Prognostics Enhanced Reconﬁgurable Control of Electro ... · Prognostics Enhanced Reconﬁgurable...

Prognostics Enhanced Reconfigurable Control ofElectro-Mechanical Actuators

Douglas W. Brown 1, George Georgoulas 1, Brian Bole 1, Hai-Long Pei 2,Marcos Orchard 3, Liang Tang 4, Bhaskar Saha 5, Abhinav Saxena 5,

Kai Goebel 5, and George Vachtsevanos 1

1 Department of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, [email protected]

[email protected] Department of Automation at South China University of Technology, Guangzhou 510640 P.R. China.

[email protected] Department of Electrical Engineering, Universidad de Chile, Santiago, Chile.

[email protected] Impact Technologies, LLC., Rochester, NY 14623, USA.

[email protected] NASA Ames Research Center, Moffett Field, CA 94035, USA.

[email protected]

ABSTRACT

Actuator systems are employed widely inaerospace, transportation and industrial processesto provide power to critical loads, such as aircraftcontrol surfaces. They must operate reliably andaccurately in order for the vehicle / process tocomplete successfully its designated mission. In-cipient actuator failure conditions may severelyendanger the operational integrity of the vehi-cle / process and compromise its mission. Theability to maintain a stable and credible opera-tion, even in the presence of incipient failures,is of paramount importance to accomplish “mustachieve” mission objectives. This paper intro-duces a novel methodology for the fault-tolerantdesign of critical subsystems, such as an Electro-Mechanical Actuator (EMA), that takes advan-tage of on-line, real-time estimates of the Re-maining Useful Life (RUL) or Time-to-Failure(TTF) of a failing component and reconfiguresthe available control authority by trading off sys-tem performance with control activity. The pri-mary goal is to complete critical mission objec-tives within a time window dictated by prognos-tic algorithms so that the fault mode is accom-modated and an acceptable level of performancemaintained for the duration of the mission. Theproposed fault-tolerant control design is mathe-matically rigorous, generic and applicable to a va-riety of application domains. An EMA is used toillustrate the efficacy of the proposed approach.

This is an open-access article distributed under the termsof the Creative Commons Attribution 3.0 United States Li-cense, which permits unrestricted use, distribution, and re-production in any medium, provided the original author andsource are credited.

1 INTRODUCTION

The emergence of complex and autonomous systems,such as modern aircraft, Unmanned Aerial Vehicles(UAVs), automated industrial processes, among manyothers, is driving the development and implementa-tion of new control technologies that are aimed toaccommodate incipient failures and maintain a sta-ble system operation for the duration of the emer-gency. Historically, when fault tolerance was an is-sue, controllers were designed targeting specific faultsand specific control actions to accommodate the cor-responding faults (Isermann, 1984). More recent ap-proaches applied modern control techniques such asadaptive or robust control to handle situations wherethe fault severity may not be known, but the systemstructure is known. While these techniques are capa-ble of handling many types of fault modes, they doso in a brute force way (Saberi et al., 2000). Forexample, if a fault condition can be modeled as achange in system parameters, an adaptive controllercan be designed to monitor the changes and constantlychange the control law accordingly (Ward et al., 2001;Monaco et al., 2004). Similarly, a robust control lawmay be designed which can control the system overa range of potential failure modes (Stoustrup et al.,1997; Zhou et al., 1996). However, what these ap-proaches lack is an active reconfiguration of the con-trol law considering failure prognostic information.Fault-Tolerant Control (FTC) methodologies typicallyhave two main objectives: Fault Detection and Isola-tion (FDI) and Control Reconfiguration (Rausch et al.,2007). Several authors have reported on the problem ofFDI (Kleer and Williams, 1987; Filippetti et al., 2000;Skormin et al., 1994; Willsky, 1976; Wu et al., 2004).Analytical methods for FTC usually assume linearmodels of the system dynamics. For large-scale sys-tems, this is generally a reasonable assumption since

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Annual Conference of the Prognostics and Health Management Society, 2009

in a region of the nominal operating point, the systemdynamics are approximately linear. Recent researchhas begun to address the issue of FTC for nonlinearsystems, such as using feedback linearization in a re-structured digital flight control system (Nguyen andLiu, 1998). The authors in (Birdwell et al., 1986;Birdwell, 1978) describe a method for reliable controlsystem design. Reliability is defined as the probabil-ity that a system will perform within specified con-straints for a given period of time. In (Watanabe andHimmelblau, 1982), the author discusses several is-sues arising in the design of reconfigurable control sys-tems including the selection of a failure representationmethod, the selection of a control law that providesrobustness to particular failures and the formulationof a diagnostic problem that exploits potentialities ina control system for diagnostic purposes. Additionalcontributions significant to the development of adap-tive based FTC can be found in (Ye and Yang, 2006;Zhang and Jiang, 2003). The authors in (Yavrucuket al., 1999) present a novel simultaneous FDI andFTC strategy. Other recent analytical approaches em-ploy a mathematical model in which failures are cap-tured as uncertainties in the model parameters (Muftiand Vachtsevanos, 1995), or controller reconfigura-tion is affected by considering the redirection of con-trol authority between parts of the system (Bajpai etal., 2001). Artificial Intelligence (AI) methods havebeen exploited to handle model-free fault diagnosisand FTC in an expert system setting (Levis, 1987;Isermann, 1997). Recent extensions to expert systemapproaches to fault tolerance include (Wu, 1997), inwhich past performance is used to dynamically updatethe database of fault controllers / parameters. An al-ternative hybrid systems approach to FTC combinesmodeling with AI and expert systems (Heck et al.,2003). Many existing reconfigurable control strategiesfall naturally into this category (Boskovic and Mehra,2001; Liu, 1996). More recently, hybrid hierarchicalapproaches to FTC have been proposed (Vachtsevanoset al., 2005; Gutierrez et al., 2003; Guler et al., 2003;Kamen et al., 1994). For example, in (Clements,2003), the high-level of the architecture includes situ-ation awareness and fault diagnosis routines, whereasthe middle-level consists of three modules that ac-tively reconfigure the controls, subsystem interconnec-tions and local controller gains; the low-level con-sists of the individual subsystems and correspondinglocal controller (Clements et al., 2000). In anothermanifestation, the high level performs mission adap-tation functions (Drozeski and Vachtsevanos, 2005;Drozeski et al., 2005; Tang et al., 2008).

In contrast to FTC, little work has been publisheddiscussing the role of prognosis in control systems. In,(Bogdanov et al., 2006; Gokdere et al., 2006) the au-thors describe a framework to consider long-term life-time prediction, performance and design constraints.To account for the lifetime constraint, the authors con-sider a parametrization of a family of LQR controllerswith a single adaptation parameter, and then optimizethe parameter to satisfy the lifetime constraint. Al-though novel, more work is required in the area ofprognostic-based control to handle uncertainties asso-ciated with long-term prediction.

This paper is organized as follows. Section 2.1 iden-

Figure 1: Photo of the triplex redundant EMA.

tifies the EMA under investigation and presents a gen-eral overview of the FTC architecture; Section 3 intro-duces a particle filtering framework for fault diagnosisand fault prognosis and follows using an EMA with aselected failure mode as an example; Section 4 givesa formulation for a prognosis-based control law utiliz-ing Model Predictive Control (MPC) and evaluates thefeasibility of the approach using the EMA example;Section 5 highlights major accomplishments.

2 BACKGROUND2.1 Actuator subsystemThe actuator evaluated for proof of concept of the pro-posed fault-tolerant or reconfigurable control schemeis a triplex redundant rotary EMA, designed to oper-ate with a triplex redundant Electronic Control Mod-ule (ECM). The EMA, shown in Figure 1, consists ofthree Brushless DC (BLDC) motors, each using a re-solver for motor commutation, where all motors aredriving a single string output shaft drive mechanismthrough a gear system (Brown et al., 2009).1 Thisactuator is suitable for this study since it can oper-ate in a single channel (simplex) mode or in fully re-dundant, active-active-active system mode, providinga two fault-tolerant system. In the active-active-activesystem, all three motors are actively driven in a torquesharing mode where the torque applied to the load isthe cumulative sum of the three motor torques. A Ve-hicle Management Computer (VMC) determines thedrive for each motor/channel and the correspondingservo controllers. The VMC also monitors each motorchannel for failures or degraded performance, so it canshut it down when necessary. A block diagram of thenominal system illustrating the production controllerand three motor components is depicted in Figure 2.

Figure 2: Block diagram of the triplex redundantEMA.

1Copyright © Moog Inc. Photo courtesy of Moog Inc.

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Figure 3: Reconfigurable control architecture 3-tier hierarchical strategy.

2.2 Fault-Tolerant Control Architecture

The reconfigurable control methodology introduced inthis paper is a constituent module of a more general in-telligent / hierarchical FTC architecture comprised ofthree levels: A low-level, a middle-level and a high-level, as illustrated in Figure 3. Each level of the con-trol hierarchy is responsible for different tasks wherethe three levels are coordinated via supervisory rou-tines and contribute synergistically to system fault tol-erance.

Figure 4 depicts the main elements of the low-levelreconfigurable control architecture. The control ar-chitecture is comprised of two controllers: the orig-inal production controller (§1030) and the reconfig-ured controller (§1040). Initially, the production con-troller is utilized while diagnostic routines continu-ously monitor the system for one, or more, fault modes(§1100). Once a fault is detected the RUL require-ments are check to assess if the mission can be accom-plished without control reconfiguration (§1300), if not,the MPC routine is called upon (§1400).

The functionality of the MPC routine is given bythe flowchart in Figure 5. Soft constraints are initial-ized (§1410), the RUL of the failing motor is evalu-ated (§1420) and the RUL requirements are checked(§1430) to assess if the mission can be accomplished;if not, the soft constraints are updated to relax perfor-mance requirements in the MPC (§1450). Then, theMPC computes the next control sequence (§1460). Af-ter the control sequence is applied, the performance isevaluated (§1470) and compared to the required per-formance (§1440). If the performance requirementsare satisfied the control sequence is reiterated (§1490).However, if the requirements are not satisfied, or thesoft boundaries can no longer be adapted (§1440), acontrol redistribution algorithm (§1500) is activated atthe middle-level of the control hierarchy.

It should be noted that control redistribution is not

Figure 4: State transition diagram for low-level recon-figurable control.

addressed in this paper. Also, it is assumed that, in thepresence of an incipient failure, the system (actuator)dynamics remain essentially the same. This assump-tion is valid when the incipient failure or fault is de-tected at an early stage of its initiation and evolutionand thus has not affected severely the actuator dynam-ics. Under these conditions, restructuring of the sys-tem dynamics is not absolutely necessary in the controlformulation. However, if the motor fault significantlyinfluences the system dynamics, then a restructuringstep (§1200) can precede the reconfigurable controlroutine so the current state of the system is reflectedin the control formulation.

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Figure 5: Flowchart of the reconfiguration state.

3 FAULT DETECTION AND FAILUREPROGNOSIS

3.1 Actuator ModelA high-fidelity 5th order state-space model was devel-oped to represent higher order dynamics for a closed-loop actuator position controller. The model, whichcan be expressed by the linear state-space system(Am,Bm,Cm), is employed to relate the control in-puts and measured outputs of the actuator to the inter-nal system states of the BLDC motor,{

˙xm = Am xm + Bmumym = Cm xm

(1)

where xm0 = xm (0). The internal state xm =[ im �m !m �ℓ !ℓ ]⊤ ∈ ℝ5 is defined by themotor current, motor position, motor speed, load po-sition and load speed, respectively; the control inputum = [ �ref Tload ]⊤ ∈ ℝ2 is defined by the ref-erence position and external load disturbance; and thecontrol output ym = [ �ℓ im ]⊤ ∈ ℝ2 is defined bythe load position and motor current.

The transition matrix, Am ∈ ℝ5×5, is defined as apiecewise linear model,

Am =

{A1 : !m ≥ 0A2 : !m < 0 (2)

where the matrices A1 and A2 ∈ ℝ5×5 are defined in(3) and (4) accordingly.

A1 =

⎡⎢⎢⎢⎢⎢⎣−RttLtt

−kp1kp2

Ltt

−ke−kp1

Ltt0 0

0 0 1 0 0ktJm

−kcsJmN2

cm

−bm−Tf

Jm

kcsNclJmNcm

0

0 0 0 0 1

0 kcsNclJℓNcm

0−kℓ−kcsN2

clJℓ

−bℓJℓ

⎤⎥⎥⎥⎥⎥⎦ (3)

A2 =

⎡⎢⎢⎢⎢⎢⎣−RttLtt

−kp1kp2

Ltt

−ke−kp1

Ltt0 0

0 0 1 0 0ktJm

−kcsJmN2

cm

−bm+Tf

Jm

kcsNclJmNcm

0

0 0 0 0 1

0 kcsNclJℓNcm

0−kℓ−kcsN2

clJℓ

−bℓJℓ

⎤⎥⎥⎥⎥⎥⎦ (4)

The control and observation matrices Bm ∈ ℝ5×2

and Cm ∈ ℝ2×5 are defined in (5) and (6), respec-tively.

Bm =

[kp1kp2Ncm

LttNcl0 0 0 0

0 0 0 0 −1Jℓ

]⊤(5)

Cm =

[0 0 0 1 01 0 0 0 0

](6)

3.2 Failure Modes and EffectsResults from a Failure Modes and Effects CriticalityAnalysis (FMECA) study of the EMA suggest thatthe leading modes of failure are associated with thebearings (Schoen et al., 1995; Zhang et al., 2008a;Bodden et al., 2007), position feedback sensors (Mur-ray et al., 2002; Brown et al., 2008), electronic compo-nents (Baybutt et al., 2008) and electric motors (Brownet al., 2008; 2009). In this study, the BLDC mo-tor was selected as the component of interest wherethe primary failure mechanisms is breakdown of in-sulation between turns of the same winding. Accord-ing to (Malik et al., 1998; Nandi and Toliyat, 1999;Tavner and Penman, 1987), stator insulation can faildue to several reasons: high stator core or windingtemperature; contamination from oil, moisture anddirt; short circuit or starting stresses; electrical dis-charges; and leaking in the cooling system. For theEMA under investigation, winding temperature is thedominant failure mechanism due to the excessive en-vironmental factors.

The principle effects of a turn-to-turn winding in-sulation short result in a three-phase impedance im-balance in the stator windings (Xianrong et al., 2003).This leads to asymmetries in the stator phase currents,shown in Figure 6, resulting in increased harmonicgeneration and overall performance degradation (Pen-man et al., 1994).

3.3 Particle Filtering in Real-Time FaultDiagnosis and Failure Prognosis

Particle filtering is an emerging and powerful method-ology for sequential signal processing with a wide rageof applications in science and engineering. Foundedon the concept of sequential importance sampling andthe use of Bayesian theory, particle filtering is partic-ularly useful in dealing with difficult nonlinear and/or

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Figure 6: Simulation illustrating phase current asym-metry.

non-Gaussian problems. The underlying principle ofthe methodology is the approximation of relevant dis-tributions with particles (samples from the space ofthe unknowns) and their associated weights. Com-pared to classical Monte-Carlo methods, sequentialimportance sampling enables particle filtering to re-duce the number of samples required to approximatethe distributions with necessary precision, and makesit a faster and more computationally efficient approachthan Monte-Carlo simulation. This is of particular ben-efit in diagnosis and prognosis of complex dynamicsystems, such as engines, gas turbines and gearboxes,because of the nonlinear behavior when operating un-der fault conditions. Moreover, particle filtering allowsinformation from multiple measurement sources to befused in a principled manner (Orchard, 2007).

Particle filtering has a direct application in the FDIarena. Once the current state of the system is known, itis natural to implement FDI procedures by comparingthe process behavior with patterns regarding normal orfaulty operating conditions.

3.4 Fault DiagnosisA fault diagnosis procedure involves the tasks of faultdetection, fault isolation and identification (assess-ment of the severity of the fault). The proposedparticle-filter-based diagnosis framework aims to ac-complish these tasks, under general assumptions ofnon-Gaussian noise structures and nonlinearities inprocess dynamic models, using a reduced particle pop-ulation to represent the state pdf (Orchard et al., 2008).A compromise between model-based and data-driventechniques is accomplished by the use of a particlefilter-based module built upon the nonlinear dynamicstate model,⎧⎨⎩ xd (t+ 1) = fb (xd (t) , n (t))

xc (t+ 1) = ft (xd (t) , xc (t) , w (t))fp (t) = ℎt (xd (t) , xc (t) , v (t))

(7)

where fb, ft and ℎt are non-linear mappings, xd is acollection of Boolean states associated with the pres-ence of a particular operating condition in the sys-tem (normal operation, fault type #1, #2, etc.), xc isa set of continuous-valued states that describe the evo-lution of the system given those operating conditions,fp is a feature measurement, ! and v are non-Gaussiandistributions that characterize the process and feature

noise signals, respectively. The function ℎt is a map-ping between the feature value, fp (t), and the faultstate xc (t). In the case of a turn-to-turn winding in-sulation short circuit fault, the values of fp (t) andL (t) are related by the operating parameters, motorspeed, !m and motor current, im, as will be shownexplicitly in a future publication. For simplicity, n (t)may be assumed to be zero-mean i.i.d. uniform whitenoise. At any given instant of time, this frameworkprovides an estimate of the probability masses associ-ated with each fault mode, as well as a pdf estimatefor meaningful physical variables in the system. Oncethis information is available within the FDI module,it is processed to generate proper fault alarms and toinform about the statistical confidence of the detec-tion routine. Furthermore, pdf estimates for the sys-tem continuous-valued states (computed at the mo-ment of fault detection) may be used as initial con-ditions in failure prognostic routines. As a result, aswift transition between the two modules (FDI andprognosis) may be performed and reliable prognosiscan be achieved within a few cycles of operation af-ter the fault is declared. This characteristic is oneof the main advantages of the proposed particle-filter-based diagnosis framework. Customer specificationsare translated into acceptable margins for the type Iand/or II errors, as defined by (Kutner et al., 2004;Hines et al., 2003), in the detection routine. The algo-rithm itself will indicate when the type II error (falsenegatives) has decreased to the desired level. Figure 7depicts the major modules of the proposed architecturefor a fault detector.

In this architecture, real-time measurements and in-formation about the current operational mode are pro-vided on-line. Then data is pre-processed and de-noised before computing the features that will assistto efficiently monitor the behavior of the system. Bytaking the standard deviation of the average amplitudeof each phase current (a, b and c) over a finite time in-terval T , the following feature, denoted as fp (t), canbe used to describe variations in winding symmetry fora BLDC motor (Brown et al., 2009),

fp (t) = stdk∈(a,b,c)

[avg

t∈(0,T )

∣∣∣ik (t) + ik (t)∣∣∣] (8)

where the symbol ik, refers to the measured phase cur-rent and ik corresponds to the phase current after ap-plying a Hilbert transformation. Provided in Figure 8is a (a) snapshot of experimental data acquired duringseeded fault testing and (b) a plot of computed fea-tures versus time. The feature value fp (t) is computedfrom raw current data. The fault dimension L (t) wassimulated by placing a parallel resistance between oneof the winding terminals and the center-tap, therebygenerating current asymmetry. The parallel resistancesused ranged from 25Ω to 3Ω and decreasing monoton-ically with time. As the parallel resistance decreased,the fault dimension L (t) increased, resulting in an in-crease in fp (t). More detailed information regardingthe seeded fault winding insulation test can be foundin (Brown et al., 2009).

It should be noted that the principle feature, fp (t),is not the only available feature. Other diagnostic fea-tures for turn-to-turn winding insulation faults were

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Figure 7: Particle filter-based fault detection architecture.

also considered and may be used individually or incombination via fusion techniques.

Statistical analysis applied to this set of features isperformed to simultaneously arrive at the probabilityof abnormal conditions for a given false alarm rate andconfidence level (95% for example). If time and com-putational resources allow for further analysis, featureinformation can be used to complete the tasks of faultisolation, identification, and failure prognosis (Zhanget al., 2008b). The fault detector was evaluated usingsimulated phase currents generated in Simulink. Theresults of the particle-filter based fault detector usingexperimental data from Figure 8 (a) are provided inFigure 9 showing (a) the raw output from the particlefilter over time as a waterfall plot and (b) the corre-sponding fault detection confidence. The critical fea-ture value, fp,�=0.05 = 0.02 was computed for a 5%false alarm rate (� = 0.05 / type I error) using theinitial baseline data. The confidence was computedby summing all the weights associated with particlesgreater than fp,�=0.05. In this paper, confidence is de-fined as the compliment of the Type II error, �, ex-pressed as a percentage,

Confidence = 100% (1− �) (9)

3.5 Failure PrognosisPrognosis is the Achilles’ heel of fault diagnosis andfailure prognosis systems. Prognosis can be under-stood as the generation of long-term predictions de-scribing the evolution in time of a particular signal ofinterest or fault indicator. Since prognosis projects thecurrent condition of the indicator in the absence of fu-ture measurements, it necessarily entails large-grainuncertainty. This suggests a prognosis scheme basedon recursive Bayesian estimation techniques, combin-ing both the information from fault growth modelsand on-line data obtained from sensors monitoringkey fault parameters (observations or features). Pro-posed is a prognostic framework that takes advantageof a nonlinear process (fault / degradation) model,

a Bayesian estimation method using particle filteringand real-time measurements.

Prognosis is achieved by performing two sequentialsteps, prediction and filtering. Prediction uses both theknowledge of the previous state estimate and the pro-cess model to generate the a priori state pdf estimatefor the next time instant,

p (x0:t∣y1:t−1)=∫p (xt∣xt−1)p (x0:t−1∣y1:t−1) dx0:t−1 (10)

The filtering step generates the posterior state pdf byusing Bayes formula,

p (x0:t∣y1:t−1)∝p (yt∣xt)p (xt∣x0:t−1) p (x0:t−1∣y1:t−1) (11)

Expressions (10) and (11) do not have an analyticalsolution in most cases. Instead, Sequential MonteCarlo (SMC) algorithms, or particle filters, are used tonumerically solve (10) and (11) in real-time throughthe use of efficient sampling strategies (Arulampalamet al., 2002; Doucet et al., 2000). Particle filter-ing approximates the state pdf using samples of “par-ticles” having associated discrete probability masses(“weights”) as,

p (xt∣y1:t) ≈N∑

i=1

wt

(xi

0:t

)⋅ �(x0:t − xi

0:t

)(12)

where xi0:t is the state trajectory and y1:t are the mea-

surements up to time t. The simplest implementationof this algorithm, the Sequential Importance Resam-pling (SIR) particle filter, updates the weights usingthe likelihood of yt as (Orchard, 2007; Orchard et al.,2008),

wt = wt−1 ⋅ p (yt∣xt) (13)

By using the state equation to represent the evolutionof the fault dimension in time, it is possible to generatea long-term prediction for the state pdf, in the absenceof new measurements, in a recursive manner using the

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(a)

(b)

Figure 8: Plot of (a) three-phase current data and (b)features computed from experimental data.

current pdf estimate for the state,

p (xt+p∣y1:t) ≈

∫p (xt∣y1:t)

t+p∏j=t+1

p (xj ∣xj−1) dxt:t+p−1

(14)

which can be approximated as,

p (xt+p∣y1:t) ≈N∑

i=1

w(i)t

∫⋅ ⋅ ⋅∫p(xt+1∣x(i)

t

)⋅ . . .

t+p∏j=t+2

p (xj ∣xj−1) dxt+1:t+p−1

(15)

The information about the distribution of the state forfuture time instants is given by the position of the parti-cles, not by the particle weight value. A computation-ally affordable solution is based on the use of kerneltransitions and Monte Carlo resampling techniques forthe state pdf,

p (xt+k∣x1:t+k−1) ≈

N∑i=1

w(i)t+k−1K

(xt+k − E

[x(i)

t+k∣xt+k−1

]) (16)

(a)

(b)

Figure 9: Fault detection using experimental data. Il-lustrated are (a) the results after applying a particle fil-ter to the incoming feature and (b) the level of confi-dence computed from the particle weights.

Long-term predictions are used to estimate the proba-bility of failure in a system given a hazard zone that isdefined via a probability density function with lowerand upper bounds for the domain of the random vari-able, denoted as Hlb and Hup, respectively.

The probability of failure at any future time instantis estimated by combining both the weights w(i)

t+k ofpredicted trajectories and specifications for the hazardzone through the application of the Law of Total Prob-abilities. The resulting RUL pdf, ptRUL , provides thebasis for the generation of confidence intervals and ex-pectations for prognosis,

ptRUL =N∑

i=1

p(Fail∣X = x(i)

tRUL, Hlb, Hup

)⋅w(i)

RUL (17)

Fault Growth ModelThe motor winding insulation degrades at a rate relatedto the winding temperature, Tw. The fault-growth ratecan be related to temperature through Arrhenius’ law(Gokdere et al., 2006),

L (t) ∝ exp

(− EakBTw

)(18)

where the symbols Ea and kB refer to the activationenergy and Boltzmann’s constant, respectively. How-ever, this expression does not consider the current state

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of the fault dimension. By incorporating conceptsfrom Paris’ law (Paris and Gomez, 1961) into (18), therate of degradation for the winding insulation fault ismodeled as,

L = �0exp

(− EakBTw

)L (19)

where �0 > 0. This suggests that the rate of degrada-tion is proportional to the fault dimension itself wherethe constant of proportionality follows a relationshipwith winding temperature according to Arrhenius law.

Thermal ModelIn the case of the brushless DC motor, the windingtemperature is related to the power loss in the copperwindings. Note: this assumes the copper losses are theprimary source of power loss. A model describing therelationship between the power loss and winding-to-ambient temperature, Twa, as defined in (20), is shownin Figure 10 (Gokdere et al., 2006; Nestler and Sattler,1993). The symbols Ta, Cwa and Rwa refer to theambient temperature, thermal capacitance and thermalresistance of the windings, accordingly.

Twa = Tw − Ta (20)

Figure 10: Schematic of the simplified thermal model.

The power loss is computed using (21), where ikand Rk refer to the motor current and resistance ofeach winding phase (k = 1, 2, 3), respectively.

Ploss =

3∑k=1

Rki2k (21)

An equivalent state equation representation for Figure7 can be written as,

Twa =PlossRwa − Twa

RwaCwa(22)

The unknown parameters in (22) can be identified us-ing a linear reference model,

Twa = am (t)Twa (t) + bm (t)u (t) (23)

where u (t) =√

13

∑3k=1 i

2k. The unknown model pa-

rameters can be identified on-line in real-time by in-voking an indirect Model Reference Adaptive Control(MRAC) scheme (Hovakimyan, 2008) using measure-ments for Ta, Tw, and u,⎧⎨⎩

˙am = aTwae (t)

˙bm = bu (t) e (t) bm>b

bu (t) e (t) +bm − bm

bm − bm + �bm<b

e (t) = Tw (t)− Ta (t)− Twa

(24)

where a > 0 and b > 0 are adaptation gains, � > 0 isa sufficiently small number so that bm− � > 0 and theinitialization of b (0) > bm is done with correct sign.It should be mentioned that (23) does not consider thenon-linear effects that occur due to the thermal depen-dence of the winding resistance (Nave, 2008). Sincethe adaptation parameters, am and bm, vary slowlywith time (22) provides a good localized estimate forCwa and Rwa. However, a non-linear model wouldimprove the accuracy of long-term predictions over abroader range of operating conditions.

Feature-Based Fault Growth ModelPrognosis requires the definition of a process modelto incorporate information present in the feature data.Proposed in (25) is a fault / degradation growth statemodel, based on (19), for insulation degradation in abrushless DC motor. The state variable � is an un-known time-varying model parameter to be estimated.Additionally, the stochastic variables !1, !2 and v arerepresented using Gaussian distributions. Finally, thefunction ℎt is a mapping between the feature value andfault dimension L.⎧⎨⎩

L (t) = � (t) exp(− EakBTw

)L+ !1 (t)

� (t) = !2 (t)

fp (t) = ℎt (L (t) , !m, im) + v (t)

(25)

Long-term prediction of the failure evolution is basedon an estimation of the current state and a model de-scribing the fault progression, more specifically thefault-growth model. Once an incipient failure is de-tected and isolated, sensor data is collected to initializethe fault-growth model parameters used in the prog-nostic routines. Then, corrective terms are estimatedin a learning paradigm to improve model parameterestimates and/or update the operating profiles thus re-sulting in better accuracy and precision of the algo-rithm for long-term prediction. Uncertainty associatedwith long-term predictions is managed, or reduced,by using the current state pdf estimate, process noisemodel, and a record of corrections made to previouslycomputed predictions. In the first prognosis level, ap−step ahead prediction is generated on the basis ofan a priori estimate, adjusting probabilities that areassociated with the prediction according to the noisemodel structure. At the second prognosis level, thesepredictions are used to estimate the RUL pdf.

Particle filter-based prognosis was demonstrated forthe turn-to-turn winding insulation fault using artificialdata generated from the simulation model discussedearlier. A result showing the particle filter updates, di-agnostic assessment and long-term predictions of RULare provided in Figure 11.

4 RECONFIGURABLE CONTROLSTRATEGY

The primary goal in this study is to introduce a recon-figurable controller to trade-off RUL for performance.In the case of the EMA, the RUL can be increasedby lowering the applied motor current, im. Although,the motor current cannot be adjusted directly, it can becontrolled indirectly by making adjustments to the ref-erence input, �ref , shown in Figure 12. The purpose

8


Figure 11: Example of particle filter based prognosis using artificial data.

of the MPC is to find the optimal �ref for a given RULand performance requirement.

Figure 12: Block diagram showing actuator inputs andoutputs

4.1 RUL Control BoundariesThe control input associated with a specific RUL valuecan be determined from the fault-growth model in (19).However, instead of using the particle filtering frame-work as mentioned earlier, the first approach utilizes ananalytical expression for the expectation of the fault di-mension. First, consider the equations that result fromsteady-state operating conditions for the motor cur-rent, winding-to-ambient temperature, and adaptation

parameters im, Twa, am and bm, respectively. Then, asteady-state equation can be written as,

amTwa + bmi2m = 0 (26)

where u (t) =√

13

∑3k=1 i

2k. Next, the set of steady-

state expressions from (25) can be used to write theexpectation of the fault-growth dynamics in terms ofthe steady-state motor current and adaptation parame-ters, ⎧⎨⎩

E[L (t)

]= 0E [L (t)]

0 = � exp(− Ea

kbTw

)Tw = Ta − bmi

2m

am

(27)

Solving this differential equation leads to the followingexpression for the expected fault dimension, where L0is the initial value of the fault at time t = t0.

E [L (t)] = L0 exp ( 0 (t− t0)) (28)

Now, consider a value for the fault dimension Llim =L (tRUL) where tRUL is the predicted mean RUL. Anillustration showing the time-evolution of the expected

9


fault growth model from (27) is presented in Figure 13where t0, tRUL, L0 and Llim are labeled accordingly.The RUL is computed by projecting the intersection ofLlim and the expectation of the fault dimension trajec-tory, E [L (t)], onto the time axis as shown. Controlboundaries for a given tRUL corresponding to a partic-ular motor current, uRUL, are found and used as softcost constraints in the MPC cost function J , discussedin the next section.

Figure 13: Prognosis prediction of fault dimensionhighlighting the control input corresponding to the tar-geted RUL.

4.2 Model Predictive ControllerThe MPC formulation presented in this section max-imizes the system performance by minimizing thetracking error between the desired set point r and themeasured plant output y. (Cairano et al., 2007; Ca-macho and Bordons, 2004; Qin and Badgwell, 2003;Maciejowski, 2002)

System ModelA general non-linear state equation can be expressed as(29) where x, u, d, v and w represent the model states,control input, measured disturbance, measured noiseand process noise, respectively. An illustration of thenon-linear system with MPC is provided in Figure 14.⎧⎨⎩ x (t+ 1) = fm (x,u,v)

y (t) = ℎm (x,u,v,w)(29)

Figure 14: Block diagram of MPC with plant and sig-nals

Cost FunctionThe MPC is obtained by solving the optimizationproblem,

J=tk+1∫tk

[(r− y)⊤Q (r− y)+Δu⊤RΔu

]dt+��

2 (30)

where the variables r, y and Δu correspond to the in-put reference, plant output and control correction. Thesoft control boundaries, uRUL, corresponding to a par-ticular tRUL are introduced implicitly in the MPC costfunction through the terminal cost. The terminal costterm is comprised of a terminal weight �� and the slackvariable �. The weight matrices Q and R are defined a-priori as the inverse of the maximum allowable track-ing error and control correction, respectively.

Discrete MPC Cost FunctionThe discretized version of the MPC is defined as,

minΔ(k ∣ k)...Δ(m−1+k ∣ k)

[J (Δu, r,y)

](31)

using the cost function,

J =p−1∑i=0

[ny∑j=0

∣wyi+1,j yj (k+i+1∣j)− rj (k+i+1)∣2

+nu∑j=1

∣wΔui,j Δuj (k+i ∣ k)∣2

]+ ��

2(32)

where the subscript “()j” denotes the j-th componentof a vector, “(k + i ∣ k)” denotes the value predictedfor time k+i based on the information available at timek; r (k) is the current sample of the output referencesubject to,⎧⎨⎩

y (k+i+1∣k) ∈ [yj,min (i) , yj,max (i)]

u (k+i∣k) ∈ [uj,min (i) , uj,max (i)]

Δu (k+i∣k) ∈ [Δuj,min (i) ,Δuj,max (i)]

y (k+i+1∣k) ∈ [yRULmin − �V RUL

min , yRULmax + �V RUL

max ]

(33)

s.t. i ∈ (0, p− 1), ℎ ∈ [m, p− 1], � > 0 and m ≤p− 1 with respect to the sequence of input increments{Δ (k ∣ k) . . .Δ (m+ k − 1 ∣ k)} and to the slack vari-able � and by setting u (k) = u (k − 1) + Δu (k ∣ k)

∗,where Δu (k ∣ k)

∗ is the first element of the optimalsequence. In matrix form, the MPC cost function canbe written as,

J=(yp−rp)⊤W2y(yp−rp)+Δu⊤pW

2ΔuΔup+��

2 (34)

WeightsWeights for the optimal control problem in (33) arerepresented as Wu, WΔu and ��. The weights of eachterm relate to the emphasis placed on the performanceof the system tracking error, level of control correction,and prognosis, respectively.

Hard ConstraintsThe real-valued constraints ymin, ymax, umin, umax,Δumin, and Δumax set the absolute lower and upperbounds on the variables y, u and Δu, respectively.

Soft ConstraintsThe prognosis-based constraints on the internal statesxRUL

min and xRULmax are introduced as “soft” boundaries

through a slack variable �. Violations in the softboundaries are introduced as the quadratic terminalcost in (33). The constants V RUL

min and V RULmax are non-

negative entries which represent the concern for relax-ing the corresponding constraint; the larger V RUL, thesofter the constraint. For example, setting V RUL = 0implies that the constraint is a hard constraint that can-not be violated.

10


The MPC AlgorithmConsider for simplicity the prediction model given by:⎧⎨⎩ x (k + 1) = Ax (k) + Bu (k) + w (k)

y (k) = Cx (k) + v (k)(35)

where A ∈ ℝnx×nx , B ∈ ℝnx×nu , C ∈ ℝny×nx ,x ∈ ℝnx and the initial conditions for the state vari-able x and control input u are defined as x0 = x (0)and u−1 = u (0−). Then, the prediction of the futuretrajectories of the model starting at time k = 0 is,

y (i∣0) = C

[Aix (0) +

i−1∑k=0

Ai−1B ⋅ . . .(ℎ∑

j=0

�u (j) + w (ℎ)

)]+ w (i)

(36)

which, written in vector form gives,

yp = Sxx0 +Su1u−1 +SuΔup +Hwwp +Hvvp (37)

Consider the deterministic case where the randomvariables and are both omitted from the plant dynam-ics in (35). The corresponding cost function in (34)can be expressed as,

J = krΔup + Δu⊤p KΔuΔup + ��2 + const. (38)

Where the matrices kr and KΔu are functions of A,B, C, x0 and u−1. Now, reconsider the inequalityconstraints from (33) which can be written in matrixform as,

Mz zp ≤ cz (39)

where zp = [ Δup � ]⊤ ∈ ℝp+1 absorbs theslack variable into the constraint optimization prob-lem. Now, define a linear constraint mapping gz :ℝp+1 → ℝ6p ,

gz (zp) = MzΔzp − cz (40)

Next, define the LaGrangian Lz : ℝp+1 → ℝ,

Lz (zp) = kz zp + z⊤p Kz zp (41)

where kz = [ kr 0 ]⊤ ∈ ℝ1×(p+1) and Kz =diag(KΔu, ��) ∈ ℝ(p+1)×(p+1). The constraintson the system dynamics can be adjoined to the La-Grangian Lz by introducing time-varying LaGrangemultiplier vector � with gz. The result is the Hamil-tonian function,

H� = kz zp + z⊤p Kz zp + �⊤ (Mz zp − cz) (42)

By taking the partial derivative of H with respect tozp,

∂Hz∂zp

= kz + 2z⊤p Kz + �⊤Mz (43)

Finally, by setting (43) identically equal to zero, theoptimal solution z★p can be expressed as,

z★p = −1

2K−1z

(k⊤z + Mz�

★)

(44)

where �★ satisfies the following Kuhn-Tucker condi-tions (45) (Fletcher, 2000) for optimality,

⎧⎨⎩

Mz zp − cz ≤ 0

kz + 2z⊤p Kz +(�★p)⊤

Mz = 0

�★pgz = 0

�★p ≥ 0

(45)

Several algorithms exist for solving the linear inequal-ity constraints posed by the MPC such as the Dantiz-Wolfe algorithm (Bemporad et al., 2004).

4.3 Simulation ResultsThe time-evolution of the turn-to-turn winding faultsfor different operating conditions were simulated inSimulink using (28).

The model parameters am and bm were computedusing the following equation,⎧⎨⎩ am = − 1

RwaCwa

bm = R0Rwa

(46)

Using these modeling parameters, the fault dimensiontrajectories were generated for different motor cur-rents, as shown in Figure 15. The initial fault conditionwas set to L0 = 0.05 for each trajectory.

Figure 15: Fault dimension trajectories for differentcurrent values.

Notice, as the operating current decreases, the tra-jectory becomes longer for the same initial fault con-dition. The horizontal line in Figure 15 denotes thehazard zone. The hazard zone defines the maximumallowable value for the fault dimension. The intersec-tion of the hazard zone with each fault dimension tra-jectory can be used to determine the expected RUL.The expected RUL computed from Figure 15 for eachoperating condition is provided in Table 1.

According to Figure 15 the expected RUL is in-versely proportional to the magnitude of the operatingcurrent. Thus, the RUL can be extended by reducingthe operating current. The MPC controller discussedearlier takes advantage of this relationship by reducing

11


Table 1: Simulation results for the fault-growth model.

Motor Current [A] RUL [min] ΔRUL [min]

20 2200 244425 310 344.430 41.0 45.5635 6.00 6.66740 0.90 1.000

the operating current magnitude based on the RUL re-quirement. The degree of relaxation is dependent onthe weight matrices chosen during the controller de-sign phase. To demonstrate the feasibility of the ap-proach the MPC toolbox in MATLAB was used to ex-pedite the design process. The MPC controller con-tained the variables listed in Table 2. In addition, eachconstraint has an associated cost as defined in Table 3.

Table 2: Variable types.

Sym Description Constraint Min Max

�ref Reference pos. Hard -120° 120°�l Actuator pos. Hard -120° 120°im Motor current Soft -40A 40A

Table 3: Cost function weighting factors used in thesimulation.

Symbol Description Weight DoS

�ref − �l Position Error [(30/�) /100]2 0im Motor Current [1/40]2 0� Soft Violation 1 1

The actuator was simulated using the 5th order ac-tuator model from (1). Results for three different faultscenarios were generated using the MPC (parametersgiven in Table 4) with the corresponding boundariesand weights defined in Tables 2 and 3, respectively.The results are provided in Figure 16. Notice, asthe fault dimension increases (left-to-right), the MPCplaces more emphasis on reducing the magnitude ofthe motor current. As a consequence, the rise time ofthe actuator position increases and the magnitude ofthe winding temperature decreases thereby increasingthe estimated RUL.

5 CONCLUSIONSFault-tolerant and reconfigurable control strategies forimproved critical system reliability and survivabilityunder fault/failure conditions has attracted the atten-tion of the controls community in recent years. To ap-ply these technologies it is essential the system healthstatus be monitored continuously and incipient failuresbe tracked so that remedial action can be taken as soonas possible to assure its safety. Control reconfigura-tion at the component level, constitutes the first levelof the hierarchical framework for fault-tolerance. Thereconfigurable control framework was evaluated usingan EMA Simulink model. The results acquired from

the simulation demonstrated the feasibility of the ap-proach. Finally, complexity issues must be addressedfor specific application domains. Other modules of theintegrated fault-tolerant control hierarchy, such as thecontrol redistribution, mission adaptation, etc., are notaddressed in this paper but they contribute significantlytowards the development of high-confidence systems.

ACKNOWLEDGMENTThis work was supported by the United States NationalAeronautics and Space Administration (NASA) underSTTR Contract NNX08CD31P. The program is spon-sored by the NASA Ames Research Center (ARC),Moffett Field, California 94035. Dr. Kai Goebel,NASA ARC, Dr. Bhaskar Saha, MCT, NASA ARCand Dr. Abhinav Saxena, RIACS, NASA ARC, are theTechnical POCs and Liang Tang is the Principal Inves-tigator and Project Manager at Impact Technologies.

NOMENCLATURE

Table 4: List of commonly used symbols.

Sym Units Value Description

am1s – Thermal

parameter

bm∘K

s⋅A2 - ""

bℓin⋅lbfrad/s 2.50× 10−1 Load damping

bmin⋅lbfrad/s 1.00× 10−4 Motor damping

im A - Motor current

kBeV∘K 8.62× 10−5 Boltzmann’s

constant

kcsradrad 1.00× 105 Coupling

stiffness

keV

rad/s 1.10× 10−1 Back-emfcoefficient

kℓin⋅lbfrad 2.00× 10−3 Load stiffness

kp1V

rad/s 1 Controller gain

kp21s 1 ""

kp3radrad 100 ""

ktin⋅lbf

A 1.01 Motor torquecoefficient

rp - - Reference arraytRUL s - RULyRUL - - RUL output

boundu−1 - - Set-point i.c.wui - - Wt. vector for u

wΔui - - Wt. vector for

Δu

wyi - - Wt. vector for y

yp - - Measurementarray

12


(a) (b) (c)

Figure 16: Simulation results for the reconfigurable control with initial fault dimensions (a) L0 = 1 × 10−6 (b)L0 = 1× 10−2 and (c) L0 = 1× 10−1

z - - Concat. state

CwaW∘K/s 5.00× 10−5 Thermal

capacitanceEa eV 7.00× 10−1 Activation

energy

Jℓin⋅lbf1/s2 2.00× 10−3 Load inertia

Jmin⋅lbf1/s2 2.10× 10−3 Motor inertia

Llim - 2.00× 10−1 Fault dim. limitLtt H 3.00× 10−4 Turn/turn

inductanceNcl - 1 Load couplingNcm - 1 Motor couplingR0 Ω 1.60× 10−1 Nominal

resistanceRtt Ω 1.60× 10−1 Winding

resistance

Rwa∘KW 7.50× 10−1 Thermal

resistanceTwa

∘K - Winding-to-ambienttemperature

Tload in⋅lbf - Load torque

VRUL

- - Degree-of-softness

Wy - - Tracking errorweight

WΔu - - Set-point adj.weight

� 1s 1× 10−6 Fault-growth

coefficient� - - Slack var.�p - - LaGrange

coefficients

�ℓ rad - Load position�m rad - Motor position

!ℓrads - Motor speed

!mrads - Load speed

Δum - - Set-point adj.array

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Douglas W. Brown received the B.S. degree inelectrical engineering from the Rochester Institute ofTechnology in 2006 and the M.S degree in electricalengineering from the Georgia Institute of Technologyin 2008. He is a recipient of the National Defense Sci-ence and Engineering Graduate (NDSEG) Fellowshipand is currently pursuing the Ph.D. degree in electricalengineering at the Georgia Institute of Technologyspecializing in control systems. His research interestsinclude incorporation of Prognostics Health Manage-ment (PHM) for fault-tolerant control. Prior to joiningGeorgia Tech, Douglas was employed as a projectengineer at Impact Technologies where he workedon incipient fault detection techniques, electroniccomponent test strategies, and diagnostics/prognostic

algorithms for power supplies and RF componentapplications.

George Georgoulas received Diploma and PhD de-grees from the Department of Electrical and ComputerEngineering, University of Patras, Patras in 1999 and2006, respectively. He joined the ICSL in October2006 as a postdoctorate. His research interests includeintelligent data analysis and development of decisionsupport systems for complex systems.

Brian M. Bole graduated from the FSU-FAMUSchool of Engineering in 2008 with a B.S. in ECE andApplied Math. In August 2008 he joined the ISCL,where he is pursuing a PhD in ECE. His researchinterests include optimal control and fault tolerantcontrol, based on fault diagnosis and prognosisestimates. graduated from the FSU-FAMU Schoolof Engineering in 2008 with a B.S. in ECE and aB.S. in Math. Prior to joining the group he worked atthe Florida Department of Transportation StructuresResearch Center. Brian is interested in robust controlschemes utilizing fault prognosis and diagnosis.

Hai-Long Pei is a Professor and Deputy Dean ofthe College of Automation Science and Engineeringat South China University of Technology. He re-ceived the B.S. degree and the M. Sc. degree bothin electronic engineering from the NorthwesternPolytechnical University in China in 1986 and 1989separately, and the Ph.D. degree in Automation fromSouth China University of Technology in 1992. Hisresearch interest includes autonomous systems, intel-ligent control, and prognosis enhanced reconfigurationcontrol.

Marcos E. Orchard received the B.Sc. degree (1999)from the Catholic University of Chile, Santiago,Chile, and the M.S. (2005) and Ph.D. (2007) degreesin electrical and computer engineering from theGeorgia Institute of Technology, Atlanta. He iscurrently an Assistant Professor with the Departmentof Electrical Engineering, Universidad de Chile,Santiago, Chile. His current research interests includesystem identification, statistical process control andthe development of real-time frameworks for bothfault diagnosis and failure prognosis.

Liang Tang is a Sr. Lead Engineer at ImpactTechnologies LLC, Rochester, NY. His researchinterests include diagnostics, prognostics and healthmanagement systems (PHM), fault tolerant control,intelligent control, and signal processing. He obtaineda Ph.D. degree in Control Theory and Engineeringfrom Shanghai Jiao Tong University, China in 1999.Before he joined Impact Technologies, he worked asa post doctoral research fellow at Intelligent ControlSystems Laboratory, Georgia Institute of Technology.At Impact Technologies he is responsible for multipleDoD and NASA funded research and developmentprojects on structural integrity prognosis, prognosticsand uncertainty management, automated fault accom-modation for aircraft systems, and UAV controls. Dr.Tang has published more than 30 papers in his areasof expertise.

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Bhaskar Saha is a Research Programmer with Mis-sion Critical Technologies at the Prognostics Centerof Excellence, NASA Ames Research Center. Hisresearch is focused on applying various classifica-tion, regression and state estimation techniques forpredicting remaining useful life of systems and theircomponents. He has also published a fair numberof papers on these topics. Bhaskar completed hisPhD from the School of Electrical and ComputerEngineering at Georgia Institute of Technology in2008. He received his MS from the same schooland his B. Tech. (Bachelor of Technology) degreefrom the Department of Electrical Engineering, IndianInstitute of Technology, Kharagpur.

Abhinav Saxena is a Staff Scientist with ResearchInstitute for Advanced Computer Science at the Prog-nostics Center of Excellence NASA Ames ResearchCenter, Moffet Field CA. His research focus lies indeveloping and evaluating prognostic algorithms forengineering systems using soft computing techniques.He is a PhD in Electrical and Computer Engineeringfrom Georgia Institute of Technology, Atlanta. Heearned his B.Tech in 2001 from Indian Instituteof Technology (IIT) Delhi, and Masters Degree in2003 from Georgia Tech. Abhinav has been a GMmanufacturing scholar and is also a member of IEEE,AAAI and ASME.

Kai Goebel received the degree of Diplom-Ingenieurfrom the Technische Universität München, Germanyin 1990. He received the M.S. and Ph.D. from theUniversity of California at Berkeley in 1993 and 1996,respectively. Dr. Goebel is a senior scientist at NASAAmes Research Center where he leads the Diagnostics& Prognostics groups in the Intelligent Systemsdivision. In addition, he directs the Prognostics Centerof Excellence and he is the Associate Principal Inves-tigator for Prognostics of NASA’s Integrated VehicleHealth Management Program. He worked at GeneralElectric’s Corporate Research Center in Niskayuna,NY from 1997 to 2006 as a senior research scientist.He has carried out applied research in the areas ofartificial intelligence, soft computing, and informationfusion. His research interest lies in advancing thesetechniques for real time monitoring, diagnostics, andprognostics. He holds ten patents and has publishedmore than 100 papers in the area of systems healthmanagement.

George J. Vachtsevanos is a Professor Emeritus ofElectrical and Computer Engineering at the GeorgiaInstitute of Technology. He was awarded a B.E.E.degree from the City College of New York in 1962,a M.E.E. degree from New York University in 1963and the Ph.D. degree in Electrical Engineering fromthe City University of New York in 1970. He directsthe Intelligent Control Systems laboratory at GeorgiaTech where faculty and students are conducting re-search in intelligent control, neurotechnology and car-diotechnology, fault diagnosis and prognosis of large-scale dynamical systems and control technologies forUnmanned Aerial Vehicles. His work is funded bygovernment agencies and industry. He has published

over 240 technical papers and is a senior member ofIEEE. Dr. Vachtsevanos was awarded the IEEE Con-trol Systems Magazine Outstanding Paper Award forthe years 2002-2003 (with L. Wills and B. Heck). Hewas also awarded the 2002-2003 Georgia Tech Schoolof Electrical and Computer Engineering DistinguishedProfessor Award and the 2003-2004 Georgia Instituteof Technology Outstanding Interdisciplinary ActivitiesAward.

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