Ko and Ni [81] explored the recent developments
in structural health monitoring and their application to large scale bridge projects.
Senkine-Pettitte [82] noted the use of structural health monitoring in accurately
predicting the longevity of existing bridges and also designing more durable, smarter
bridges. Boller and Buderath [83] advocated use of structural health monitoring
techniques to revolutionize aircraft monitoring and design process.
Anweraer and Peeters [84] reviewed various research efforts spent on problems
of health monitoring and damage detection. They focused mainly on how reseach
efforts must be deployed to address the user needs. In the same vein, for airplane
applications, Beard et al. [85] presented a list of issues that must be addressed before
structural health monitoring systems could be used in service of commercial airplanes
23
with composite materials. Boller [86] described how structural health monitoring could
be integrated into aircraft design process, with focus on acousto-ultrasonic technique.
Beral and Speckman [87] discussed the requirements an SHM system needs to meet
before it is integrated in-service aircraft.
Structural health monitoring techniques are projected to have some practical
advantages over existing scheduled maintenance. Derriso and Olson [88] advocated
the use of structural health monitoring as a tool for condition-based maintenance in
improving maintenance and reducing lifecycle costs. In this work, Section 5 and Section
6 focus on using structural health monitoring techniques for savings in life-cycle cost
and improving safety over traditional scheduled maintenance. Telgkamp and Schmidt
[89] discussed the possibility of weight savings on the airplane, in future, using SHM
systems.
1.3 Research Objective
This work compares two maintenance strategies set to prevent fatigue failure
in fuselage panels of airplanes, caused due to excessive damage propagation. The
work focuses on damage propagation of cracks on fuselage, caused by the pressure
differential between the cabin and atmosphere. More specifically, this work quantifies
the advantage of condition-based maintenance over scheduled maintenance on various
counts. Structural health monitoring techniques, with on-board sensors and actuators,
are assumed to be used as a tool for condition-based maintenance. The objective of this
work is three-fold.
1) The first objective is to quantify cost savings by simulating damage propagation
on the fuselage panel, and modeling the maintenance processes for scheduled
maintenance and condition-based maintenance using Monte Carlo simulations. The
aim is to quantify the savings in average number of maintenance trips, and hence, the
savings in lifecycle cost of airplane, until its end of life.
24
2) The second objective is to translate the cost savings into savings in weight of the
airplane. Decreasing the weight of the airplane, reduces the fuel cost, but causes an
increase in the maintenance cost of the airplane, due to faster crack growth. This effects
an increase in lifecycle cost for reduction in weight of the airplane. The aim to quantify
the savings on the weight of the airplane, so as to maintain the same lifecycle as that of
scheduled maintenance.
3) The third objective is to synchronize condition-based maintenance with
scheduled maintenance schedule. Structural health monitoring system has a lot of
un-resolved issues to function as a stand-alone system for condition-based maintenance
(CBM). To expedite the use of structural health monitoring for CBM, structural health
monitoring technique is used to request maintenance exactly at the time of scheduled
maintenance, and also to skip the structural airframe maintenance (a subset of
scheduled maintenance), whenever deemed unnecessary. The aim is to quantify
the savings in lifecycle cost obtained by skipping unnecessary structural airframe
maintenance.
The outline of the dissertation is as follows. Damage on airplane grows whenever
the airplane is in operation. Maintenance is scheduled, at various times, during the life
of the airplane to repair damage. Chapter 2 presents the mathematical models used to
model the damage growth and the inspection models for scheduled and condition-based
maintenance for A320 airplane. Chapter 3 discusses the first two objectives. Chapter 3
quantifies the savings in lifecycle cost over scheduled maintenance, and translating
some of the cost savings into weight savings. Chapter 4 discusses synchronizing
condition-based maintenance along with scheduled maintenance. Chapter 4 presents
the savings in lifecycle cost when on-board SHM is used as a tool to skip unwanted
structural airframe maintenance. Chapter 5 uses the on-board SHM system to predict
the number of airplanes in a fleet, that would require structural airframe maintenance at
the time of next scheduled maintenance.
25
CHAPTER 2METHODOLOGY
2.1 Introduction
Nowadays, airplane structures are designed with the concept of damage tolerance.
In damage tolerance design, small damage is allowed to remain on the airplane, and
large damage, that otherwise affect the safety of the structure is repaired. Maintenance
is a tool for damage tolerance, and is scheduled to maintain a desired level of safety of
the airplane until its end of life. In this work, maintenance is set to prevent fatigue failure
due to excessive damage propagation in fuselage panels of airplanes.
Traditionally, maintenance is usually scheduled at pre-determined intervals. Such
maintenance is termed scheduled maintenance, and the maintenance interval is set to
maintain a desired level of safety of the airplane. Alternatively, damage is continuously
tracked and maintenance is requested when damage grows critical. This type of
maintenance is termed condition-based maintenance. Section 2.2 delineates the
different maintenance procedures used in this work. The mathematical models to model
damage propagation and inspection are modeled in Section 2.3
2.2 Corrective Maintenance Procedure
Corrective maintenance procedure involves scheduling / requesting maintenance
to repair / replace any damage that would otherwise threaten the safety of airplane
fuselage. In this work, damage on the fuselage is modeled as a through-the-thickness
center crack in an infinite plate. Repeated pressurization during take-off and landing of
an airplane can cause existing damage on a fuselage panel to grow. Each take-off and
landing causes one cycle of pressurization, and is termed flight cycle.
Damage growth on the fuselage depends on many factors including environmental
conditions, material properties, human factors involving pilot, etc. Since the damage
is modeled as a through-the-thickness center crack in an infinite plate, damage /
crack growth is affected by parameters of the crack growth model. In this work, the
26
rate of crack growth is controlled by, among other factors, the initial crack size due to
manufacturing or previous maintenance, the pressure differential between the cabin and
atmosphere, and the thickness of the fuselage panel. If left unattended, the cracks may
grow to cause fatigue failure of the panel. In damage tolerance design, the less frequent
the maintenance, the lower the damage size threshold for repairing/replacing panels, in
order to maintain a desired level of reliability. The action of repairing/replacing panels
to maintain a desired level of safety until the next scheduled maintenance is termed
corrective maintenance. This section explains corrective maintenance procedures
undertaken to prevent fatigue failure due to excessive damage growth.
The size of cracks in fuselage panels in a fleet of airplanes is modeled as a random
variable characterized by a probability distribution that depends on manufacturing and
the loading history of the airplane. The corrective maintenance procedure changes
this distribution by repairing large-sized cracks as illustrated in Figure 2-1. The solid
curve represents the damage size distribution of the airplane entering the maintenance
hangar. The maintenance process is designed to repair/replace panels with cracks
larger than a threshold, arep. Since damage detection is not perfect, maintenance
only partially truncates the upper tail of the distribution, as represented by the dashed
curve in Figure 2-1. It is noted that while there is uncertainty in damage detection, it
is assumed in this dissertation that the size of the detected damage is known, without
any error/noise. The area under the dashed curve (grey) represents the fraction of
panels missed during maintenance. The damage that is missed during maintenance
and happens to grow beyond the failure damage size afail before the next maintenance
affects the reliability of the airplane. Faster the crack growth rate, smaller will be the arepchosen, to maintain a desired level of reliability. However, the small arep will increase
cost as it requires more replacement of panels. In this work, the threshold, arep, is set to
maintain a specific level of reliability and to reduce the lifecycle cost of an airplane. The
27
Figure 2-1. The effect of inspection and replacement process on crack lengthdistributions
number of maintenance trips and the number of panels repaired/replaced in an airplane
directly affects its inspection and maintenance cost, and thus, its lifecycle cost.
In this work, two types of maintenance procedure are discussed: scheduled
maintenance and condition-based maintenance. In scheduled maintenance, as
name suggests, maintenance is scheduled at specific intervals. In condition-based
maintenance, damage is continuously tracked and maintenance is requested when the
damage size crosses a particular threshold.
2.2.1 Scheduled Maintenance
The flowchart in Figure 2-2 depicts an example of scheduled maintenance process,
in which maintenance is scheduled at specific pre-determined intervals (say, every Npvtflight cycles) and corrective action is taken to ensure the safety of the airplane until
the next scheduled maintenance. The desired level of reliability can be achieved by
setting a threshold value, arep, for replacing/repairing panels. Three parameters affect
the lifecycle cost of an airplane undergoing scheduled maintenance. The frequency
of scheduled maintenance determines the number of maintenance trips an airplane
undergoes during its lifetime. The thickness of the fuselage panel is assumed to control
28
Figure 2-2. Example of the scheduled maintenance process
the damage growth rate, and that along with the threshold for replacement, affect the
number of panels replaced / repaired in the maintenance hangar to ensure safety until
next scheduled maintenance. Maintenance cost, and hence, the lifecycle cost of an
airplane, depends on number of maintenance trips an airplane undergoes, and the
number of panels replaced or repaired during the maintenance trips.
Since the inspection cost during scheduled maintenance is high (in the order of
millions of dollars per airplane), the maintenance interval Npvt is high (in the order
of 4,000 flight cycles). In order to maintain a high level of reliability, the replacement
threshold, arep, is chosen such that the probability of a crack in the size of arep failing
before next maintenance cycle is less than one out of ten millions.
2.2.2 Condition-based Maintenance Procedure
Condition-based maintenance (CBM) process tracks damage continuously (or,
more practically, every 100 flight cycles) and requests maintenance when the damage
becomes threatening to safety. In this work, condition-based maintenance is assumed
here to be performed using a structural health monitoring (SHM) technique. SHM
uses on-board sensors and actuators to analyze the present damage condition of
the airplane. This process is called here maintenance assessment. SHM-based
maintenance assessment can be performed as frequently as every flight; however,
29
in this work, the assessment is assumed to be performed at every Nshm (e.g., 100)
flights due to computational constraints and slowly growing damage. This interval is also
typical of the A-checks of the airplane, i.e. small maintenance task carried out overnight
at the airliners hub hangars. It would make sense to carry out the SHM inspection at the
A-checks since only the sensors themselves would have to be embedded in the airplane
but the monitoring system could be ground based, thus reducing flying weight.
Figure 2-3 delineates the condition-based maintenance process. After damage
assessment via the on-board SHM sensors, maintenance is requested if the maximum
damage size in an airplane exceeds a particular threshold (amaint). The threshold for
requesting maintenance (damage size, amaint) is chosen to maintain a desired level
of reliability until the next scheduled damage assessment (i.e. for the next Nshm = 100
cycles). Once maintenance is requested, all panels on the fuselage are inspected for
damage in the hangar using the on-board SHM equipment, and panels with threatening
damage are repaired or replaced. The threshold for threatening damage size arep (much
lower than threshold for requesting maintenance, amaint) is set to prevent frequent
maintenance for that airplane. Condition-based maintenance by SHM is controlled
by four parameters, in this work. The thickness of the fuselage panel (t) affects the
crack growth rate. The panel thickness (t), along with the frequency of maintenance
assessment (Nshm) and the threshold for requesting maintenance (amaint) affect the
safety of the airplane. These three parameters also control the number of maintenance
trips and number of panels repaired/ replaced in an airplane and hence, affect its
lifecycle cost. Lower the threshold for replacement / repair (arep), lower the size of cracks
that remains on the airplane after a maintenance, and longer it takes for the crack
remaining on the airplane to grow to size of amaint, and hence, longer the time between
subsequent maintenance. Hence, the threshold for replacement / repair (arep)is set
only to prevent frequent maintenance and hence, affects only the lifecycle cost of the
airplane.
30
Figure 2-3. Flowchart of maintenance scheduling and assessment procedure for SHMbased inspection
The main advantage of condition-based maintenance is that only those panels
that actually threaten safety are repaired / replaced. Therefore, the number of panels
repaired/replaced will be much lower than that of scheduled maintenance. On the other
hand, condition-based maintenance has disadvantage in scheduling maintenance and
fleet management because it is difficult to predict when maintenance will be performed.
2.3 Modeling Damage Growth and Inspection Process
The fatigue lifecycle of fuselage panels is viewed as blocks of damage growth
interspersed with maintenance. The model the damage propagation and inspection for
scheduled maintenance and condition based maintenance is elaborated in this section.
31
2.3.1 Fatigue Damage Growth due to Fuselage Pressurization
Cracks or damage refer to existing flaws on the fuselage of an airplane. Damage
causes different types of fatigue failure, depending on its location on the fuselage.
Cracks emanating from bolt holes in the fuselage might interact with other cracks in the
area to cause fatigue failure due to wide spread damage (WFD) or multi-site damage
(MSD). Cracks can also form in the main portion of the fuselage and they grow long
before they cause fatigue failure (two-bay criterion).
The crack growth can be modeled in myriad ways depending on whether the critical
site is subject to MSD / WFD,two-bay crack or other type of fatigue damage. Romlay et
al. [90] used Dual Boundary Element Method to model fatigue crack growth of multiple
crack sites, while Harris et al. [91] used analytical methodology to predict the onset of
WFD in the fuselage structure. Nilsson [92] uses Dugdale model and elastic plastic
crack interaction to model crack growth interactions between a major crack and multiple
small cracks in a fuselage. Based on airframe fatigue tests on various military aircraft,
Molent et al. [93] concluded that a simple crack growth model adequately represents
well, a typical crack growth. In this section, the crack / damage refer to any crack in the
fuselage and the crack can fail due to any of aforementioned criteria like WSD/ MSD,
two bay crack.
In this section, a fuselage is modeled as a hollow uniform cylinder. Damage in the
fuselage panel of an airplane is modeled as a through-the-thickness center straight
crack in an infinite plate in tension. The life of an airplane can be viewed as consisting
of damage propagation cycles, interspersed with inspection and repair. The damage
/ crack propagation could be modeled in myriad ways. Beden et al. [94] provided an
extensive review of crack growth models. Mohanty et al. [95] used an exponential model
to model fatigue crack growth. Scarf [96] advocated the use of simple models, when the
objective was simply to demonstrate methodology. In this work, a simple Paris model is
32
considered to describe the crack growth behavior. However, other advanced models can
also be used.
The damage propagation, in this section, is modeled using the Paris model [97],
which gives the rate of damage size growth with number of flight cycles (N) as a function
of damage half size (a), pressure differential (p), thickness of cylindrical fuselage
representation (t), fuselage radius (r) and the Paris parameters, C and m in Eq. 2–1 as.dadN = C (�K)m (2–1)
where the range of stress intensity factor is approximated in Eq. 2–2 as�K = Aprt √πa (2–2)
The coefficient, A in the stress intensity factor (SIF) is a correction factor intended to
compensate for modeling the fuselage as a hollow cylinder, lack of stiffeners in the
model and for bulging effects.
The half crack size after N flight cycles of propagation, aN is obtained by solving the
differential equation in Eq. 2–1 and given by Eq. 2–3aN = (a01−m/2 + (1−m/2)× N × C × (prt √π)m) 11−m/2 (2–3)
The critical half crack size that can cause failure of the panel is defined in Eq. 2–4 asa r = ( KICprt √π
)
(2–4)
where KIC is the fracture toughness in Mode I.
It is assumed that all panels are composed of aluminum alloy 7075-T651 with
dimensions of 609.6mm (2’) × 609.6mm (2’) × 2.48mm (0.1”). Newmann et al. (Pg 113,
Fig. 3)[98] showed the experimental data plot between the damage growth rate and
the stress intensity factor under Mode I loading. The Paris model parameters, C and m,
are estimated from the intercept and slope, respectively, of the region corresponding
33
to stable damage growth. As the region of the stable damage growth can be bounded
by a parallelogram, the estimates of the bounds of the parameters, C and m, are
obtained from the figure (Fig. 3, Newmann et al. [98]). However, due to variability in
test specimen and measurement environment, the measured parameters, C and m,
also show uncertainty. Therefore, the uncertainty in model parameters needs to be
considered in modeling damage growth.
For a given value of intercept C, there is only a range of slope (m) permissible in
the estimated parallelogram. To parameterize the bounds, the left and right edges of
the parallelogram were discretized by uniformly distributed points. Each point on the left
edge corresponds to a value of C. For a given value of C, there are only certain possible
values of the slope, m. Figure 2-4 plots those permissible ranges of slope (m), for a
given value of intercept (C). In calculating damage growth, the random combination of
C and m is populated from the parallelogram in Figure 2-4. It can be clearly seen from
Fig. 2-4 that the slope and log(C) are negatively correlated; the correlation coefficient is
found to be about -0.8.
Figure 2-4. Possible region of Paris model parameters
34
2.3.2 Inspection Model
Kim et al.[99], Packman et al.[100], Berens and Hovey[101], Madsen et al.[102],
Mori and Ellingwood [103], and Chung et al. [104] have modeled the crack detection
probability as a function of crack size. Coppe et al. [105] modeled the crack detection
probability as a function of crack size and its location on a fuselage panel. In this work,
the inspection of panels for crack is modeled using the Palmberg equation [106] given
by, Pd(a) = (2a/ah)β1 + (2a/ah)β (2–5)
The expression gives the probability of detecting crack with size 2a. In Eq. 2–5, ah is
the crack size corresponding to 50% probability of detection, and β is the randomness
parameter. The parameter ah represents average capability of the inspection method,
while β represents the variability in the process. Different values of the parameters,ah and β , are considered to model the inspection for scheduled maintenance, and
also for SHM-based maintenance assessment. Generally, the inspection technique for
scheduled maintenance is very thorough and would easily detect large cracks. Hence,
a truncated inspection model with truncation at crack size, ten times ah is considered for
scheduled maintenance. Any crack present, with crack size greater than the truncation
limit, will always be detected, for scheduled maintenance.
In this dissertation, probability of detecting a crack is associated with its location on
the panel. The location probability of a crack is proportional to the ease of its detection.
Cracks in the center of the panel are easier to detect ad hence have a lower location
probability. The location probability is set to be uniformly distributed between [0, 1]
to simulate randomness in location of the crack. A crack will be detected only if its
probability of detection exceeds the location probability.
2.4 Monte Carlo Simulation
The lifecycle of the airplane (incl. damage growth and inspection) is simulated
using monte carlo simulations (MCS). A fleet is assumed to have 2000 airplanes. Each
35
airplane is assumed to have 500 panels. Each panel is assumed to have one crack.
Uncertain parameters of the damage growth model, initial damage size, Paris Law
parameters are sampled from their respective distributions and assigned to each panel.
The damage size on each panel after certain known cycles of propagation is obtained
from the closed form solution of Paris Law (see Eq. 2–3. Inspection is performed at
pre-determined intervals. In scheduled maintenance, inspection is performed on all
airplanes at the pre-determined scheduled times. For condition-based maintenance, the
inspection is simulated at the time of every maintenance assessment to decide which
airplanes require maintenance presently. The inspection process is simulated according
to Palmberg expression. Detection of damage is governed by its detection probability.
Maintenance is performed on the airplane whenever deemed necessary (for
CBM), to replace / repair damage critical to the airplane’s safety. Detected damage is
identified to be critical to the safety of the airplane if its size exceeds the replacement
threshold at the time of maintenance. Replacement of such damage is simulated by
sampling damage from the initial crack size distribution and assigning to the panel in
which a damage was identified to be critical to the safety of the airplane. The damage
sizes on the panel of each airplane is updated after every maintenance. The damage
propagation and inspection process continues in a loop until the end of life of the
airplane.
36
CHAPTER 3COMPARING SCHEDULED MAINTENANCE AND
CONDITION BASED MAINTENANCE
3.1 Damage Growth Parameters
The fatigue lifecycle of a short range airplane (like, A320) is modeled in this
section. The values of the parameters for the short range airplane are set to satisfy
certain constraints (to represent reality). The constraints and the procedure to set the
parameters are described in Appendix A.
The inspection process for scheduled maintenance and condition based maintenance
is modeled using Palmberg expression, given in Section 2.3. The values of uncertainties
and parameters of damage growth model and inspection model, for the short range
aircraft, A320, are tabulated in Table 3-1. Uncertainty is considered in the loading
Table 3-1. Parameters of damage growth model and inspection model and their valuesParameter Type ValueInitial half crack size (a0) Random LN(0.2, 35% COV) mmPressure (p) Random LN(0.06, 0.003) MPaRadius of fuselage (r) Deterministic 1.95 mThickness of fuselage panel (t) Deterministic 2 mmParis Law constant (C) Random U[log10(5E-11),log10(5E-10)]Paris Law exponent (m) Random U[3, 4.3]Correction factor for SIF (A) Deterministic 1.255Palmberg parameter forscheduled maintenance (ah−s h) Deterministic 0.63 mm
Palmberg parameter forscheduled maintenance (βs h) Deterministic 2.0
Palmberg parameter for SHMbased inspection (ah−shm)
Deterministic 5 mm
Palmberg parameter for SHMbased inspection (βshm)
Deterministic 5.0
condition and the Paris model parameters.
Since modeling of the structural details of the fuselage is outside the scope of this
work we use a generic model for the fuselage panels and the corresponding damage
growth. The parameters of this generic model are set such as to be representative
37
of fuselage fatigue damage on real short range aircraft. The panel thickness, initial
damage size, correction factor for the stress intensity factor, and the damage replacement
threshold are the parameters of our model we need to set. These are determined such
that our model satisfies certain constraints (such as probabilities of failure until end of
life and between maintenance stops) More detailed description of the constraints and
the optimization processes to determine the parameters are given in Appendix A.
Table 3-2 tabulates crack size thresholds found to be representative of reality in
the aforementioned sense. These thresholds were calculated using direct integration
procedure (see Appendix C). There are 10 scheduled maintenance trips for an
Table 3-2. Parameters of CBM processes and the constraints set to determine themParameter Type ConstraintThreshold for requestingmaintenance for CBM(2× amaint) 79 mm To maintain Pf ∼ 10−8,
between maintenanceassessments
Replacement threshold forscheduled maintenance(2× arep) 12 mm To maintain a Pf ∼ 10−8
until next scheduledmaintenance
airplane, and the replacement threshold, arep will ensure a 10−7 probability of failure until
end of life of an airplane. For CBM, the threshold for requesting maintenance, amaintwould be ensure safety until the next maintenance when a crack size equal to amaint is
present on the airplane. If the number of times, an airplane encounters a crack of sizeamaint on it is less than 10 times, the probability of failure of a panel until end of life of
airplane would be < 10−7.3.2 Comparison Between Maintenance Processes
A typical lifecycle of short range aircrafts fuselage (e.g. fuselage of an A320) is
modeled in this section, with focus on the fatigue life of the airplane due to excessive
crack propagation. Typically for this type of airplanes, the first maintenance is after
20,000 flights and the subsequent maintenance is every 4,000 flights until its end of
lifecycle, which is 60,000 flights.
38
In this section, a scheduled maintenance process of A320 airplane is compared
with a condition-based maintenance process for the same airplane. The maintenance
processes are compared on the basis of average number of maintenance trips an
airplane undergoes, the average percentage of panels replaced per airplane, and
the probability of failure of a panel, until the end of life of an airplane. In scheduled
maintenance, the number of maintenance trips depends on the pre-determined
frequency of maintenance (see Figure 2-2, whereas in condition-based maintenance,
it depends on the damage size and damage growth parameters. The replacement
threshold at each maintenance is set at 12 mm (see Appendix A) for both the maintenance
processes.
The lifecycle of the airplane is simulated using Monte Carlo simulations (MCS).
A fleet of 2,000 airplanes with 500 panels per airplane is considered. Each panel is
assumed to contain a single crack. The equivalent initial flaw size (EIFS) and damage
growth parameters (C, m) are sampled from their respective distributions and assigned
to each panel. Maintenance processes are simulated according to Palmberg expression
(Section 2.3.2), which provides the probability of detecting a crack as a function of
crack length. MCS yields the number of maintenance trips and percentage of panels
replaced in each airplane, until its end of life, for a fleet of 2000 airplanes. Table 3-3
compares the different maintenance processes on the average number of maintenance
trips and percentage of panels replaced per airplane. The number in the parenthesis is
the standard deviation due to the limited number of MCS samples for airplanes.
Table 3-3. Comparing scheduled and condition-based maintenance on reliability andcriteria contributing to lifecycle cost with same replacement threshold (=12mm) for both maintenance strategies
Type of maintenance Probability offailure of a paneluntil end of life
Avg no. ofmaintenancetrips / airplane
Avg. percentageof panels replaced/ airplane
Scheduled 1E-7 10 6.6 (2.5)Condition-based < 1E-7 2.3 (0.7) 6.6 (2.5)
39
It is noted that for a better level of reliability, condition-based maintenance leads to
fewer number of maintenance trips. This is because, CBM tolerates a larger damage
size than scheduled maintenance (see Table 3-2). The scheduled maintenance has
a fixed scheduled for maintenance it replaces panels with crack size exceeding the
replacement threshold (=12mm). Condition-based maintenance request maintenance
only when the damage exceeds the threshold for requesting maintenance (= 79mm).
The percentage of replaced panels remains equal because of same replacement
threshold set for both processes Hence, CBM causes less frequent maintenance trips as
compared to scheduled maintenance, and by extension, savings in maintenance cost.
A cost model based on literature and detailed in Appendix B is used in the present
section to facilitate comparisons between the different maintenance processes, on the
basis of their maintenance cost (inclusive of material and labor cost). The maintenance
cost is an algebraic sum of airframe maintenance and engine maintenance cost. The
engine maintenance and non-structural airframe maintenance is always scheduled at
the time of scheduled maintenance. Only structural maintenance is requested by CBM
based on the current damage status of the airplane.
Based on the empirical expressions and airplane parameters (Table B-1), the
airframe maintenance cost is $1,139 / flight and the engine maintenance cost is
$258 / flights. The aircraft makes 60,000 flights during its lifetime, and undergoes
ten scheduled maintenance. Hence, the cost of one scheduled airframe maintenance
(S) is $6.84 million and the cost of one scheduled engine maintenance (E) is $1.55
million. Scheduled airframe maintenance is further classified into structural airframe
maintenance and non-structural airframe maintenance. Structural airframe maintenance
concerns with preventing failure on airframe structures (like, fuselage) due to excessive
crack propagation. A cost of $1.84 million is assumed for scheduled structural airframe
maintenance.
40
During scheduled structural airframe maintenance, a lot of time is spent of detecting
cracks on the airplane, and identifying the panels to be repaired / replaced. When
maintenance is requested by CBM, the on-board SHM equipment assesses the current
damage status of the airplane, and identifies the panels to be repaired / replaced.
Hence, structural airframe maintenance requested by CBM at the time of scheduled
maintenance will cost only a fraction as compared to scheduled maintenance. The
fraction is denoted as kSHM , and a range of [0.3, 0.7] is assumed for kSHM .
An unscheduled maintenance trip, requested by CBM, is more expensive than
maintenance requested by CBM at the time of scheduled maintenance due to two
reasons. A shorter advance notice the airliner has for accommodating the unscheduled
maintenance as well as due to the fact that the structural airframe maintenance and
the other maintenance (engine, non-structural) are not done at the same time. A
factor, kuns h ( ≥ 1) is set to denote the higher cost incurred and a range of [1.2, 2] is
chosen for kuns h. Factors kuns h and kSHM are independent of each other and the cost of
unscheduled airframe maintenance, requested due to SHM is the product of kuns h, kSHMand the cost of one scheduled airframe maintenance (S).
Since both kuns h and kSHM are independent of each other, the best and worst case
costs for each CBM process would when parameters kuns h and kSHM are both at their
lower and upper limits respectively. Table 3-4 compares the best and worst case costs
of different CBM processes with the cost for scheduled maintenance. It is noted that
Table 3-4. Comparing the best and worst case costs of CBM with the cost of scheduledmaintenance
Maintenance cost (M$)Type kuns h = 1.2, kSHM = 0.3 kuns h = 2, kSHM = 0.7
Scheduled 83.9 83.9CBM 67 (0.4) 71.7 (0.5)
the performing condition-based maintenance is cheaper than scheduled maintenance to
41
prevent fatigue failure in fuselage panels of airplanes. The savings come from the fewer
maintenance trips caused due to higher damage tolerance by CBM.
CBM saves in 7.7 structural airframe maintenance trips per airplane on average, per
airplane through the lifecycle of the airplane. Based on the cost model, each structural
airframe maintenance costs $1.85 million dollars netting a total savings of $14.2 million
dollars. The effect of combination of factors kSHM and kuns h on the savings is observed in
Table 3-4.
3.3 Weight Savings
The previous section concluded that condition-based maintenance leads to savings
in cost over scheduled maintenance while maintaining the same level of safety. This
section focuses on translating some of the cost savings into weight savings of the
airplane.
The fuselage of an airplane has been modeled as an uniform hollow cylinder.
The radius and the length of the fuselage section is obtained from SimCAD [107]. The
thickness of the fuselage section is set based on certain constraints (see Appendix A).
In this section, the weight of the fuselage is controlled by changing the thickness of
the fuselage. It is noted that it is the representative thickness of the uniform cylinder
fuselage model that is changed to account for change in weight.
3.3.1 Minimum Thickness
Weight of the airplane is controlled by varying the thickness of the fuselage. For
the same pressure differential load, thinner cylinder accelerates the crack growth.
To maintain the same level of reliability, extra maintenance needs to be scheduled
to prevent fatigue failure due to excessive crack growth. In addition, the pressure
differential between the cabin and atmosphere also causes hoop stress on the fuselage
cylinder. The hoop stress could cause yielding of the fuselage cylinder if the thickness
is reduced too low. The minimum operable thickness is computed using yielding
constraints. The fuselage cylinder will fail by yielding if the hoop stress exceeds the
42
yield stress of the material. The minimum thickness required to prevent yielding is set
according to Equation 3–1. p.rt ≤ σY⇒ t ≥ p.r
σY (3–1)
where, p is the pressure differential between the cabin and atmosphere, r is the radius of
the fuselage cylinder, t is the thickness of the fuselage cylinder, σY is the yield stress of
the fuselage material (Al 7075-T651)
The dimensions and material properties of fuselage cylinder (Al 7075-T651) are
tabulate in Table 3-5. A safety factor of 1.5 is considered on the yield stress, and a
Table 3-5. Dimensions and material properties of fuselage cylinderParameter ValueRadius of fuselage, r (m) 1.95Pressure differential, p (MPa) 0.08Yield stress, σY (MPa) 503
factor of 3 is considered on the pressure load to account for stress concentration effects.
Based on the properties, stress constraints and safety factors, the minimum thickness to
prevent yielding is 1.39mm. It is noted that the real airframe is composed of stiffeners,
frames, and varying thickness at the intersection of wings, tail. This minimum thickness
of 1.39mm is an representative of equivalent minimum thickness for a uniform hollow
cylinder fuselage model.
3.3.2 Effect of Varying Thickness
Reducing the fuselage panel thickness will reduce the weight of the airplane, and
will reduce the fuel cost to fly the airplane. But, reducing the fuselage panel thickness
accelerates the crack growth for the same loading condition. Faster crack growth will
require more structural airframe maintenance trips for CBM strategy, to maintain the
same level of reliability, increasing the maintenance cost.
43
Figure 3-1 plots the change in cost (in M$)from that of cost at thickness = 2mm, for
the various contributors of lifecycle cost as a function of change in fuselage thickness,
while maintaining the same probability of failure. Fuel cost is based on $126.1 / barrel
[1]. As noted in Figure 3-1, the cost increase in maintenance cost is much greater
that the cost savings for fuel, for the same change in fuselage thickness. Decreasing
1.65 1.7 1.75 1.8 1.85 1.9 1.95 2−4
−2
0
2
4
6
8
10
12
14
Thickness (mm)
Cha
nge
in c
ost u
ntil
end
of li
fe (
M$)
Manufacturing cost for CBMFuel cost for CBMMaintenance cost for CBM
Figure 3-1. Change in cost from that of cost at thickness = 2mm, for various contributorsfor lifecycle cost, for change in fuselage thickness to maintain same level ofprobability of failure
the fuselage thickness from 2mm to 1.65mm, decreases the fuel cost by 3 M$ while
maintaining the same probability of failure of a panel until end of life. But the same
thickness decrease also amounts to a 14 M$ increase in the maintenance cost of
the airplane, causing an increase in fuel+maintenance cost until the end of life of an
airplane. Figure 3-2 plots the variation of fuel+maintenance cost as a function of the
44
fuselage panel thickness for CBM. In Fig 3-2, The solid horizontal line on the top
Figure 3-2. Comparing variation of fuel + maintenance cost for CBM with fuselagethickness, with fuel + maintenance cost for scheduled maintenance atfuselage thickness = 2mm, for different cases of weight increase due toonboard SHM equipment
represents the fuel + maintenance cost for scheduled maintenance at panel thickness
= 2 mm, until end of life of airplane. At fuselage panel thickness of 2mm, the savings
in fuel +maintenance cost for CBM over scheduled maintenance is substantial. As the
fuselage panel decreases, the weight of the airplane decreases, but cause an increase
in fuel + maintenance cost. Hence, decrease in panel thickness cause a decrease in
savings in fuel + maintenance of CBM over scheduled maintenance.
As noted in Figure 3-2, if the on-board SHM equipment causes an higher increase
in weight of the fuselage panel, lower the savings of fuel + maintenance cost of CBM
over that of scheduled maintenance.
The important idea of this section is to translate the cost savings of CBM into weight
savings of the fuselage. Based on Figure 3-2, for the case of CBM with 10% weight
increase, fuel + maintenance cost equals that of scheduled maintenance at fuselage
panel thickness of 1.68mm. In other words, the cost savings at fuselage panel thickness
45
Table 3-6. Cost and weight savings from the original fuselage design, to the fuel +maintenance cost of scheduled maintenance
Type of maintenance Cost savings atfuselage panelthickness = 2mm(M$)
Weight savingsto maintain samefuel + maintenancecost as scheduledmaintenance (%)
Scheduled – –CBM with 5% weightincrease due to onboardSHM equipment
4.2 15
CBM with 10% weightincrease due to onboardSHM equipment
2.8 7
of 2mm could be translated to weight savings of 16% to maintain the same cost as
scheduled maintenance.
Even if we assume that it takes 6 M$ to install SHM system on the airplane, the
CBM saves about 2.8 M$ considering the 10% fuselage mass increase due to the
onboard SHM equipment. The savings in fuel + maintenance cost could be translated
into potential weight savings of 7% as noted in Table 3-6. If the SHM system is set to
increase the airplane weight by 5%, the CBM would lead to 15% weight savings from
the original weight of the airplane, for the same fuel + maintenance cost as scheduled
maintenance.
3.4 Summary
Condition-based maintenance strategy uses on-board structural health monitoring
(SHM) system to track damage, and hence, has a tolerance to larger crack size than
scheduled maintenance. Tolerance to larger crack size causes fewer maintenance for
the commercial airplane, and thereby, savings in maintenance cost, while maintaining
the same level of reliability. The presence of on-board SHM system will increase the
weight of the airplane, thereby causing an increase in the fuel cost of the airplane.
Condition-based maintenance is found to lead to savings in the fuel+maintenance cost
46
of the airplane over scheduled maintenance. The savings in fuel+maintenance cost of
condition-based maintenance over scheduled maintenance is translated to savings in
weight, while maintaining the same level of reliability.
47
CHAPTER 4SKIPPING UNWANTED PREVENTIVE MAINTENANCE USING CBM
4.1 Introduction
In practice, condition-based maintenance with SHM has been implemented in
military and space applications (Goggin et al.[108]), but is yet to be implemented in
commercial airplanes. Farrar and Worden [109] and Goggin et al. [108] summarized the
challenges for SHM systems to be incorporated on commercial airplanes. Ikegami [110]
observed the complexity of using SHM systems on commercial airplanes, but predicts
technology to overcome such difficulty in the near future.
It becomes quite evident that condition-based maintenance needs to work in
tandem with scheduled maintenance, before it is accepted as a stand-alone system.
Fitzwater et al. [111] combined SHM with traditional scheduled maintenance to
minimize lifecycle cost of F-15 fighter frame station 626 bulkhead. In this section,
the condition-based maintenance is used to complement scheduled maintenance
and enable to skip maintenance when deemed necessary. The fundamental idea
is that there will be many cases in which no damage is detected during scheduled
maintenance. If the SHM system is used, such unnecessary maintenance can be
skipped.
At the time of scheduled maintenance, the airplane is taken to a hangar and
undergoes a series of maintenance activities, including the airframe and engine
maintenance. Structural airframe maintenance is a subset of scheduled maintenance,
and focuses on detecting and replacing cracks that would otherwise threaten the
safety of the airplane. Since the maintenance schedule for commercial airplanes is
designed for a low probability of failure (10−7), there is a possibility of no critical cracks
detected on an airplane during a scheduled maintenance, earlier in the life of the
airplane. But, intrusive inspection of all panels in the airplane need to be performed, by
48
non-destructive inspection (NDI) and detailed visual inspection (DVI), to determine the
presence / absence of critical cracks, that otherwise cause fatigue failure.
In this chapter, on-board SHM system determines the current damage status
of the airplane, at the time of scheduled maintenance. Firstly, inspection by SHM
equipment is much cheaper once the SHM system is in place than existing techniques
like NDI or DVI. Secondly, inspection by SHM could detect when scheduled airframe
structural maintenance is unnecessary due to damage being if any non-critical, thus
avoiding time-consuming inspection processes based on manual NDI or DVI. This
chapter focuses on the savings in lifecycle cost due to skipping these manual structural
inspections of the airframe.
4.2 Maintenance Strategies to Skip Unnecessary Structural AirframeMaintenance
In this section, two maintenance strategies to skip unnecessary structural airframe
maintenance are discussed. The strategy discussed in Section 4.2.1, Sched-SHM is a
completely hypothetical procedure. It is neither practical nor advocated. Sched-SHM
procedure is discussed to the effect how inspection using SHM could help skip
unnecessary structural airframe maintenance. On the other hand, CBM-skip discussed
in Section 4-2 is much more practical in its execution, and also focus on skipping
unnecessary structural airframe maintenance.
4.2.1 Sched-SHM
Maintenance schedule is designed such that a panel has a low probability of failure
(∼ 10−7) until its end of life. This causes only a fraction of airplanes to experience
structural airframe repair at earlier scheduled maintenance times. But, in scheduled
maintenance, intrusive inspection of panels need to be performed to ascertain the
presence / absence of large cracks that affect the safety of the airplane. In Sched-SHM,
inspection of panels for damage is performed by the on-board SHM system. The
49
on-board SHM system can help skip structural airframe maintenance, if there are no
life-threatening cracks on the airplane at the time of scheduled maintenance.
The schedule for Sched-SHM maintenance is exactly same as that considered for
scheduled maintenance (see Figure 2-2). The only difference is that the inspection of
the fuselage panels is carried out by the on-board SHM system, before the airplane
enters the maintenance hangar. Figure 4-1 depicts the Sched-SHM maintenance
process. If the maximum crack size detected in the airplane is less than the threshold,ath−skip, the SHM system recommends skipping the current structural airframe maintenance.
Since damage assessment by on-board SHM is less accurate than NDI techniques used
for scheduled maintenance, SHM-Sched would lead to lower level of reliability than
scheduled maintenance.
Figure 4-1. Flowchart of the Sched-SHM maintenance process
50
4.2.2 Condition based Maintenance Procedure - skip (CBM-sk ip)
Using SHM, the damage status can be evaluated, not just at the time of scheduled
maintenance, but as frequently as needed. The frequency of damage status evaluation
(henceforth called maintenance assessment) is assumed here to coincide with A-checks
of the airplane ( 100 flights); i.e., a small maintenance task carried out overnight at the
airliner’s hub hangars. It would make sense to carry out the SHM-based maintenance
assessment at the A-checks since only the sensors themselves would have to be
embedded in the airplane but the monitoring system could be ground based, thus
reducing flying weight and monitoring system costs.
CBM-skip has same objective as Sched-SHM in terms of skipping unneeded
structural airframe maintenance. However, the frequent monitoring of the damage
status would ensure the level of reliability same as scheduled maintenance. If a crack
missed at the time of scheduled maintenance grows critical in between two consecutive
scheduled maintenances, CBM-skip recommends structural airframe maintenance to
be performed immediately. This calls for un-scheduled maintenance, which is costlier.
The threshold for requesting unscheduled maintenance (amaint), is set to prevent a
crack grow beyond critical size between consecutive maintenance assessments.
Figure 4-2 plots the procedure for CBM-skip. The damage assessment is performed at
scheduled maintenance time, as well as every 100 flights. CBM-skip is controlled by
three parameters. The threshold for requesting unscheduled maintenance (amaint) affects
the safety of the airplane. This parameter, along with ath−skip and arep, control the number
of maintenance trips and number of panels repaired/ replaced in an airplane and hence,
affect its lifecycle cost.
4.3 Comparison Between Different Maintenance Processes
A typical lifecycle of short range aircrafts fuselage (e.g. fuselage of an A320) is
modeled in this section, with focus on the fatigue life of the airplane due to excessive
crack propagation. Typically for this type of airplanes, the first maintenance is after
51
Figure 4-2. Flowchart depicting maintenance scheduling and assessment procedure forCBM-skip
20,000 flights and the subsequent maintenance is every 4,000 flights until its end of
lifecycle, which is 60,000 flights.
The damage growth is modeled by a simple Paris Law model (Section 2.3.1).
The values of the parameters are tabulated in Table 3-1. Uncertainty is considered on
the loading condition and the material properties of the fuselage panel. Some of the
parameters of the damage growth model are set to satisfy certain constraints on the
reliability of a panel between maintenance assessment and until end of life of airplane.
The description of the constraints and the optimization processes to fix the parameters
are given in Appendix A. Constraints are to maintain a desired level of safety of the
fuselage panel between subsequent preventive maintenance and also until the end of
life of the airplane. The panel thickness, initial damage size on the panel, correction
52
factor for the stress intensity factor and the damage replacement threshold at each
preventive maintenance are the parameters set to satisfy the constraints.
Maintenance assessment for condition-based maintenance is performed everyNshm = 100 flights. The threshold for requesting maintenance for CBM is set at 79 mm
such as to maintain a probability of failure of 10−8 between maintenance assessments
(i.e. every Nshm = 100 cycles). For CBM-skip, the threshold for skipping a scheduled
preventive maintenance, ath−skip is set at 12 mm. This threshold is set to maintain
a probability of failure of 10−8 until the next scheduled preventive maintenance. All
thresholds of damage size, set to maintain a specific level of reliability, are calculated
using a direct Integration procedure (Appendix C).
The lifecycle of the airplane is simulated using Monte Carlo simulations (MCS)
detailed in Section 2.4. The different types of maintenance are compared on the
basis on the number of maintenance trips and percentage of panels replaced. The
replacement threshold for all maintenance strategies have the same replacement
threshold (arep) of 12mm. Table 4-1 compares the different maintenance processes
on the number of maintenance trips and percentage of panels replaced per airplane.
The number in the parenthesis is the standard deviation. The variants of the CBM
Table 4-1. Comparison of different maintenance processes on the number ofmaintenance trips, percentage of panels replaced per airplane, andprobability of fatigue failure of a single panel until the end of life
Type Avg no. ofmaintenancetrips / airplane
Percentage ofpanels replaced/ airplane
Avg. no. ofunscheduledmaintenancetrips / airplane
Pf of singlepanel until endof life
Scheduled 10 6.6 (2.5) – 1E-7Sched-SHM 3.3 (1.0) 6.6 (2.5) – 2.9E-6 (2E-6)CBMskip 3.3 (1.0) 6.6 (2.5) 0.02 < 1E-7CBM 2.3 (0.7) 6.6 (2.5) 2.3 < 1E-7
procedure, Sched-SHM and CBM-skip, skips unwanted structural airframe maintenance,
and leads to low number of maintenance trips/ airplane. The percentage of panels
53
replaced is constant for all cases, as they all have the same replacement threshold.
Sched-SHM has a higher probability of failure because of on-board SHM missing large
cracks, critical to the safety of the airplane, at the time of scheduled maintenance. Rest
all maintenance strategies are designed for a specific probability of failure.
Figure 4-3 plots the fraction of airplanes in a fleet that undergo structural airframe
maintenance during a given scheduled maintenance. The fraction of airplanes requiring
structural airframe maintenance is low during earlier lifecycle and increases with life.
Sched-SHM helps to skip unneeded structural airframe maintenance, and the result is
reflected in Table 4-1.
Due to the poorer detection capability of SHM, Sched-SHM could miss cracks
critical to airplane’s safety, when invoked at the time of scheduled maintenance, causing
a higher probability of failure than desired. However, frequent damage assessment
in CBM and CBM-skip recovers the same level of probability of failure with scheduled
maintenance. In order to maintain 1E-7 level of probability of failure, CBM-skip calls for
about 0.6% (0.02 unscheduled maintenance trips out of 3.3 maintenance trips) of the
airplanes to have an un-scheduled maintenance trip per lifetime. On the other hand, all
of the structural airframe maintenance requested by CBM are un-scheduled, but it does
lead to fewer structural airframe maintenance trips per airplane, while maintaining the
same level of reliability.
4.4 Cost Comparisons
The information in Table 4-1 can be used to make decisions on the best maintenance
approach only with knowledge of the costs associated with each option. To illustrate
the process, a cost model based on literature and detailed in Appendix B is used
to facilitate comparisons between the different maintenance processes, on the
basis of their maintenance cost (including material and labor cost). In this model
the maintenance cost is the sum of airframe maintenance and engine maintenance
cost, where structural maintenance is a subset of airframe maintenance. The engine
54
Figure 4-3. Fraction of airplanes undergoing structural airframe maintenance (i.e. repair)at each scheduled maintenance
maintenance and non-structural airframe maintenance are always performed at the time
of scheduled maintenance intervals. Only structural maintenance is requested by CBM
based on the current damage status.
Based on the empirical expressions and airplane parameters in Table B-1 in
Appendix B, the airframe maintenance cost is $1,139/flight and the engine maintenance
cost is $258/flight. The aircraft makes 60,000 flights during its lifetime, and undergoes
ten scheduled maintenances. Hence, the cost of one scheduled airframe maintenance
(A) is $6.84 million and the cost of one scheduled engine maintenance (E) is $1.55
million. The cost for structural airframe maintenance (S) is assumed to be $1.8 million.
During scheduled maintenance, most of the time is spent for detecting cracks on
the airplane and identifying the panels to be repaired/replaced. When maintenance is
requested by CBM, the on-board SHM equipment assesses the current damage status
of the airplane, and identifies the panels to be repaired/replaced. Hence, structural
airframe maintenance requested by CBM will cost only a fraction as compared to
55
scheduled maintenance. The fraction is denoted as kSHM , and a range of [0.3, 0.7] is
assumed for kSHM .
An un-scheduled maintenance trip, requested by CBM, is more expensive than
maintenance requested by CBM at the time of scheduled maintenance due to less
advance notice as well as due to the fact that the structural airframe maintenance and
the other maintenance (engine, non structural) are not done at the same time. A factor,kuns h ( > 1) is set to denote the higher cost incurred for un-scheduled maintenance, and
a range of [1.2, 2] is chosen for kuns h. Factors kSHM and kuns h are independent of each
other and the cost of un-scheduled airframe maintenance, requested due to CBM is the
product of kuns h, kSHM and the cost of one scheduled structural airframe maintenance
(S). The total maintenance cost is given by the Eq. 4–1:
Maintenance cost = (E + (A− S)).Np + kSHM .S .NSA + (kuns h − 1).kSHM .S .Nuns h (4–1)
where E is engine maintenance cost, A is airframe maintenance cost, S is structural
airframe maintenance cost. Hence, (A - S) is the non-structural airframe maintenance
cost. Np is the number of scheduled maintenance trips, NSA is the number of times
structural airframe maintenance is performed at the time of scheduled maintenance, andNuns is the number of un-scheduled structural maintenance trips requested by on-board
SHM.
Since both kuns h and kSHM are independent of each other, the best and worst case
costs for each CBM process would be when parameters kuns h and kSHM are both at their
lower and upper limits respectively. Table 4-2 compares the best and worst case costs
of different CBM processes with the cost for scheduled maintenance. CBM requests
only the structural airframe maintenance. All other maintenance (non-structural airframe,
engine) happen at pre-determined scheduled maintenance times. The cost for structural
airframe maintenance is 1.8 million dollars. Saving in about 6.7 maintenance trips /
airplane for Sched-SHM causes about 12 M$ for Sched-SHM. the best case and worst
56
Table 4-2. Comparing the best and worst case costs of different CBM processes with thecost for scheduled maintenance
Maintenance cost (M$)Type kuns h = 1.2, kSHM = 0.3 kuns h = 2, kSHM = 0.7
Scheduled 83.9 83.9SchedSHM 66 (0.5) 69.3 (0.6)CBMskip 67 (0.5) 70.1 (0.6)
CBM 67 (0.4) 71.7 (0.5)
case of cost savings depends on the chosen values of parameters, kSHM and kuns h. It is
noted that even the worst case cost scenarios for CBM lead to substantial savings in the
maintenance cost of an airplane.
SHM uses on-board sensors and actuators, and they cause increase in weight
of the airplane, and hence, cause an increase in fuel cost. An assumption on the
mass of the on-board sensors and actuators, as a percentage of the fuselage mass,
is considered. Table 4-3 compares the fuel cost between preventive maintenance
and CBM, for different cases of fuselage mass increase due to on-board sensors and
actuators. Based on Table 4-3, CBM could cost about 3.5 M$ in excess over scheduled
Table 4-3. Lifetime Fuel cost (based on $/gal) for scheduled maintenance and CBM, fordifferent cases of fuselage mass increase due to on-board sensors andactuators. Fuel cost based on $126.1 / barrel [1]
Scheduled With SHM (5%fuselage massincrease)
With SHM (10%fuselage massincrease
With SHM (20%fuselage massincrease
210.5 M$ 212.1 M$ 213.8 M$ 217.1 M$
maintenance for the excess fuel, until end of life. But, based on Table 4-2, CBM could
lead to at least 12 M$ in savings in maintenance cost over scheduled maintenance.
Based on Tables 4-2 and 4-3, CBM is found to lead to substantial savings over the
lifetime of the aircraft, considering maintenance and fuel costs. Considering the extreme
case, ”CBM”, with kuns h =2 and kSHM = 0.7 in Table 4-2, and SHM with 10% mass
increase, in Table 4-3, the savings for CBM is about 8M$. If an SHM system can be
57
installed on board the airplane for less than this number than the maintenance cost can
be reduced by performing CBM.
Assuming a savings of 5 M$ for CBM over scheduled maintenance for an airplane
until its end of life. Now, a A320 airplane undergoes about 5 -6 flights every day, and
hence, takes 2000 flights in an year. Savings of 5 M$ over the life of an airplane (60,000
flights) is translated to savings of $166,000 per year per airplane. In Fiscal Year 2011,
U.S. Airways reported a profit of $71 million, and it reported a profit of $ 502 million in
FY2010 [112]. Considering a net profit of $ 300 million per year, and with a fleet of 650
airplanes, U.S. Airways records a net profit of $400 million dollars per airplane per year.
Hence, use of CBM will increase the profit by 40%.
4.5 Effect of Parameters Affecting CBM-skip on Maintenance Cost
The maintenance cost for CBM-skip is affected by two parameters ath−skip and arep.The parameter ath−skip controls the number of unscheduled maintenance trips, and arepcontrols the frequency of maintenance. These two parameters have a direct bearing on
the maintenance cost. This section focuses on finding the optimal combination of these
parameters.
A range of [10, 40]mm and [0, 30]mm were chosen for parameters 2 × ath−skip and2 × arep respectively. Simulation of CBM-skip maintenance strategy was performed
on randomly chosen combinations in the range of these parameters. The number
of maintenance trips and the percentage of panels replaced were computed for
each combination of the parameters, ath−skip and arep. Figure 4-4 plots the effect of
parameters, ath−skip and arep on the no. of structural airframe maintenance trips, the no.
of unscheduled maintenance trips, and the percentage of panels replaced. As seen in
Fig. 4-4, the higher the value of ath−skip, the more structural airframe maintenance would
be skipped, than actually needed to be done. To maintain a desired level of probability of
failure, more unscheduled maintenance trips need to be scheduled. Lower the value ofath−skip, fewer maintenance would be skipped, that actually needed. Though lowering the
58
Figure 4-4. Effect of parameters, ath−skip and arep on the no. of structural airframemaintenance trips, the no. of unscheduled maintenance trips, and thepercentage of panels replaced for CBM-skip maintenance strategy
value of ath−skip decreases the number of unscheduled maintenance trips, this leads to
more structural maintenance trips per airplane than necessary.
The replacement threshold, arep controls the frequency of the maintenance
trips. Lower replacement threshold leads to more panels replaced during a given
maintenance, but it delays the onset of next maintenance, causing fewer maintenance
trips. But replacing more panels at a given maintenance will cause an increase of
maintenance cost. Figure 4-5 plots the effect of the parameters, ath−skip and arep, on the
maintenance cost, for various combinations of maintenance cost parameters, kSHM andkuns h, and panel replacement cost. Based on Fig. 4-5, the maintenance cost increases
with increase in replacement threshold, arep. The variation of cost with parameter,ath−skip doesn’t follow a definite variation. There is no appreciable effect of the panel
replacement cost.
To find the optimal combination of parameters, a pareto front of the parameters
affecting the maintenance cost, no. of maintenance trips and percentage of panels
59
Figure 4-5. The effect of the parameters, ath−skip and arep, on the maintenance cost, as afunction of parameters, kSHM and kuns h, and panel replacement cost forCBM-skip maintenance strategy
replaced, is constructed as shown in Figure 4-6 A factor, kuns h of 1.2 is considered to
account for un-scheduled maintenance trips. It is noted that the results do not change
even if kuns h = 2. As seen in Figure 4-6, the optimal combination of 2×arep and 2×ath−skipis marked as a star. The optimal values are arep = 20 mm and ath−skip = 10mm.
4.6 Summary
Two maintenance strategies, Sched-SHM and CBM-skip are modeled in this
chapter to skip unnecessary structural airframe maintenance for a short range airplane
(A320). These maintenance strategies are compared with scheduled maintenance
and condition-based maintenance on the number of structural airframe maintenance
trips and airplane undergoes, and the number of panels repaired in each airplane. The
maintenance strategies are also compared on the basis on maintenance costs. It is
60
Figure 4-6. Pareto front constructed based on parameters affecting maintenance cost
concluded that if on-board SHM system could be installed on the airplane for less than 8
M$, CBM strategy could lead to savings on the lifecycle cost of the airplane.
Two parameters, threshold for skipping structural airframe maintenance, ath−skipand replacement threshold, arep are analyzed for their effect on maintenance cost for
CBM-skip strategy. The optimal combination of these parameters is found that leads to
minimum maintenance cost for CBM-skip strategy.
61
CHAPTER 5MAINTENANCE PREDICTION
5.1 Introduction
Structural health monitoring has been established as a tool to track damage as
often as required. Information obtained from the SHM could be use to predict future
scenarios (prognosis) and be better prepared for the future. Literature is filled with
techniques and methodologies to compute the remaining useful life of a structure. Work
has been done in laboratory using material samples to predict remaining useful life.
Crichlow and McCulloch [113] compared and verified different methods for fatigue life
predictions for airframe.
Engel et al. [114] detail different real issues involved in prediction of remaining
useful life. Keller and Ray [115] observe that residual life prediction could be made
possible for aircraft structures by real-tracking non-destructive techniques like ultrasonic.
Hoeppner and Krupp [116] compare three different fatigue growth models on their
prediction of component life. Coppe et al. [117] show that SHM techniques could be
used to predict the remaining useful life of a structure.
A similar idea of prognosis of remaining useful life is used in this section to predict
the time of next structural airframe maintenance for CBM-skip maintenance strategy.
Prediction of next airframe maintenance is done for a fleet of airplanes. Predicting
maintenance will give airplane companies, time to prepare for necessary corrective
action during structural airframe repair.
The damage status of the airplane is analyzed as frequently as possible using
the onboard SHM system. The CBM-skip (Section 4-2 maintenance methodology
is used. Once damage is detected, its crack growth is extrapolated, assuming a
certain value of damage growth parameters. The crack growth would be under- / over-
predicted based on the difference between the assumed and actual damage growth
62
parameters, associated with the detected damage. The optimum value of damage
growth parameters to make a proper prediction is computed in this section.
5.2 Maintenance Prediction
In this section, fatigue life of panels due to crack growth is modeled, for a short
range airplane’s (A320’s) fuselage. The life of the airplane is modeled as blocks of crack
propagation interspersed with maintenance. Paris model (see Section 2.3.1) is used to
represent crack growth.
The values of the Paris model parameters are tabulated in Table 3-1 (Section 3.1).
Uncertainty is limited to the loading condition and the Paris model parameters. The
panel thickness, initial damage size, correction factor for the stress intensity factor, and
the damage replacement threshold are the parameters selected to satisfy the reliability
constraints. More detailed description of the constraints and the optimization processes
to determine the parameters are given in Appendix A.
The lifecycle of the airplane is simulated using Monte Carlo simulations (MCS)
described in Section 2.4. As soon as a crack is detected, crack growth for that crack
is predicted. The analytical solution of Paris model is used to make the prediction,
considering a deterministic value of material parameters (m, C). The deterministic value
of material parameters is randomly chosen from their distribution. Given the detected
size of the crack, structural airframe maintenance (i.e. need for repair) is predicted at
the time of subsequent scheduled maintenance, if the detected crack is predicted to
grow beyond the replacement threshold, arep, at the time of aforementioned scheduled
maintenance. This prediction process is followed for each airplane in the fleet at every
maintenance assessment.
At each maintenance assessment, based on the detected damage sizes, the
fraction of airplanes in the fleet that would require structural airframe maintenance
(repair) at the next scheduled maintenance is predicted. This prediction at each
maintenance assessment is compared with actual fraction of airplanes undergoing
63
structural airframe repair at the time of scheduled maintenance. The plot of prediction
of fraction of airplanes requiring structural airframe maintenance at the time of next
scheduled maintenance, as a function of maintenance assessment is termed the
prediction plot.
The value of (m, C) chosen is an important parameter to make the prediction.
Figure 5-1 shows the prediction plot, considering the extremities and the mean of (m, C)
joint distribution(see Fig. 2-4). The solid vertical lines represent the times of scheduled
maintenance. The triangles represent the actual fraction of airplanes undergoing
structural airframe maintenance at the time of scheduled maintenance. It is seen that
Figure 5-1. Prediction plot considering the extremities and mean values of jointdistribution of (m, C)
the prediction plot for right top value of (m, C) distribution (in (b)) initially over-predicts
(conservative) in-between scheduled maintenances. Prediction plot for right top value of
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(m, C) distribution predicts a higher fraction of airplanes to undergo maintenance than
the fraction of airplanes that actually undergoes. The over-prediction subsides as the
life of airplane moves closer to the next scheduled maintenance. Similarly, the bottom
values of (m, C) (in (c) and (d)) distribution initially under-predict (un-conservative)
in between scheduled maintenances. This is because, the right top values of (m, C)
distribution predict a faster crack growth than experienced, while the bottom values of
(m, C) distribution predict a slower crack growth than experienced.
It is also noted that considering the mean value of (m, C) distribution (in (e)) still
leads to un-conservative predictions. Based on our choice of (m, C) values, we can end
up conservative / un-conservative predictions.
5.3 Choosing Optimal Value of (m, C)
To find the optimal value of (m, C), we need to ask ourselves two questions. What
is the ideal shape of the prediction plot, we would like to see, and what values of (m, C)
could give such a plot.
The ideal prediction plot should be able to predict the fraction of airplanes
undergoing structural airframe maintenance at the subsequent scheduled maintenance,
right after the present scheduled maintenance. Hence, the ideal prediction plot will
have horizontal lines in between scheduled maintenances as shown in Figure 5-2. To
compute the ideal value of (m, C), a series of values were randomly sampled from the
uniform distribution of (m, C)(see Fig. 2-4). The prediction plot was constructed for
each sampled combination of (m, C). The root mean square (rms) of the difference in
prediction between the obtained prediction plot and ideal prediction plot is minimized to
find the optimal value of (m, C). The optimal values of (m, C) were obtained at the end of
each scheduled maintenance.
Figure 5-3 plots the predictions plots, when value of (m, C) is optimized by
minimizing the rms value of difference in prediction until the nth maintenance, where
n ∈ [3, 10]. The optimal value for each case is noted on the legend of the subplot.
65
Figure 5-2. Ideal prediction plot
Figure 5-4 plots all these 8 optimal values on the distribution of (m, C). The blue region
Figure 5-3. Prediction plots when (m, C) were optimized considering rms of the areadifference until the nth maintenance
represents the full gamut of distribution of (m, C) and the green spots represent the
optimal values of different cases considered in Figure 5-3. The numbers on the plot
represent the nth maintenance considered to compute the rms error. It is noted that the
66
Figure 5-4. Optimal values of (m, C) for cases considered in Figure 5-3
optimal values of (m, C) for the various prediction plots are concentrated around the top
right corner of the distribution, the location with the fastest crack growth rate.
Now, the optimal values of (m, C) obtained until the end of a scheduled maintenance
are used to predict the fraction of airplanes requiring maintenance at the time of next
scheduled maintenance. Figure 5-5 compares such a prediction plot. The error in
Figure 5-5. Prediction plot when optimal values of (m, C) until end of a scheduledmaintenance is used to predict the maintenance for the next scheduledmaintenance
prediction in Figure 5-5 is plotted in Figure 5-6. During prediction, an airplane may
be wrongly predicted to require maintenance (over-predicted), or an airplane requiring
maintenance may not be predicted to have maintenance(under-predicted). Figure 5-6
plots both the errors The solid line represents the ideal prediction plot. The dotted line
represents the fraction of airplanes, for which maintenance is predicted accurately. The
67
Figure 5-6. Plot of errors in the prediction plot
difference between the dotted line and solid line represent the fraction of airplane, which
required maintenance and wasn’t predicted to (under-prediction error)
The difference between dashed line and solid line in the plot represent the
fraction of airplanes for which, maintenance was predicted, but didn’t require any
(over-prediction error). It is noted that the error are high at the end of a scheduled
maintenance, and they die down to zero fairly quickly before the next scheduled
maintenance.
5.4 Summary
This chapter a methodology to predict the fraction of airplanes in a fleet requiring
structural airframe maintenance at the time of next scheduled maintenance, when the
maintenance is performed based on CBM-skip strategy. The chapter computes the
optimal value of damage growth parameters, (m, C) to make a proper prediction, at
the end of each scheduled maintenance. The optimal value of (m, C), computed at the
time of a scheduled maintenance, is used to predict the fraction of airplanes in a fleet
requiring structural airframe maintenance at the time of next scheduled maintenance.
68
The error in prediction is computed and is found to reduce to die down to zero quickly
before the next scheduled maintenance.
69
CHAPTER 6EFFECT OF DAMAGE QUANTIFICATION ERROR OF ONBOARD
SHM SYSTEM
SHM provides on-board diagnostics of the existing damage on the system. There
have been some serious concern raised about the accuracy of damage detection and
damage quantification of the on-board SHM system. In this work, the SHM system the
loss in accuracy of damage detection is modeled by having a less accurate inspection
model for SHM system compared for that of inspection by NDI or GVI. The Palmberg
parameter, ah is modeled in accordance. This chapter focuses on the effect of accuracy
of damage quantification of the on-board SHM system.
6.1 Classifying Management Error Arising from Damage Quant ification Error
The damage quantification error could lead to three kinds of management error.
These errors adversely affect the decision to request maintenance by the on-board SHM
system.
Error 1: A crack critical to the safety of the airplane, is not detected by SHM system.
In this work, error 1 is expressed as a percentage of times a crack critical to the safety of
the airplane was missed, due to error in damage detection.
Error 2: A crack critical to the safety of the airplane is detected, but is measured
to be NOT critical by the on-board SHM system. In this work, error 2 is expressed as a
percentage of times a crack critical to the safety of the airplane was missed, due to error
in damage quantification.
Error 3: A crack NOT critical to the safety of the airplane, is detected but it is
measured to be critical by the on-board SHM system. In this work, error 3 is expressed
as a percentage of pre-mature maintenance visits, an airplane undergoes.
It is noted that errors 1 and 2 have adverse effect of the safety of the system.
Errors 1 and 2 cause the maintenance NOT to be requested when there is a need for
one. Error 3 is of conservative nature wherein the maintenance would be requested
70
earlier than when it is actually desired. The effect of damage quantification error on the
management error would be analyzed in the following sections.
6.1.1 Condition-based Maintenance
In this section, the effect of detection error is analyzed for a condition-based
maintenance strategy (see Section 2.2.2). The simulation of maintenance procedure
is done according to Monte Carlo simulations as described in Section 2.4. The
maintenance assessment is done every 100 cycles. The replacement threshold and
the threshold for requesting maintenance are set based on Table 3-2.
6.1.2 Constant Ratio between Detected and Actual Crack Size
This section focuses on damage quantification error of on-board SHM system
when a constant ratio is maintained between actual and detected crack sizes. Such
error would occur if the on-board SHM system consistently over- / under - predicts a
crack size, depending on the location of the crack with respect to the SHM system. The
effect of damage quantification error is analyzed by adding a noise to the crack size.
The noise is a measure of the damage quantification error arising from the distance
between the crack and the on-board SHM system. When a crack is first detected, its
detected crack size would be sampled from a normal distribution with mean as its actual
crack size, and the with a constant known coefficient of variation (COV). Every time
the crack is detected henceforth, a constant ratio between detected and actual crack
size is maintained. For instance, let us assume the actual crack size is 10mm, when
it first detected. Due to noise in damage quantification, the crack size was quantified
as 8mm. Every time henceforth, the crack is detected, the same ratio between actual
and detected crack sizes would be maintained. If the actual crack size grows to 50mm,
the crack would be detected of size 40mm. Table 6-1 tabulates the effect of threshold
for requesting maintenance on the number of maintenance trips, percentage of panels
replaced, and the probability of failure of a panel until the end of life of an airplane when
the error in damage quantification of on-board SHM is 10%. It is noted that the CBM
71
Table 6-1. Effect of threshold for requesting maintenance on the number of maintenancetrips, percentage of panels replaced, and the probability of failure of a paneluntil the end of life of a A320 airplane, with a life of 60,000 flight cycles
Case Avg. no. ofmaintenancetrips / airplane
Percentage ofpanels replaced /airplane
Pf of a panel untilend of life (60,000flights) of airplane(A320)
SHM with 0% errorPerfect detection
2.3(0.7) 6.6(2.5) <1E-7
SHM with 10% COVerror, 2× amaint =79.8mm
2.3(0.7) 6.6(2.3) 6.7E-4
SHM with 10% COVerror, 2× amaint =70mm
2.5(0.8) 6.8(2.2) 9E-5
SHM with 10% COVerror, 2× amaint =60mm
2.5(0.8) 6.8(2.3) < 1E-6
strategy is designed for a probability of failure of 1E-7. Due to the error in measurement,
some critical cracks are missed and the probability of failure increases to 6E-4. It is also
noted that there isn’t an appreciable effect of the noise in damage measurement on the
number of maintenance trips and the percentage of panels replaced in the airplane.
Fig. 6-1 illustrates why probability of failure increases due to damage quantification
error, and also explains the definition of Error 2. Figure 6-1 plots an illustration of crack
growth of an actual and detected crack. The crack was first detected when the actual
crack size was 10mm. Due to damage quantification error, the crack was detected as
8mm. The position of maintenance assessment intervals is noted as black dotted lines
in the right side of the plot. The location of maintenance assessment intervals is not
plotted in earlier segments for clarity purposes. Let us assume 2× amaint is ∼ 80mm as
shown in (a) in Figure 6-1. The system fails when the crack grows un-detected beyond
95mm. When the actual crack size is 80mm, the detected crack size is measured at
68mm. Structural airframe maintenance is not requested as the detected crack size is
less than 2 × amaint. By the time the detected crack size grows beyond 80mm, the actual
72
Figure 6-1. Explaining the effect of damage quantification error
crack has crossed 95mm and hence, the system fails. The inaccuracy of the damage
quantification system has contributed to the failure of the airplane.
Consider another case when 2 × amaint is reduced to 70mm as shown in (b) in
Figure 6-1. When the actual crack size is 70mm, the detected crack size is 56mm.
Hence, maintenance will not be requested when it should be. When the detected crack
size reaches 70mm, the actual crack size is 90mm, and the system hasn’t failed yet.
Hence, reducing 2× amaint improves the reliability of the system.
Structural airframe maintenance was requested 5 maintenance assessments
after the actual crack size crossed 2 × amaint (= 70mm). So, in 4 of those maintenance
assessments, structural airframe maintenance was NOT requested even thought there
was a large damage on the system. From the time the actual crack size crossed 70mm,
73
there were 4 maintenance assessment wherein the correct management decision wasn’t
taken (requesting structural airframe maintenance). So, error 2 in this case would be 4 /
5 = 80%.
This illustration is for a single crack. Table 6-2 tabulates the errors for a fleet of 2000
airplanes and 500 panels per airplane. The simulation of condition-based maintenance
strategy (see Section 2.2.2 is performed for a short range airplane like A320. Table
6-2 tabulates the different management error resulting from damage quantification
error for various combinations of threshold for requesting maintenance, amaint and
the COV of damage quantification (DQ) error. In Table 6-2, the management error
Table 6-2. Management error resulting from damage quantification error for variouscombinations of threshold for requesting maintenance, amaint and the COV ofdamage quantification (DQ) error when a constant ratio is maintainedbetween the detected and actual crack sizes
Case Critical crackmissed due toerror in detection(% of times)
Critical crackmissed due toerror in damagequantification (%of times)
Pre-maturemaintenancevisits (%)
Pf
DQ COV =10%, 2× amaint= 79.8mm
0 40.4 26.6 6.7E-4
DQ COV =10%, 2× amaint= 70mm
0 46.1 32.1 9E-5
DQ COV =10%, 2× amaint= 60mm
0 51.0 33.3 < 1E-6
DQ COV = 5%,2× amaint =79.8mm
0 24.7 18.9 1.9E-4
DQ COV = 5%,2× amaint =70mm
0 24.9 23.4 < 1E-6
DQ COV = 5%,2× amaint =60mm
0 25.2 25.8 < 1E-6
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is quantified as the percentage of incorrect decisions that happened due to damage
detection quantification error. As the amaint decreases, the distance between amaint anda rit increases, and hence, there presents more opportunities to detect a crack critical to
the safety of the airplane. The presence of more opportunities increase the percentage
of management errors, but help decrease the probability of failure, as described by
Figure 6-1
Also, a higher COV of DQ error leads to more the noise in damage quantification,
and hence, greater percentage of management errors. It is noted that Error 3 is of
conservative nature, and causes a pre-mature request for maintenance.
6.1.3 Constant Difference between Detected and Actual Crac k Size
This section focuses on damage quantification error of on-board SHM system
when a constant difference is maintained between actual and detected crack sizes.
This is a case of bias in the damage quantification by on-board SHM system. The effect
of damage quantification error is analyzed by adding a noise to the crack size. The
noise quantifies the amount of bias involved with damage quantification, for a crack.
When a crack is first detected, its detected crack size would be sampled from a normal
distribution with mean as its actual crack size, and the with a constant known coefficient
of variation (COV). Every time the crack is detected henceforth, a constant difference
between detected and actual crack size is maintained. For instance, let us assume the
actual crack size is 10mm, when it first detected. Due to noise in damage quantification,
the crack size was quantified as 9mm. Every time henceforth, the crack is detected,
the same difference between actual and detected crack sizes would be maintained. If
the actual crack size grows to 50mm, the crack would be detected of size 49mm. Table
6-3 tabulates the different management error resulting from damage quantification
error for various combinations of threshold for requesting maintenance, amaint and the
COV of damage quantification (DQ) error. As noted in Table 6-3, the errors caused
by maintaining a constant difference between the actual and detected crack sizes is
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Table 6-3. Management error resulting from damage quantification error for variouscombinations of threshold for requesting maintenance, amaint and the COV ofdamage quantification (DQ) error when a constant difference is maintainedbetween the detected and actual crack sizes
Case Critical crackmissed due toerror in detection(% of times)
Critical crackmissed due toerror in damagequantification (%of times)
Pre-maturemaintenancevisits (%)
Pf
DQ COV =10%, 2× amaint= 79.8mm
0 5.3 3.7 < 1E-6
DQ COV =10%, 2× amaint= 70mm
0 5.6 4.4 < 1E-6
DQ COV =10%, 2× amaint= 60mm
0 7.4 5.2 < 1E-6
DQ COV = 5%,2× amaint =79.8mm
0 3.1 1.9 < 1E-6
DQ COV = 5%,2× amaint =70mm
0 3.0 1.9 < 1E-6
DQ COV = 5%,2× amaint =60mm
0 2.8 2.3 < 1E-6
much smaller than that caused by maintaining a constant ratio between the actual and
detected crack sizes. This is because there is little difference between the actual and
detected crack growth path in case of constant difference between actual and detected
crack sizes.
6.2 Countering Damage Quantification Error
The damage quantification error can have adverse effects on the probability of
failure of a panel and management decisions as noted in Tables 6-2and 6-3. The
damage quantification error could be countered by always considering a conservative
approach in damage quantification. The detected crack size could be assumed to be of
76
a 10% larger size than quantified by the on-board SHM system. Considering a larger
detected crack is a means of incorporating a positive bias on the crack size quantified by
on-board SHM system. A larger detected crack will reduce error 2, i.e. the error caused
by critical crack missed by damage quantification, but will cause an increase in error 3,
i.e. the number of pre-mature maintenance visits. But error 3 is of conservative nature
and may cause a slight increase in the number of maintenance trips, an airplane goes
to.
The effect of considering a larger detected size is considered for CBM strategy
with a constant ratio between the detected and actual crack sizes. The threshold for
requesting maintenance, 2×amaint is set at 70mm, and the COV of damage quantification
error is set at 10%. Table 6-4 compares the management errors arising considering the
detected crack size to be larger than the crack size quantified by on-board SHM system.
As noted in Table 6-4, greater the value of detected crack size as compared to that
Table 6-4. Management error resulting from considering detected crack size (aDet) to beof a value greater than that quantified (aQuant) by on-board SHM system,when threshold for requesting maintenance, amaint = 70mm and the COV ofdamage quantification (DQ) error = 10% when a constant ratio is maintainedbetween the detected and actual crack sizes
Case Critical crackmissed due toerror indetection (% oftimes)
Critical crackmissed due toerror in damagequantification(% of times)
Pre-maturemaintenancevisits (%)
Pf
aDet = aQuant 0 46.1 32.1 9E-5aDEt = 1.05 × aQuant 0 37.0 53.5 2E-5aDEt = 1.1 × aQuant 0 34.1 69.8 < 1E-6
quantified by on-board SHM system, lower percentage of critical cracks missed due to
damage quantification, but cause a higher percentage of pre-mature visits. The increase
in maintenance visits caused due to increase in pre-mature visits was not found to be
significant.
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6.3 Summary
The effect of damage quantification error of the on-board SHM system on
management errors is analyzed in this chapter for CBM strategy. The management
errors include not requesting maintenance when a critical crack was present, or
requesting maintenance pre-maturely, because of error in quantification of crack
size. The quantified crack size is modeled as having either a constant ratio or a constant
difference with the actual crack size. The effect of the noise in damage quantification
and threshold for requesting maintenance on the management error are discussed,
for various cases of damage quantification error (constant difference and constant
ratio). Considering the detected crack size to be of a greater crack than quantified by
the on-board SHM system was found to reduce the probability of failure and cause
conservative management decisions.
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CHAPTER 7CONCLUSIONS
This work first compares condition-based maintenance strategy with scheduled
maintenance, set to prevent fatigue failure due to excessive crack propagation in the
fuselage panels of commercial airplanes. Condition-based maintenance strategy uses
on-board structural health monitoring (SHM) system to track damage, and hence, has
a tolerance to larger crack size than scheduled maintenance. Tolerance to larger crack
size causes fewer maintenance for the commercial airplane, and thereby, savings in
maintenance cost, while maintaining the same level of reliability. The savings in cost of
condition-based maintenance over scheduled maintenance is translated to savings in
weight, while maintaining the same level of reliability.
Inspection by on-board SHM system is cheaper than the intrusive inspection
performed by non-destructive inspection during scheduled maintenance. Condition-based
maintenance strategies, Sched-SHM and CBM-skip using inspection by on-board
SHM is modeled to skip unnecessary structural airframe maintenance at the time
of scheduled maintenance. These maintenance strategies were found to lead to
savings in lifecycle cost over scheduled maintenance. The optimum combination of two
parameters affecting CBM-skip, threshold for skipping structural airframe maintenance
and replacement threshold, is found by minimizing the maintenance cost.
For CBM-skip maintenance strategy, a methodology is developed is predict the
fraction of airplanes in a fleet that would require structural airframe maintenance at the
time of next scheduled maintenance. The optimal values of damage growth parameters,
(m, C) to make a proper is determined at the time of each scheduled maintenance.
The optimal values of damage growth parameters computed during a scheduled
maintenance were used to predict the fraction of airplanes in a fleet requiring structural
airframe maintenance at the time of subsequent scheduled maintenance. The error
79
in the prediction is found to reduced to zero well before the subsequent scheduled
maintenance.
There might an error involved in the damage quantification by the on-board SHM
system. The error in damage quantification could cause management errors that might
result in higher probability of failure of a panel than desired. The effect of damage
quantification error of the on-board SHM system on management errors is analyzed
for CBM strategy. The management errors include not requesting maintenance when
a critical crack was present, or requesting maintenance pre-maturely, because of
error in quantification of crack size. The quantified crack size is modeled as having
either a constant ratio or a constant difference with the actual crack size. The effect of
the noise in damage quantification and threshold for requesting maintenance on the
management error are discussed, for various cases of damage quantification error
(constant difference and constant ratio). Considering the detected crack size to be of
a greater crack than quantified by the on-board SHM system was found to reduce the
probability of failure and cause conservative management decisions.
The on-board SHM system could inspect the airplane and track damage on the
airplane, as frequently as needed. Continuous tracking of the damage could identify
those airplanes that has a faster crack growth and would require more structural
airframe maintenance than the rest of the fleet. A methodology, modified Hierarchical
sampling is developed to identify such anomalies in a fleet of airplanes.
80
APPENDIX AIDENTIFYING PARAMETERS FOR PARIS LAW
In this work, damage / crack refers to damage in any location of the fuselage,
and the crack growth is modeled using a simple Paris Law model. Since the practical
fuselage structure is different from the idealized Paris model, the parameters of the Paris
Law are adjusted to satisfy certain constraints, in order to mirror realistic circumstances.
Following are the parameters of the Paris Law that need to be set.
• Thickness of the fuselage panel, t
• Correction factor for the stress intensity factor, A
• Replacement threshold for the preventive maintenance, arep−pvt• Initial damage size distribution
The constraints that help mirror reality are:
• Probability of failure of a panel until end of life, for preventive maintenance = 10−7• Probability of failure of a panel between successive preventive maintenance = 10−8• The sensitivity of inspection interval to fuselage panel thickness, for preventive
maintenance must match reality.
Inspection interval is the time taken (in flight cycles) for a crack of size, 2 × arep−pvt , to
grow critical with a probability of failure of 10−8. The probability of failure is calculated
by the direct integration procedure (Appendix C). A plot for the variation of inspection
interval as a function of panel thickness for various stringer lengths is obtained from
the literature[118]. The parameters of the Paris Law need to be adjusted to maintain a
similar sensitivity of inspection interval to panel thickness to mirror reality.
The parameters affecting the inspection interval are varied individually to find the
optimum set of parameters. Figure A-1 compares the sensitivity of inspection interval
to panel thickness for the optimized set of parameters and reality. The optimized set of
parameters that satisfy aforementioned constraints is noted in the caption The optimal
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Figure A-1. Comparing the sensitivity of inspection interval for optimal set of parametersand the trend observed in reality
parameters that satisfy aforementioned constraints are SIF correction factor, A = 1.255,
replacement threshold (2× arep) = 12 mm, and fuselage panel thickness, t = 2 mm.
The distribution of EIFS is assumed to lognormal with 35% coefficient of variation.
The mean of the initial damage size distribution is set to maintain a probability of failure
at the time of first maintenance, which is 20,000 flights. Direct integration procedure is
used to compute the probability of failure for a given set of parameters. The optimized
mean of EIFS is found to be 0.2 mm
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APPENDIX BCOST MODEL FOR SHORT RANGE AIRPLANE (A320)
In order to estimate the cost efficiency of the SHM systems, it is necessary to
discuss about the cost model first. Trip-cost of an airplane includes, among others, fuel
cost, airframe maintenance cost and engine maintenance cost. These cost elements are
given in terms of empirical expression in Kundu [119]. Fuel cost is given in Eq. B–1 as
Fuel charges = block fuel × fuel costblock time
(B–1)
The airframe labor cost is given in Eq. B–2 as
(0.09×Wairframe + 6.7− 350Wairframe + 75)×(0.8 + 0.68× (t − 0.25)t )
× R (B–2)
where Wairframe is the maximum empty weight (MEW) of the airplane less the engine
weight, in tons, R is the labor rate in $/hour, and t is the block time of airplane per flight.
The airframe material cost is given in Eq. B–3 by
(4.2 + 2.2× (t − 0.25)t )
× Cairframe × R (B–3)
where Cairframe is the price of airplane less engine price, in millions of dollars. The
airframe maintenance cost per flight is given as the sum of airframe labor and airframe
material cost. Engine labor cost is given in Eq. B–4 by0.21× R × C1 × C3 × (1 + T )0.4 (B–4)
where, T is the sea level static thrust, in tons, C1 = 1.27−0.2×BPR0.2, where BPR is the
bypass ratio of the engine, C3 = 0.032 × n + K , where n is the number of compressor
stages, K = 0.50 for one shaft, 0.57 for two shafts and 0.64 for 3 shafts. Engine material
cost is given in Eq. B–5 as 2.56× (1 + T )0.8 × C1 × C2 × C3 (B–5)
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where, C2 = 0.4 × (OAPR/20)1.3 + 0.4, where OAPR is the overall pressure ratio of the
engine.
The engine maintenance cost (labor + material) per flight, is given in Eq. B–6 byNe × (
engine labor cost + material costt + 1.3t − 0.25) (B–6)
Parameters affecting the cost model are obtained from aircraft preliminary design
software (SimCAD) [107] and engine specifications[120]. Parameters affecting the
cost model are tabulated in Table B-1. Fuel cost is calculated on the basis of $126.1/
Table B-1. Airplane parameters affecting costParameter Value
MWE (tons) 51.6Engine wt (tons) 13.0Labor rate ($ / hr) 63
block time (hr) 1.1Wairframe (tons) 38.6Cost airframe (M$) 83
Sea level static thrust (tons) 24.6Engine bypass ratio (BPR) 6
No. of compressor stages (n ) 9K 0.57
Overall pressure ratio (OAPR) 31.3No. of engines (Ne) 2
Block fuel (kg) 3604.3Fuel cost ($/kg) 0.9
barrel of jet fuel[1]. A barrel houses 42 gallons of jet fuel and the density of jet fuel is 6.8
lb/gallon
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APPENDIX CDIRECT INTEGRATION PROCEDURE
The direct integration procedure is a method used to compute the probability of an
output variable with random input variables. In this work, the direct integration process
is used to compute the probability of having a specific damage size. The damage size
distribution is a function of initial damage size, pressure differential, and Paris model
parameters (m, C), which are all random as given by Eq. C–1fN(a) = h (a0, f (p), J(C ,m)) (C–1)
where a0, fN(a), f (p) represent the initial damage size, the probability density
functions of damage size after N cycles and pressure differential, respectively. J(C ,m)is the joint probability density of the Paris model parameters (m, C). The probability of
damage size being less than aN after N cycles is the integration of the joint probability
density of input parameters over the region that results in a damage size being less than
or equal to aN ; that is given by Eq. C–2Pr(a < aN) = [∫CaN a0.J(C ,m).f (p).dCaN ℄ (C–2)
where CaN represents the region of (a0, C , m, p) which will give a ¡ aNBased on preliminary analysis, the effect of random pressure differential was
averaged out over a large number of flight cycles. Therefore, the average value of the
pressure differential is used in the following calculation. Hence, Eq. C–3 reduces to be a
function of m, C, as FN(40) = [∫∫A J(C ,m).dC .dm℄ (C–3)
where A represents the region of (C,m) that would give aN¡ 40 mm for a given initial
damage size, a0. Figure C-1 plots the region of (C, m) for initial damage size, a0 = 1mm
after N = 50,000 cycles. The parallelogram represents all possible combinations of (C,
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m). The region in grey results in a damage size (aN) ¿ 40 mm. The points 1 and 2 that
define the grey region are computed first using the analytical expression of Paris model
and the area of the polygon is computed from basic geometry.
Figure C-1. Regions of (C,m) for N = 50,000 and a0 = 1mm
If the initial damage size is distributed, then the integrand is evaluated at different
values in the range of the initial damage size, and the trapezoidal rule is used to
compute the probability at the desired damage size.
86
APPENDIX DIDENTIFYING ANOMALIES IN A FLEET OF AIRPLANES
D.1 Introduction
Structural health monitoring techniques, once installed on the airplanes, will help
track the damage on airplane continuously. The continuous tracking enables prediction
of onset of next structural airframe maintenance, as discussed in Chapter 5. In addition,
tracking damage continuously improves our knowledge of the crack growth encountered
by the airplane. The knowledge of crack growth by each airplane in a fleet could be
utilized to detect airplanes that have a deviant crack growth behavior than the rest
of the fleet. This chapter focuses methodology to identify the airplanes that requires
more maintenance than the rest of the fleet. Identification of such airplanes, early in its
lifecycle, would provide the airplane companies, to make necessary corrective action,
like, retiring the airplane early, selling the airplane off, or be better prepared financially.
An airplane passes through stringent inspections before it is cleared to fly. The
deviatory behavior for an airplane could arise from factors like, the material used for
airplane, environmental conditions the plane is flown in, human factors (like, pilot).
These factors could cause varying rate of crack growth on the airplane. In automobile
industry, the automobiles that require more frequent maintenance than the nominal ones
are called ’lemons’. In this chapter, the same terminology has been used to qualify the
anomalies in a fleet of airplanes that require more frequent maintenance than the rest of
the fleet.
D.2 Methodology
A fleet of 200 airplanes are inspected based on CBM methodology discussed
in Section 2.2.2.The maintenance assessment is done every 100 flights, and the
simulation of lifecycle of the airplane is done according to monte carlo simulation
process detailed in Section 2.4.
87
During each maintenance assessment, the on-board SHM device will provide
information on whether a crack is detected or not at a given location, and if detected,
the crack size at that given location. It is assumed that there is no error in damage
quantification, once the crack is detected.
Cumulative no. of cracks detected in panels (CDP)is the parameter defined to
classify the airplanes into nominal and deviant. It is the cumulative count of number
of cracks detected in the airplane with each maintenance assessment. The logic for
choosing such parameter is as follows. Airplanes with faster crack growth warrant
frequent maintenance. Faster crack growth causes large cracks to form on an airplane
than the rest of the fleet. Larger cracks have higher probability of detection. Hence,
airplanes with faster crack growth will have more cracks detected on it, than the rest of
fleet.
’Lemon’ airplanes will have a higher CDP value than the rest of the fleet. This
section focuses on classifying an airplane as a lemon or nominal, based on its CDP
value. During each maintenance assessment, based on the CDP value for each
airplane, two clusters of airplanes are formed, a lemon cluster and a nominal fleet
cluster. While forming a cluster, it is imperative to find whether the CDP values of
airplanes on each cluster are significantly different from each other, or if it is simply an
abberation. This distinction is made through clustering techniques.
There are many clustering techniques available in literature. Patcha and Park
[121] presents an overview of anomaly detection techniques currently practiced.
Wu and Zhang [122] performed anomaly detection and clustering techniques using
factor analysis for network intuition problem. Wang [123] use kernel-based clustering
techniques to identify outliers for an automobile application. Ramos [124] used
hierarchical clustering techniques to analyze variability in rainfall distribution pattern.
Srivastava [125] discovered recurring anomalies in aerospace problem using high
88
dimensional clustering techniques. A modified version of Hierarchical clustering is used
in this section.
In Hierarchical clustering, first the points are arranged as leaves of a tree. All
points are then merged into their own clusters. When there is more than one cluster,
the closest pair of clusters is merged together. To determine the distance between the
clusters, they use single link, average link or complete link as described in Figure D-1.
In Hierarchical clustering, average link is a means to join clusters. Average Link is
Figure D-1. Explaining Hierarchical clustering and different ways to compute distancebetween clusters
used as a means of distinguishing between clusters of CDP values in this section. Two
clusters of CDP values would be separated from each other by a break-off CDP value.
The break-off CDP value is computed such that distance between the mean of clusters
on either side of the break off CDP value is maximum.
During each maintenance assessment, based on the current CDP value of each
airplane on the fleet, a break-off CDP value is computed. Airplanes with CDP values
greater than the break-off CDP value, will be classified as lemons. The accuracy of such
classification is investigated in this chapter.
89
D.3 Error Quantification
Lemons are first created in a fleet of airplanes such that they have a higher rate of
crack growth than nominal airplanes. During simulation of airplane lifecycle, an airplane
is classified as a lemon or nominal, using Hierarchical clustering, based on its CDP
value at a given maintenance assessment. The different types of error that creeps up
whenever a classification is such made, is quantified in this section.
Null hypothesis: H0: Airplane is a nominal airplane Alternate hypothesis: Ha:Airplane is a lemon Type I error (α): Rejecting a null hypothesis when it is actually true.
i.e. to call a nominal airplane as a lemon. Type II error (β): Accepting a null hypothesis
when it is a false. i.e. to fail to detect a lemon when it is one.
The immediate history of an airplane is considered before classifying it as a lemon.
4 different cases of classifying a lemon based on immediate history is considered.
An airplane is classified as lemon if it has been classified as a lemon Case 1: At that
maintenance assessment Case 2: in atleast 10% of its ”immediate” past maintenance
assessments Case 3: in atleast 25% of its ”immediate” past maintenance assessments
Case 4: in atleast 75% of its ”immediate” past maintenance assessments The last 1000
cycles (10 maintenance assessments) is considered as the immediate past.
D.4 Modeling Lemon
Airplanes with deviant behavior than the rest of the fleet (lemon airplane), are
first modeled in different ways. The higher crack growth rate for lemons is modeled by
increasing the initial crack size or the pressure differential acting of lemon airplanes. It is
noted here, that the increase in initial crack size or the increase in pressure differential is
simply a modeling aspect, and not necessarily represent the actual case. In reality, the
faster crack growth could be attributed to different material of airplane or environmental
conditions.
The lifecycle of the airplane is simulated and the airplanes are classified as
lemon or nominal airplane at each maintenance assessment. The error involved in
90
wrongly classifying a nominal airplane or a lemon is computed at each maintenance
assessment. The variation of the error in classification with maintenance assessment is
plotted to find the effectiveness of the clustering technique.
D.4.1 Modeling Lemon by Initial Crack Size
Lemons are created with higher initial crack size than the rest of the fleet. In
practice, the stringent norms on inspection, before the airplane enters service, wouldn’t
allow such disparity in initial crack size between airplanes. The higher initial flaw size
is simply to simulate the faster crack growth in lemons. The nominal fleet of airplanes
have a initial crack size, distributed as LN(0.2, 0.07) mm. In this section, the lemons
are modeled to differ in the mean of the initial crack size situation. Three cases of 0.5
mm mean, 0.4 mm mean and 0.3 mm mean are considered for the lemons. All other
parameters remain constant between nominal and lemon airplanes.
A fleet of 200 airplanes is considered. Each airplane has 500 panels. 10% of
the 200 airplanes are modeled lemons. Maintenance assessment is performed every
100 cycles. CDP value is computed for each airplane during those maintenance
assessments. Based on the CDP value of the fleet, hierarchical clustering is used
to classify each airplane as nominal / lemon. Figure D-2 plots the variation of Type I
and II errors with maintenance assessments, for various cases of immediate history
considered to classify a lemon As noted in Figure D-2, when there is a significant
difference between the crack growth of nominal airplane and lemon airplane, the error in
classifying them accurately dies down to zero at around 10,000 flight cycles, well before
the time of first maintenance. Airplane companies could be able to make a decision on
the lemon airplane, very early in its lifecycle.
If the lemon and nominal airplane are not significantly different, there will be some
error remaining in their clustering of lemon and nominal airplane. It is noted that there
is no appreciable effect of considering the immediate history in classifying a lemon,
91
Figure D-2. Variation of Type I and II errors with maintenance assessments, for variouscases of immediate history considered to classify a lemon
concluding that once an airplane is classified as a lemon, it was always classified a
lemon.
D.4.2 Modeling Lemon by Pressure Differential
In this section, the lemons are modeled by being acted on a different pressure
differential than nominal airplanes. Nominal airplanes are acted on a pressure
differential, with a distribution of LN(0.06, 0.003) MPa. The lemons are modeled
with a higher mean pressure differential. Two cases of pressure differential, 0.07
MPa mean and 0.08 MPa mean, were considered for the lemons. Figure D-3 plots
the variation of Type I and II errors with maintenance assessments, for various cases
of immediate history considered to classify a lemon As seen in Figure D-3, a mean
pressure differential of 0.08 MPa for lemons creates a significant difference between the
nominal and lemon airplanes, and the all errors for this case vanishes at around 30,000
flight cycles, i.e. around the half the life of the airplane. For less significant difference,
there remains an error in classifying the airplane as nominal or lemon. It is noted that
there is no appreciable difference between considering immediate history. It reiterates
that once an airplane was classified as a lemon, it always was.
92
Figure D-3. Variation of Type I and II errors with maintenance assessments, for variouscases of immediate history considered to classify a lemon based ondifference in pressure differential
D.5 Summary
Continuous tracking of damage by on-board SHM system could help identify the
airplanes that have faster crack growth than the rest of the fleet, and hence, require
more structural airframe maintenance visits than the rest of the fleet. A modified
Hierarchical clustering method is used to identify such anomalies in a fleet of airplanes,
using cumulative number of detected panels as the measure to cluster the anomalies
from nominal ones. The anomalies are modeled different from the nominal fleet based
on their initial crack size and pressure differential. The modified Hierarchical clustering
identifies the anomalies when there is significant difference between the anomalies and
the rest of the fleet of airplanes.
93
REFERENCES
[1] “Iata,” 11 Feb 2012.
[2] B. Beral and H. Speckman, “Structural health monitoring (shm) for aircraftstructures: A challenge for system developers and aircraft manufacturers,” inStructural Health Monitoring, F.-K. Chang, Ed. DEStech Publications, 2003.
[3] C. Boller, “Next generation structural health monitoring and its integration intoaircraft design,” International Journal of Systems Science, vol. 31, no. 11, pp.1333–1349, 2000.
[4] J. E. Mcbreaty, “Fatigue and fail safe airframe design,” Tech. Rep., SAE, 1956.
[5] K. Amer, “A new philosophy of structural reliability, fail safe versus safe life,” inAHS, Annual Forum, 44th, June 1988, pp. 3–16.
[6] D. Broek, “Concepts in fail-safe design of aircraft structures,” Tech. Rep., Defensemetals information center, 1971.
[7] F. Queslati and S. Sankar, “Performance of a fail-safe active suspension withlimited state feedback for improved ride quality and reduced pavement loading inheavy vehicles,” in International Truck and Bus Meeting and Exposition, Nov 1992.
[8] D. G. Breese and F. Gordaninejad, “Semi-active, fail-safe magneto-rhelogical fluiddampers for mountain bicycles,” International Journal of Vehicle Design, vol. 33,no. 1, pp. 128–138, 2003.
[9] P. Sun, J. Arora, and E. Haug Jr, “Fail-safe optimal design of structures,” Engi-neering Optimization, vol. 2, pp. 43–53, 1976.
[10] F. Moses, “Reliability based structural design,” Structural Division, vol. 96, no. 2,pp. 221–244, 1970.
[11] D. Broek, “Concepts of fracture control and damage tolerance analysis,” in ASMInternational, 1996, pp. 410–419.
[12] J. L. Rudd, “Airforce damage tolerance design philosophy,” in Damage Toleranceof Metallic Structures: Analysis Methods and Applications, J. Chang and J. Rudd,Eds., ASTM STP 842, pp. 134–141. American Society for Testing and Materials,1984.
[13] N. C. Lind, “A measure of vulnerability and damage tolerance,” ReliabilityEngineering and System Safety, vol. 48, no. 1, pp. 1–6, 1995.
[14] M. R. Artley, “Probabilisitc damage tolerance method for metallic aerospacestructure,” Tech. Rep., Wright Research and Development Center, 1989.
94
[15] R. Lazzeri, “A comparison between safe-life, damage tolerance and probabilisiticapproaches to aircraft structure fatigue design,” Aerotecnica Missil e Spazio, vol.81, no. 2, pp. 53–64, 2002.
[16] M. Alam and C. Jenkins, “Damage tolerance in naturally compliant structures,”International Journal of Damage Mechanics, vol. 14, no. 4, 2005.
[17] D. Broek, “Fail safe design procedures,” Tech. Rep., NATO Advisory Group forAerospace RD, 1974.
[18] P. M. Toor, “A review of some damage tolerance design approaches for aircraftstructures,” Engineering Fracture Mechanics, vol. 5, no. 4, pp. 837–876, 1973.
[19] T. Swift, “Development of the fail-safe design features of the dc-10,” in DamageTolerance in Aircraft Structures, ASTM STP 486, pp. 164–214. American Societyfor Testing and Materials, 1971.
[20] M. J. Graves and P. A. Lagace, “Damage tolerance of composite cylinders,”Composite Structures, vol. 4, no. 1, pp. 75–91, 1985.
[21] S. G. Russell, W. Lin, H.-P. Kan, and R. B. Deo, “Damage tolerance and fail-safetyof composite sandwich panels,” Tech. Rep., SAE Technical Paper, 1994.
[22] K. T. OBrien, “Towards a damage tolerance philosophy for composite materialsand structures,” in Composite Materials: Testing and Design, S. P. Garbo, Ed.,vol. 9 of ASTM STP 1059, pp. 7–33. American Society for Testing and Materials,1990.
[23] B. Hayman, “Approaches to damage assessment and damage tolerance forfrp sandwich structures,” Sandwich Structures and Materials, vol. 9, no. 6, pp.571–596, 2007.
[24] L. Lazzeri and U. Mariani, “Application of damage tolerance principles tothe design of helicopters,” International Journal of Fatigue, vol. 31, no. 6, pp.1039–1045, 2009.
[25] U. Zerbst, K. Madler, and H. Hintze, “Fracture mechanics in railway applications -an overview,” Engineering Fracture Mechanics, vol. 72, no. 2, pp. 163–194, 2005.
[26] F. Mistree, T. Lyon, and J. Shupe, “Design of damage tolerant offshore structures,”in Oceans 82, Sep 1982, pp. 1201–1206.
[27] C. C. Chamis, “Damage tolerance and reliability of turbine engine components,” inRTO AVT Workshop, Oct 1998.
[28] X. Zhang and Y. Li, “Damage tolerance and fail safety of welded aircraft wingpanels,” AIAA Journal, vol. 43, no. 7, pp. 1613–1623, 2005.
95
[29] N. Salgado and M. Aliabadi, “An object oriented system for damage tolerancedesign of stiffened panels,” Engineering Analysis with Boundary Elements, vol. 23,no. 1, pp. 21–34, 1999.
[30] M. Alibdai, P. Wen, and N. Salgado, “Boundary element analysis for damagetolerance assessment of aircraft panels,” International Journal of ComputerApplications in Technology, vol. 15, no. 4, pp. 147–156, 2002.
[31] R. G. Eastin and J. B. Mowery, “30 years of damage tolerance - have we got itright?,” in ICAF 2009, Bridging the Gap between Theory and Operational Practice,M. Bos, Ed. Springer, 2009.
[32] Y. Sherif and M. Smith, “Optimal maintenance models for systems subject tofailure- a review,” Naval Research Logistics, vol. 28, no. 1, pp. 47–74, 1981.
[33] H. Wang, “A survey of maintenance policies of deteriorating systems,” EuropeanJournal of Operational Research, vol. 139, no. 3, pp. 469–489, 2002.
[34] R. Bea, “Marine structural integrity programs,” Marine Structures, vol. 7, no. 1, pp.51–76, 1994.
[35] A. Styuart and K. Lin, “Maintenance planning for aircraft damage tolerancecomposite structures based on risk assessment,” in 48th SMDM Conference,2007.
[36] G. W. Breen, “Aircraft scheduled structural maintenance programs: Currentphilosophies and methods in united states and their applicability to royal australianair force,” M.S. thesis, Air Force Institute of Technology, 1988.
[37] S.-H. Baek, S.-S. Cho, H.-S. Kim, and W.-S. Joo, “Reliability design of preventivemaintenance scheduling for cumulative fatigue damage,” Mechanical Science andTechnology, vol. 23, no. 5, pp. 1225–1233, 2009.
[38] S. Manning, J. Yang, F. Pretzer, and J. Marler, “Reliability centered maintenancefor metallic airframes based on stochastic crack growth approach,” in Advances inFatigue Lifetime Predictive Techniques, M. Mitchell and R. Landgraf, Eds., ASTMSTP 1122, pp. 422–434. American Society for Testing and Materials, 1992.
[39] S. le Yang, D. M. Frangopol, and L. C. Neves, “Optimum maintnenace strategyfor deteriorating bridge structures based on lifetime functions,” EngineeringStructures, vol. 28, no. 2, pp. 196–206, 2006.
[40] S. Oke and O. Charles-Owaba, “An approach for evaluating preventivemaintenance scheduling cost,” International Journal of Quality and ReliabilityManagement, vol. 23, no. 7, pp. 847–879, 2006.
[41] C. Jing and W. Huawei, “Optimal maintenance of aircraft structure based onimperfect inspection,” Nanjing University of Aeronautics and Astronautics, vol. 4,2009.
96
[42] A. Brot, “Evalluating strategies for minimizing fatigue failures in metallicstructures,” in USAF Aircraft Structural Integrity Program Conference, Dec2004.
[43] N. M. Okasha and D. M. Fangopol, “Lifetime-oriented multi-objective optimizationof structural maintenance considering system reliability, redundancy and life-cyclecost using ga,” Structural Safety, vol. 31, no. 6, pp. 460–474, 2009.
[44] A. Akdeniz, “Aeroplane structural maintenance and corrosion prevention,” AircraftEngineering and Aerospace Technology, vol. 68, no. 3, pp. 3–7, 1996.
[45] A. Ahmadi, P.Soderholm, and U. Kumar, “An overview of trends in aircraftmaintenance program development:past, present and future,” in European Safetyand Reliability Conference, 2007, pp. 2067–2076.
[46] D. Hagemaier, “Inspection of aging aircraft - a manufacturer’s perspective,” inInternational Conference on Aging Aircraft and Structural Airworthiness, Nov1991, p. 231.
[47] U. G. Goranson, “Fatigue issues in aircraft maintenance and repairs,” InternationalJournal of Fatigue, vol. 19, no. 93, pp. 3–21, 1997.
[48] R. Singh and C. Koenke, “Simulation framework for risk assessment of damagetolerant structures,” Computers and Structures, vol. 77, no. 1, pp. 101–115, 2000.
[49] N. Nechval, K. Nechval, M. Purgailis, and V. Strelchonok, “Planning inspections inthe case of damage tolerance approach to service of fatigued aircraft structures,”International Journal of Performability Engineering, vol. 7, no. 3, pp. 279–290,2011.
[50] A. A. Kale and R. T. Haftka, “Trade-off of weight and inspection cost inreliability-based structural optimization,” Journal of Aircraft, vol. 45, no. 1, pp.77–85, 2008.
[51] D. L. Simpson and C. L. Brooks, “Tailoring the structural integrity process to meetthe challenges of aging aircraft,” International Journal of Fatigue, vol. 21, no. 1, pp.1–14, 1999.
[52] Y.-T. Tsai, K.-S. Wang, and L.-C. Tsai, “A study of availability-centered preventivemaintenance for multi-component systems,” Reliability Engineering and SystemSafety, vol. 84, no. 3, pp. 261–270, 2004.
[53] F. M. Grimslev, J. W. Lincoln, and M. L. Zeigler, “Usaf strategy for aging aircraftstructures research and development,” in RTO AVT Specialists’ Meeting, Oct2001.
[54] A. Starr, “A structured approach to the selection of condition-based maintenance,”in 5th International Conference on FACTORY 2000. The Technology ExploitationProcess, 1997.
97
[55] A. K. Jardine, D. Lin, and D. Banjevic, “A review on machinery diagnostics andprognostics implementing condition-based maintenance,” Mechanical Systemsand Signal Processing, vol. 20, no. 7, pp. 1483–1510, 2006.
[56] L. Dieulle, C. Berenguer, A. Grall, and M. Roussignol, “Sequential condition-basedmaintenance scheduling for a deteriorating system,” European Journal ofOperational Research, vol. 150, no. 2, pp. 451–461, 2003.
[57] M. Marseguerra, E. Zio, and L. Podofillini, “Condition-based maintenanceoptimization by means of genetic algorithms and monte carlo simulation,” Reliabil-ity Engineering and System Safety, vol. 77, no. 2, pp. 151–165, 2002.
[58] D. Chen and K. S. Trivedi, “Optimization for condition-based maintenance withsemi-markov decision process,” Reliability Engineering and System Safety, vol.90, no. 1, pp. 25–29, 2005.
[59] A. Ghasemi, S. Yacout, and M. Ouali, “Optimal condition based maintenance withimperfect information and the proportional hazards model,” International Journalof Production Research, vol. 45, no. 4, pp. 989–1012, 2007.
[60] B. Castanier, A. Grall, and C. Barenguer, “A condition-based maintenance policywith non-periodic inspections for a two-unit series system,” Reliability Engineeringand System Safety, vol. 87, no. 1, pp. 109–120, 2005.
[61] D. Chen and K. S. Trivedi, “Closed-form analytical results for condition-basedmaintenance,” Reliability Engineering and System Safety, vol. 76, no. 1, pp.43–61, 2002.
[62] A. Grall, C. Berenguer, and L. Dieulle, “A condition based maintenance policy forstochastically deteriorating sytems,” Reliability Engineering and System Safety,vol. 76, no. 2, pp. 167–180, 2002.
[63] J. A. Hontelez, H. H. Burger, and D. J. Wijnmalen, “Optimum condition-basedmaintenance policies for deteriorating systems with partial information,” ReliabilityEngineering and System Safety, vol. 51, no. 3, pp. 267–274, 1996.
[64] C. Boller, F. Chang, and Y. Fujino, Encyclopedia of structural health monitoringVol. 1, Wiley and Sons, 2009.
[65] C. Boller and C. Biemans, “Structural health monitoring in aircraft - state of the art,perspectives and benefits,” Tech. Rep., Technomic Publishing Co Inc, 1997.
[66] E. Johnson, H. Lam, L. Katafygiotis, and J. Beck, “A benchmark problem forstructural health monitoring and damage detection,” in 3rd international workshopon Structural control, 2001.
[67] C. Boller, “Ways and options for aircraft structural health management,” SmartMaterials and Structures, vol. 10, no. 3, pp. 432, 2001.
98
[68] V. Giurgiutiu, A. Zagrai, and J. J. Bao, “Piezoelectric wafer embedded activesensors for aging aircraft structural health monitoring,” Structural Health Monitor-ing, vol. 1, no. 1, pp. 41–61, 2002.
[69] M. Friswell and J. Penny, “Crack modeling for structural health monitoring,”Structural Health Monitoring, vol. 1, no. 2, pp. 139–148, 2002.
[70] J.-B. Ihn and F.-K. Chang, “Pitch-catch active sensing methods in structural healthmonitoring for aircraft structures,” Structural Health Monitoring, vol. 7, no. 1, pp.5–19, 2008.
[71] S. C. Galea, I. G. Powlesland, S. D. Moss, M. J. Konak, S. P. van der Velden, A. A.Baker, and B. Stade, Eds., Development of structural health monitoring systemsfor composite bounded repairs on aircraft structures, vol. 246 of SPIE 4327, 2001.
[72] H. Sohn, C. R. Farrar, and N. F. Hunter, “Structural health monitoring usingstatistical pattern recognition techniques,” Dynamic Systems Measurement andControl, vol. 123, no. 4, pp. 706–711, 2001.
[73] H. Zhang, M. Schulz, A. Naser, F. Ferguson, and P. Pai, “Structural healthmonitoring using transmittance functions,” Mechanical Systems and SignalProcessing, vol. 13, no. 5, pp. 765–787, 1999.
[74] J. L. Rose, “Ultrasonic guided waves in structural health monitoring,” KeyEngineering Materials, vol. 270, pp. 14–21, 2004.
[75] H. Sekine, S.-E. Fujimoto, T. Okabe, N. Takeda, and T. Yokobori, “Structural healthmonitoring of cracked aircraft panels repaired with bonded patches using fiberbragg grating sensors,” Applied Composite Materials, vol. 13, no. 2, pp. 87–98,2006.
[76] M. Vanik, J. Beck, and S. Au, “Bayesian probabilistic approach to structural healthmonitoring,” Engineering Mechanics, pp. 738–745, 2000.
[77] A. A. Mufti, “Structural health monitoring of innovative canadian civil engineeringstructures,” Structural Health Monitoring, vol. 1, no. 1, pp. 89–103, 2002.
[78] I. Kang, M. J. Schulz, J. H. Kim, V. Shanov, and D. Shi, “A carbon nanotube strainsensor for structural health monitoring,” Smart Materials and Structures, vol. 15,no. 3, pp. 737–748, 2006.
[79] W. Baker, I. McKenzie, and R. Jones, “Development of life extension strategies foraustralian military aircraft, using structural health monitoring of composite repairsand joints,” Composite Structures, vol. 66, no. 1, pp. 133–143, 2004.
[80] C. Boller and E. Al, “Fundamentals of damage monitoring,” in Smart Structuresand Materials: Implications for Military Aircraft of New Generation, 1996.
99
[81] J. Ko and Y. Ni, “Technology developments in structural health monitoring of largescale bridges,” Engineering Structures, vol. 27, no. 12, pp. 1715–1725, 2005.
[82] C. Sekine-Pettite, “Structural health monitoring,” Bridges, vol. 8, no. 2, pp. 36–38,2005.
[83] C. Boller and M. Buderath, “Fatigue in aerostructures - where structural healthmonitoring can contribute to a complex subject,” Philosophical Transactions of TheRoyal Society A, vol. 365, no. 1851, pp. 561–587, 2007.
[84] H. van der Aueraer and B. Peeters, “International research projects on structuralhealth monitoring: An overview,” Structural Health Monitoring, vol. 2, no. 4, pp.341–358, 2003.
[85] S. J. Beard, A. Kumar, X. Qing, H. Chan, C. Zhang, and T. K. Ooi, “Practicalissues in real-world implementation of structural health monitoring systems,” Tech.Rep., Accelent Technologies Inc, 2005.
[86] C. Boller, “Next generation structural health monitoring and its integration intoaircraft design,” International Journal of Systems Science, vol. 31, no. 11, pp.1333–1349, 2000.
[87] B. Beral and H. Speckman, “Structural health monitoring for aircraft structures: Achallenge for system developers and aircraft manufacturers,” in Structural HealthMonitoring, F.-K. Chang, Ed., pp. 12–29. DEStech Publications, 2003.
[88] M. Derriso and S. Olson, “The future of structural health monitoring for air vehicleapplications,” in Structural Health Monitoring, F.-K. Chang, Ed., pp. 17–25.DEStech Publications, 2005.
[89] J. Telgkamp and H.-J. Schmidt, “Benefits by the application of structural healthmonitoring systems on civil transport aircraft,” in Structural Health Monitoring,F.-K. Chang, Ed., pp. 285–292. DEStech Publications, 2003.
[90] F. Romlay, H. Ouyang, A. Ariffin, and N. Mohamed, “Modeling of fatigue crackpropagation using dual boundary element method and gaussian monte carlomethod,” Engineering Analysis with Boundary Elements, vol. 34, no. 3, pp.297–305, 2010.
[91] C. E. Harris, J. C. Newman Jr, R. S. Piascik, and J. H. Starnes Jr, “Analyticalmethodology for predicting the widespread fatigue damage in fuselage structure,”in Proceedings of FAA-NASA Symposium on the Continued Airworthiness ofAircraft Structures, C. A. Bigelow and W. J. Hughes, Eds., pp. 63– 88. NationalTechnical Information Service, 1996.
100
[92] K.-F. Nilsson, “Elasto-plastic models for interaction between major crack andmultiple smalll cracks,” in Proceedings of FAA-NASA Symposium on the Contin-ued Airworthiness of Aircraft Structures, C. A. Bigelow and W. J. Hughes, Eds.,pp. 197–224. National Technical Information Service, 1996.
[93] L. Molent and S. A. Barter, “A comparison of crack growth behavior in severalfull-scale airframe fatigue tests,” International Journal of Fatigue, vol. 29, no. 6, pp.1090–1099, 2007.
[94] S. Beden, S. Abdullah, and A. Ariffin, “Review of fatigue crack propagation modelsfor metallic components,” European Journal of Scientific Research, vol. 28, pp.364–397, 2009.
[95] J. Mohanty, B. Verma, and P. Ray, “Prediction of fatigue crack growth and residuallife using an exponential model: Part ii (mode-i overload induced retardation),”International Journal of Fatigue, vol. 31, no. 3, pp. 425–432, 2009.
[96] P. A. Scarf, “On the application of mathematical models in maintenance,” Euro-pean Journal of Operational Research, vol. 99, no. 3, pp. 493–506, 1997.
[97] P. Paris and F. Erdogan, “A critical analysis of crack propagation laws,” Journal ofBasic Engineering, vol. 85, no. 4, pp. 528–534, 1963.
[98] J. Newman Jr, E. Phillips, and M. Swain, “Fatigue life prediction methodologyusing small crack theory,” International Journal of Fatigue, vol. 21, no. 2, pp.109–119, 1999.
[99] S. Kim and D. M. Frangopol, “Optimum inspection planning for minimizing fatiguedamage detection delay of ship hull structures,” International Journal of Fatigue,vol. 33, no. 3, pp. 448–459, 2011.
[100] P. Packman, H. Pearson, J. Owens, and G. Young, “Definition of fatigue cracksthrough non-destructive testing,” Journal of Materials, vol. 4, pp. 666–700, 1969.
[101] A. P. Berens and P. W. Hovey, “Evaluation of nde reliability characterization,” Tech.Rep., AirForce Wright Aeronautical Laboratory, 1981.
[102] H. Madsen, R. Torhaug, and E. Cramer, “Probability based cost benefit analysisof fatigue, design and maintenance,” in Marine Structural Inspection, Maintenanceand Monitoring Symposium, 1991, pp. 1–12.
[103] Y. Mori and B. Ellingwood, “Maintaining reliability of concrete structures i: Role ofinspection / repair,” Structural Engineering, vol. 120, no. 3, pp. 824–845, 1994.
[104] H.-Y. Chung, L. Manuel, and K. Frank, “Optimal inspection scheduling of steelbridges using non-destructive testing techniques,” Bridge Engineering, vol. 11, no.3, pp. 305–319, 2006.
101
[105] A. Coppe, R. T. Haftka, N. H. Kim, and P. Ramu, “Optimization of distributionparameters for estimating probability of crack detection,” Journal of Aircraft, vol.46, no. 6, pp. 2090–2097, 2009.
[106] B. Palmberg, A. Blom, and S. Eggwertz, “Probabilistic damage tolerance analysisof aircraft structures,” Probabilistic Fracture Mechanics and Reliability, vol. 10, pp.275–291, 1987.
[107] L. Jaeger, C. Gogu, S. Segonds, and C. Bes, “Multidisciplinary optimization underuncertainty for preliminary aircraft sizing,” in SAE 2011 Aerotech Congress, Oct2011.
[108] P. Goggin, J. Huang, E. White, and E. Haugse, “Challenges for shm transitionto future aerospace systems,” in Structural Health Monitoring, F.-K. Chang, Ed.DEStech Publications, 2003.
[109] C. R. Farrar and K. Worden, “An introduction to structural health monitoring,”Philosophical Transactions of The Royal Society A, vol. 365, pp. 303–315, 2007.
[110] R. Ikegami, “Structural health monitoring: Assessment of aircraft customer needs,”in Structural Health Monitoring, F.-K. Chang, Ed. DEStech Publications, 2003.
[111] L. M. Fitzwater, C. L. Davis, T. Torng, and J. Poblete, “Cost/benefit analysisfor integration of non-deterministic analysis and in situ monitoring for structuralintegrity,” Tech. Rep., USAF CBM+ initiative AFLMA Report, 2003.
[112] U. A. G. Inc., “Form 10-k,” Tech. Rep., United States Securities and ExchangeCommission, 2011.
[113] W. Crichlow and A. McCulloch, “An engineering evaluation of methods for theprediction of fatigue life in airframe structures,” Tech. Rep., Flight DynamicsLaboratory, 1962.
[114] S. Engel, B. Gilmartin, K. Bongort, and A. Hess, “Prognostics, the real issuesinvolved with predicting life remaining,” in Aerospace Conference Proceedings.IEEE, 2000.
[115] E. Keller and A. Ray, “Real-time nondestuctive evaluation of airframe structures forhealth monitoring and residual life prediction,” in Digital Avionics Systems. DASC,2001.
[116] D. Hoeppner and W. Krupp, “Prediction of component life by application of fatiguecrack growth knowledge,” Engineering Fracture Mechanics, vol. 6, no. 1, pp.47–62, 1974.
[117] A. Coppe, R. Haftka, and N.-H. Kim, “Uncertainty identification of damage growthparameters using non-linear regression,” AIAA, vol. 49, no. 12, pp. 2818–2821,2011.
102
[118] J. M. Gaillardon, H.-J. Schmidt, and B. Brandecker, “Ageing airplane repairassessment program for airbus a300,” in International Conference on AgeingAircraft and Structural Airworthiness, Nov 1991, p. 283.
[119] A. K. Kundu, Aircraft Design, Cambridge University Press, 2010.
[120] “Cfm international, makers of cfm56 family,” 11 Feb 2012.
[121] A. Patcha and J.-M. Park, “An overview of anomaly detection techniques: Existingsolutions and latest technological trends,” Computer Networks, vol. 51, no. 12, pp.3448–3470, 2007.
[122] N. Wu and J. Zhang, “Factor-analysis based anomaly detection and clustering,”Decision Support System, vol. 42, no. 1, pp. 375–389, 2006.
[123] C.-H. Wang, “Outlier identification and market segmentation using kernel-basedclustering techniques,” Expert Systems with Applications, vol. 36, no. 2, pp.3744–3750, 2009.
[124] M. Ramos, “Divisive and hierarchical clustering techniques to analyse variabilityof rainfall distribution patterns in a mediterranean region,” Atmospheric Research,vol. 57, no. 2, pp. 123–138, 2001.
[125] A. Srivastava, “Enabling the discovery of recurring anomalies in aerospaceproblem using high-dimensional clustering techniques,” in Aerospace ConferenceProceedings. IEEE, 2006.
103
BIOGRAPHICAL SKETCH
Sriram Pattabhiraman was born in Tiruchirappalli, India, in 1985. He completed his
Bachelors (B.Tech) in Mechanical Engineering at the National Institute of Technology,
Tiruchirappalli (NIT-T) in 2007. He moved to United States in August 2007 to join the
Multidisciplinary Optimization Group in the Department of Mechanical and Aerospace
Engineering at the University of Florida. He enrolled into the direct-PhD program, and
graduated with a PhD in May 2012, working with Prof. Nam Ho Kim and Prof. Raphael T.
Haftka
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