Non-Deterministic Tunneling Analysis Using a.I. Based Techniques Genetic Programming vs ANNs

8/12/2019 Non-Deterministic Tunneling Analysis Using a.I. Based Techniques Genetic Programming vs ANNs

1/17

12thICSGE10-12 Dec. 2007

Cairo - Egypt

Ain Shams University

Faculty of Engineering

Department of Structural Engineering

Twelfth International Colloquium on Structural and Geotechnical Engineering

NON-DETERMINISTIC TUNNELING ANALYSIS

USING A.I. BASED TECHNIQUES

GENETIC PROGRAMMING VS ANNs

A. A. AhmedProfessor of Geotechnical and Structural Engineering

Faculty of Engineering, Ain Shams University, Cairo, Egypt

Email: [email protected]

H. A. Ali

Assistant Professor of Geotechnical and Structural Engineering

Faculty of Engineering, Ain Shams University

S. M. ElAraby



T. M. ElKateb



S. M. Noureldin

Ph.D. Candidate, Faculty of Engineering, Ain Shams University

Business Development Manager/ Projects Engineer,

ECG Engineering Consultants Group S.A.

P.O. Box 1167 Cairo 11511 Egypt

Email: [email protected]/[email protected]

ABSTRACT

The term Non-Deterministic Analysis refers to a collection of analyses that include

reliability analysis, risk-based analysis, and probabilistic analysis. Such techniques have

been undergoing development since the last decade. Application to structural

engineering problems has generally preceded applications in geotechnical engineering.

Geotechnical problems, especially underground/ tunnel structures, often involve certain

complexities that are not found in structural problems.

Despite the significant body of literature that has been published, proposing and

detailing various methodologies and applications; developments in non-deterministic

analyses approaches mostly focus on analytical methods. Shortcomings of these
mailto:[email protected]:[email protected]/mailto:[email protected]:[email protected]:[email protected]/mailto:[email protected]


2/17

methods and their implications on tunneling reliability analysis implementation shall be

investigated. Previous publications of the author(s) have introduced alternative AI based

approaches using Evolutionary Generalized Feedforward Networks to overcome

shortcomings/ limitations associated with the currently used analytical non-

deterministic approaches.

In this study, Genetic Programming (GP) AI-based approach is introduced. GP is a type

of programming that imitates genetic algorithms and helps develop computer programs

to solve specific problems. The performance of the GP approach shall be assessed and

compared to the ANN based approach as well as traditional non-deterministic

techniques. The advantages and limitations of the introduced three (3) approaches are

investigated.

KEYWORDS

tunneling, reliability-based design, Artificial Intelligence (A.I), ANN, uncertainty,

probability, geostatistics, decision making.

1 NON-DETERMINISTIC DESIGN APPROACH

The term Non-Deterministic Analysis refers to a collection of analyses that include

reliability analysis, risk-based analysis, and probabilistic analysis. Such techniques have

been undergoing development since the last decade. Application to structural

engineering problems has generally preceded applications in geotechnical engineering.

Geotechnical problems, especially underground/ tunnel structures, often involve certain

complexities that are not found in structural problems.

The Reliability/ Probabilistic approach extends the traditional safety factor concept to

incorporate uncertainty in the design parameters. This uncertainty can be quantifiedthrough statistical analysis of existing data or judgmentally assigned. Even if

judgmentally assigned, the probabilistic results will be more meaningful than the

deterministic approach because the engineer provides a measure of the judgment

uncertainty in each parameter. Baecher [1] briefly summarized the steps of performing

reliability analysis as follows:

a)Establish an explicit analytical model to compute the factor of safety, or any othermeasure of performance.

b)Estimate statistical descriptions of the parameters which include the properties of thegeotechnical materials, loads and geometry. Usually, the parameters are described by

their means, variances, and covariances.

c)Calculate the statistical moments of the performance function by means of simulationmethods. The most widely used technique is the Mote Carlo Simulation (MCS)

algorithm. MCS model mainly requires a random number generator based on the

probability distribution function of the input design parameter. This iterative process

continues until the simulation reaches a definite stopping criterion.

d)Compute the probability of failure/ performance measure on condition that theperformance function has a well defined probabilistic description, such as the normal

distribution. Otherwise, where the distribution is not known or the intersection of the

performance function with the probabilistic description of the parameters is not


3/17

simple, the calculation of the probability of failure is likely to involve further

approximations.

2 CURRENTLY USED RELIABILITY APPROACHES

Application of reliability principles was primarily developed to perform probabilisticslope stability analysis using different approaches, such as analytical approaches and

MCS. Analytical approaches were primarily apprehensive, obtaining closed form

solutions for the statistical properties of the factors of safety which do not provide

information about the output probability distribution. Besides, it becomes highly

complicated when taking into account different sources of uncertainty. Some of these

approaches shall be described hereinafter.

The First Order Second Moment (FOSM) method is a relatively straightforward method

of considering the effects of uncertainty of input parameters on a resulting dependent

variable. The FOSM algorithm uses the Taylor series expansion of the function to be

evaluated. This expansion is reduced after the linear term or the first order term. Themodified expansion is then used, along with the first two moments of the random

variable(s), to establish the values of the first two moments of the dependent variable

(second moment). Limitations of FOSM are obvious when the limit sate function is

nonlinear and the random variables are inherently normally distributed. Therefore, it is

necessary to linearize the limit state function to compute the second moment

parameters. However, in the case that some variables follow other non-normal types of

known probability distributions, it is a must to incorporate the additional information by

transforming these non-normal distributions locally to equivalent normal variables. This

procedure is called the extended FOSM method [1].

The Response Surface Method (RSM) is a technique that adopts a polynomialexpansion (the response surface) to describe the dependency of the output variable on

the independent variables. In spite of the highly nonlinear nature of a problem, linear

expressions for the corresponding failure surfaces in the transformed space are usually

interpolated by means of Minimum Squares procedure [8]. Bottom line is that a

predefined distribution, normal distribution in most cases, is being assigned to the

distribution of the unknown limit state function to cope with the previously mentioned

assumptions.

The Statistical Finite Element Methods (SFEMs) incorporate, in most cases, big number

of deterministic Finite Element (FE) calculations to represent the case adequately.

However, in most cases the number of deterministic FE calculations that should be

carried out is impractical to be implemented. To overcome the previous point, moststudies concentrate on a maximum of three (3) uncertain parameters. While in highly

sophisticated studies, like those associated with tunneling, more parameters should be

considered in the analyses.

Shortcomings of the currently used reliability and probabilistic techniques may be

summarized as follows:

a) In many complicated and nonlinear problems, where the analyses involve the use ofnumerical procedures such as the finite element method, it is difficult to express the

problem explicitly in terms of the random variables. Therefore, the limit state and the

performance functions can only be expressed implicitly rather than in a closed-form

solution [4].


4/17

b)The currently used techniques are considered difficult to implement; as to achieveaccurate results thousands of finite element analysis runs are needed.

c)The variation of the input parameters undergoes mathematically defined parametercombinations which should be randomly set.

3 SOURCES OF UNCERTAINTY IN GEOTECHNICAL DESIGN

Baecher [1] discussed the uncertainties that evolve with geotechnical applications and

categorized them into three (3) main categories:

a)Natural variability.Associated with the inherent randomness of natural processes,the natural variability is modeled as variability over time for a phenomena that take

place at a single location (temporal variability); variability over space for

phenomena that take place at different locations at a single time (spatial variability);

or as variability over both time and space. Such natural variability is approximated

using mathematical simplifications or models.

b)Knowledge uncertainty. Attributed to lack of data, information about events,processes, or understanding of physical laws that limit the ability to model the real

world, and can be considered as a more common description of epistemic

uncertainty.

Knowledge uncertainty divides into three major sub-categories for geotechnical

applications:

i. Site characterization uncertainty. Which deals with the adequacy ofinterpretations of the subsurface geology resulting from data and exploration

uncertainties, including measurement errors, inconsistency or inhomogeneity of

data, data handling, transcription errors, and inadequate representativeness of datasamples due to time and space limitations.

ii.Model uncertainty. Has to do with the degree to which a chosen mathematicalmodel perfectly mimics reality incorporating two or three dimensional FEA.

iii.Parameter uncertainty. Involved with the precision to which model parameterscan be estimated which results from inaccuracy in evaluating parameter values

from test or calibration data and is aggravated by limited observations and

resulting statistical imprecision.

c)Decision and operational uncertainies. Concerned with the implementation ofdesigns in practice, incorporating the economic issues related to benefit-cost

calculations. Operational uncertainties are involved with construction, manufacture,

deterioration, maintenance, human factors, and the impact of tuunneling

technologioes. Decision uncertainties describe the incapability to know social

objectives, the length of a planning horizon, desirable temporal consumption-

investment trade-offs or the social aversion to risk.

As a result, tunneling is subject to a diversity of uncertainties compared to other areas of

geotechnical engineering (Table 1). These uncertainties comprise geologic conditions

(natural variability and knowledge uncertainty), the parameters which affect excavation

and tunnel support system (knowledge and parameter uncertainty), the advance rates

which vary due to effects of human and equipment performance, construction material

properties and unforeseen construction events, even while encountering constant


5/17

geologic and geotechnical conditions (decision and operation uncertainties).

Consequently, it is never possible to unerringly predict tunneling conditions. However,

it is possible to determine the range over which those parameters may vary. Such

deliverable can in turn serve as a basis for risk analysis and decision making under

uncertainty. In this paper, it is proposed to judge the variability of the following designparameters:

a) shear strength,b)friction angle,c) soil modulus of elasticity, andd)the stress release corresponding to confinement loss.

Table 1: Uncertainties Associated with Tunneling

Uncertainty Natural

Variability

Knowledge

Uncertainty

Decision/

OperationalUncertainty

Geologic/ Geotechnical Conditions

Excavation Modeling

Tunnel Support Modeling

Construction Material Properties/

Unforeseen Conditions

4 SIMULATION OF TUNNELING USING THE CONVERGENCE-

CONFINEMENT METHOD

The convergence-confinement method (CCM), which is a simplified method of

analyzing the interaction between the ground and support, shall be used in the tunnelexcavation simulation. Actually, the stress development generated by a tunnel

excavation is a three-dimensional problem because it depends on the distance to the

working face. However, a simplification is applied using the CCM by considering a

plane strain calculation in the plane perpendicular to the shield advance through two (2)

construction simulated phases:

a)The first phase incorporates simulation of tunneling by applying a stress boundarycondition at the periphery of the tunnel. The principle counts on removing the soil

inside the excavation boundary and to replace it by conjured stress supporting

vectors which equilibrate the initial state.

b)The second step is to model the complete interaction between the soil and thestructure.The process is idealized using Plaxis Code by generating the initial stress field and

applying the eventual external loads that are present before the tunnel construction. The

first construction phase is simulated by deactivating the tunnel cluster(s) without

activation of the tunnel lining and applying an ultimate level of Mstage equal to (1-)

"Stress Release Factor". The final phase is accomplished by activating the tunnel lining.


6/17

5 GEOSTATISTICAL ANALYSIS OF LOT 42, GREATER CAIRO METRO,

LINE NO. 2

Geostatistics studies were developed to assist in the estimation of changes in ore grade

within a mine; however, since its development in the early 1960s, geostatistics has

been applied to many disciplines including: groundwater hydrology and hydrogeology;

surface hydrology; earthquake engineering and seismology; pollution control;

geochemical exploration; and geotechnical engineering. Geostatistics can be applied to

any natural phenomena that are spatially or temporally associated. Excellent review is

conducted by Jaksa [6], El-Ramly [2], and ElKateb [3].

Lot 42 (part of Phase 2A, Greater Cairo Metro Line No. 2) extending from ElDokki to

ElGezira, shall be this papers case study. Previously recorded laboratory measures for

the soil strength/ elasticity parameters are used whenever possible beside the SPT N-

value recorded during the geotechnical investigation of the case study. SPT is used for

cross correlation with strength and elasticity parameters due to its abundance in nearly

all the geotechnical investigations of tunneling projects due to its simplicity, financialviability, and strong-positive correlation to strength and elasticity parameters. Results of

the Geostatsistical soil parameters study is summarized in Figure (1) and Table (2).

Fig. (1):Soil Log at Lot 42 Location

Table 2: Soil Geotechnical Parameters at Lot 42

Clay Sand Layer (1) Sand Layer (2)Property

Distribution Mean S.D. Mean S.D. Mean S.D.

Mod. Of Elasticity,

Eref(kPa)

Variable min. 9E+03 max 20E+03

1.25E+04 5.52E+03 6.49E+04 5.52E+03

Angle of Friction, Normal N/A N/A 360 20 410 20

Cohesion, C (kPa) Normal 60 20 N/A N/A N/A N/A


7/17

6 OVERVIEW OF NEURAL NETWORKS

An Artificial Neural Network (ANN) is an information processing paradigm that is

inspired by the biological nervous systems information processing. The key element ofthis paradigm is the novel structure of the information processing system. It is

composed of a large number of highly interconnected processing elements (neurons)

working in harmony to solve specific problems. The ANN system learns by example

and so configured for a specific application, such as pattern recognition or data

classification, through a learning process.

A neuron is the fundamental cellular unit of this complex nervous system. It is a simple

processing element that receives and combines signals from other neurons throughout

input paths called dendrites.

Figure (2) represents the various components of a biological neuron. Each signal

coming into the neuron along a dendrite passes through a synapse or a synaptic junction.This junction is an infinitesimal gap in the dendrite that is filled with neurotransmitter

fluid produces electrical signals that go to the nucleus or soma of the neuron. The

adjustment of the impedance or the conductance of the synaptic gap is a critically

important process. Indeed, these adjustments lead to memory and learning. As the

synaptic strengths of the neurons are adjusted, the brain learns and stores information.

Fig. 2:Structure of Biological Neuron

6.1 Artificial Neural Networks

Artificial neural networks (ANN) are highly distributed interconnections of adaptive

nonlinear Processing Elements (PEs), Figure (3). The PE is a simple sum of products

followed by nonlinearity (McCulloch-Pitts neuron). The network weights can be

adapted such that the networks output matches a desired response.


8/17

Distributed processing, adaptation and nonlinearity, are considered the hallmark of

ANN processing systems. Distributed computation has the advantages of reliability,

fault tolerance and high throughput (division of computation tasks). Adaptation is the

ability to change the system parameters according to some rule, normally, minimization

of an error function and enables the system to search for optimal performance.Nonlinearity produces more powerful computation schemes when compared to linear

processing.

6.2 Artificial Neural Network (ANN)/ Monte Carlo Simulation (MCS) Hybrid

System

The use of Artificial Neural Networks (ANNs) in geomechanics has significantly

increased in the last decade [9 and 10]. Moreover, their successful applications in other

fields of decision-making and in computer and electrical engineering is expected to lead

to further interest and confidence in their applications in all fields of civil engineering.

Fig. 3:Structure of ANN

The expert judgments that must routinely be made in geotechnical engineering make it

an excellent field for ANN application. The objective of this paper is to utilize the ANN

technique in obtaining an A.I. based expression that approximately represents the

performance function. A Hybrid Model Using ANN/ MCS shall be developed to

calculate the statistical moments of the performance function (the mean and variance of

the performance function).

The Hybrid ANN/ MCS technique was innovated by virtue of generating and compiling

a Dynamic Link Library file (DLL) for the ANN and embedding it to a macro

application written in Microsoft Visual Basic Language, Figure (4). This linkage,

as illustrated in Figure (4), overcame a major shortcoming of ANNs. This shortcoming

is related to information storage. The information acquired during training is stored in

the connection weights in a complex manner that is often difficult to interpret. In


9/17

general, the rules governing the relationships between the network input/output

variables are difficult to quantify, and thus ANNs are often criticized for being black

boxes. The technique presented in this paper is considered a utility to overcome this

black box limitation. Other techniques used to overcome the shortcomings of ANNs

using neuro-fuzzy techniques have been tackled by Shahin et al. [11].

The technique utilized for reaching the optimal neural network for the study conducted

in this paper is the Evolutionary Generalized Feedforward Network "EGFFN" which is

a generalization of the Multilayer Perceptron (MLP), such that connections can jump

over one or more layers. In theory, a MLP can solve any problem that a Generalized

Feedforward Network can solve. In practice, however, EGFFNs often solve the problem

much more efficiently. A standard MLP requires hundreds of times more training

epochs than the EGFFNs containing the same number of processing elements.

Fig. 4: Simulation Cycle using Hybrid ANN/ MCS System

7 BACK-ANALYSIS USING NON-DETERMINISTIC APPROACH TO

DEMONSTRATE THE STRESS RELEASE CORRESPONDING TO

CONFINEMENT LOSS

The monitored settlement profiles for Cairo Metro Line No. 2 revealed the following

[9]:

a)The back-calculated distance for the point of inflection i varied at different Lotsand different locations between 5.8 m and 8.3 m. Some of the observed relationships

for i/aversus z/2a(ais the tunnel radius) varied between 1.0 and 2.0 for Phase 1 and

between 1.3 and 1.85 for Lots 40, 42 and 46 (Phase 2A).

b) The back-calculated volume losses at the Cairo Metro Line No. 2 at the beginning oftunneling for Phase 1 at Lots 12, 14 and 16 averaged at 0.5% and exceeded 0.8% at

some locations. On the other hand, the back-calculated volume loss for Phase 2A was

estimated at 0.3% average and 0.5% maximum.

In order to determine the stress release corresponding to the confinement loss occurred,

an ANN/MCS Hybrid System Back-Analysis Framework HSBAF was used to

express the probabilistic parameters of the stress release under the uncertainty of the soil


10/17

parameters including shear strength parameters and the modulus of deformation

following two aspects:

a)Measured surface settlement at the lot under study: HSBAF-1b)Values of volume loss mentioned in literature: HSBAF-2.The test section is analyzed through approximately 300 runs using the geotechnical

finite element code Plaxis version 7.2. The main goal of the FEA is to carry out a

non-deterministic parametric study for the stress release factor at Lot 42, and to

facilitate a source of input data that can represent the performance of tunneling in the

section under study. The soil was modeled by 127 fifteen-node elements. The Mohr-

Coulomb elastic perfectly plastic model was used to represent the nonlinear, stress-

strain behavior of the soil. The angle of friction (), the cohesion (C), and the modulus

of elasticity (E) were introduced to the analysis as random variables with Probability

Distribution Functions (PDFs) as mentioned in Table (2).

Sixty percent (60%) of the FEA runs were used for training, while the rest were dividedequally between the cross validation and testing data sets. The neural network algorithm

was then used to determine the Stress Release Z (, C, E, Smax) & Z (, C, E, Vs),

which represent the stress release occurred as a function of the random variables , C,

Esand, Eclay and the maximum surface settlement at the centerline of the tunnel

Smax or the volume of the settlement profile at the ground surface Vs.

The optimal neural network constituted of six (6) input neurons representing the input

variables, one hidden layer containing four (4) neurons, and one (1) output neuron

representing the Stress Release factor (1-). EGFFN Model configuration and results

are illustrated in Figure (4) and the evaluation of the ANN model performance is

demonstrated in Tables (3) and (4).Table (3): HSBAF-1: Data Sets Performance

Performance Training Cross Validation Testing

MSE (Mean Square Error) 0.001 0.001 0.001

NMSE (Normalized MSE) 0.022 0.041 0.036

MAE (Mean Average Error) 0.021 0.025 0.025

Max Absolute Error 0.067 0.141 0.109

r (correlation) 0.990 0.985 0.982

Table (4): HSBAF-2: Data Sets Performance

Performance Training Cross Validation Testing

MSE (Mean Square Error) 0.001 0.001 0.003NMSE (Normalized MSE) 0.035 0.023 0.089

MAE (Mean Average Error) 0.023 0.021 0.028

Max Absolute Error 0.098 0.072 0.368

r (correlation) 0.989 0.990 0.957

The final forecast charts (Figures 5 and 6) reflect the combined uncertainty of the

assumption on the models output. The analysis of both the first and the second

approaches revealed that the stress release occurred has a mean value of 16% and 19%

with a Standard Deviation of 6% and 7% respectively having a best fit of Gamma

Probability Distribution Function.


11/17

8 GENETIC PROGRAMMING (GP) BASED NON-DETERMINISTIC BACK-

ANALYSIS APPROACH

Genetic programming (GP) is a domain-independent, problem-solving approach in

which computer programs are evolved to find problems solutions. The solution

technique is based on the Darwinian principle of survival of the fittest [7]. GP is

closely related to the field of Genetic Algorithms (GA); however, three (3) important

differences exist between GA and GP [12]:

a)Structure: GP usually evolves tree structures while GA evolves binary or real numberstrings.

b)Active vs. Passive: Because GP usually evolves computer programs, the solutionscan be executed without post processing (active structures), while GA typically

operate on coded binary strings (passive structures), which require post-processing.

c)Variable vs. fixed length: Traditionally, GA, the length of the binary string is fixedbefore the solution procedure begins. However, GP parse tree can vary in lengththroughout the run. Although it is recognized that in more advanced GA work,

variable length strings are used.

Fig. 5: Configuration of ANN for Predicting Stress Release Factor


12/17

Fig. 6: HSBAF-1, PDF of (1-) corresponding to Max. Surface Settlement of 10

mm, Gamma Distribution, Loc.=.09, Scale=0.05, Shape=1.50

Fig. 7: HSBAF-2, PDF of (1-) corresponding to Vs=0.30%, Gamma Distribution,

Loc.=0.10, Scale=0.05, Shape=1.93

Every solution evolved by GP is constituted of two (2) sets of principal nodes; terminals

and functions. The terminal set contains nodes that provide an input to the GP system

while the function set contains nodes that process values already in the system.


13/17

Constants can be used in GP by including them in the terminal set. Once the

evolutionary process is started, the GP system randomly selects nodes from either set

and thus may not utilize all of the available nodes. However, increasing the size of each

node set enlarges the search space. Therefore, only a relatively simple node set is

initially provided and nodes are usually added only if required.

In order to solve a problem using GP, Koza [7] specified the following requirements:

a)The terminal set: set of input variables.b)The function set: set of domain specific functions used in conjunction with the

terminal set to construct potential solutions to a given problem. For symbolic

regression this could consist of a set of basic mathematical functions, while Boolean

and conditional operators could be included for classification problems.

c)The fitness function: Fitness is a numeric value assigned to each member of apopulation to provide a measure of the appropriateness of a solution to the problem

in question.d)The algorithm control parameters: This includes the population size and the

crossover and mutation probabilities.

e)The termination criterion (stopping criterion): This is a predefined number ofgenerations or a fitness error tolerance.

The first three (3) components determine the algorithm search space, while the last two

(2) components affect the quality and speed of search.

The above mentioned GP approach, as illustrated in Figure (8), was utilized to find an

explicit closed-form-solution for the stress release factor (1-) using the optimization

parameters described in Table (5). The terminal set constituted of the 300 FEA runs.Results are illustrated in Table (6). After approximately 18,300 iterations, the following

Genetic Regression model was concluded:

(1-) = 1/Pa(A1.C + A2EC + A3.ES) + A4.tan1+ A5.tan2 + A6.Vs (1)

where An is constant

Pa is the atmospheric Pressure

C is the Cohesion

EC is the elasticity modulus of Clay

ES is the elasticity modulus of Sand

1 is the friction angle for Sand Layer 12 is the friction angle for Sand Layer 2

VS Volume loss

Table (5): Genetic Programming Optimization Parameters

Mode Real value mode "no encoding"

Population size 20

Mutation Rate 0.01

Crossover rate 0.85

Crossover type Random


14/17

Mode Real value mode "no encoding"

Selection type Absolute top mate

Stop criteria Tolerance/ iteration

Convergence tolerance 1E-10

Table (6):Genetic Programming Approach Performance Results for Equation (1)

A1 4.186E-6

A2 9.58E-6

A3 0.11

A4 0.0004

A5 2.36E-6

A6 0.31

Root of Mean Square Error (RMSE): 0.072

Sum of Square Error (SSE): 1.654

Correlation Coef. (R): 0.907

r (correlation) 0.822

Chi-Square: 6.891

Applying the same aspects of the back analysis technique discussed in the previous

section, MCS was carried out using Equation (1). The volume loss was preset to 0.3%

in order to determine the probabilistic values of the unloading factor; results are

illustrated in Figure (8).

Fig. 8: Genetic Programming Cycle


15/17

Fig. 9:GP Approach, Forecasting (1-)

Triangular Distribution, Min. = 0.18, Likeliest = 0.22, Max. = 0.28

9 SUMMARY AND CONCLUSION

In this study, Genetic Programming (GP) AI-based approach is introduced, assessed and

compared to an ANN based approach as well as traditional non-deterministic

techniques. The advantages and limitations of the introduced three (3) approaches areinvestigated.

The evolutionary neural network algorithm is introduced to develop an approximate

limit state surface expression overcoming most of the shortcomings of the currently

used techniques. By implementing a hybrid system using ANN/ MCS, it is possible to

estimate the probabilistic value of soil unloading/ deformation parameters associated

with soft ground tunneling conditions by using a practical technique and an easy to

implement number of FEA runs, Figure (10) . The proposed Hybrid System

Backanalysis Framework (HSBAF) has proven to be a promising technique in

probabilistic assessment of non-deterministic factors. Besides, coupling both neural

networks and Genetic Algorithm (Evolutionary Generalized Feedforward Network,

EGFFN) technique has proven to be reliable, effective and efficient in refining and

improving the performance of neural network architectures.

The Genetic Programming is capable of developing an explicit closed-form-solution for

the performance function. However, it has been shown that in spite of using the whole

300 FEA runs for the GP terminal set (set of input variables), less accuracy has been

achieved compared to the results obtained by the EGFFN. The following table, Table

(7) illustrates a comparison between the results achieved by using both approaches.

Both A.I based approaches managed to produce accurate Reliability Analysis

Frameworks with a significantly reduced number of FEA runs.


16/17

Table 7: Summary of Results for Forecasting of (1-) corresponding to 0.3% Volume

Loss using EGFFN and GP

Unloading Factor (1-) EGFFN GP

Distribution Gamma Triangular

Mean S.D. 0.190.07 0.220.02

Min. 0.10 0.18

Max. 0.18 0.28

Model Correlation (r) 0.96 0.82

Fig. 10: Decrease in the Overall Number of FEA Runs Required by the Proposed

Hybrid Model

10 ACKNOWLEDGEMENT

We, the authors, would like to express our gratitude to all those who gave us the

possibility to complete this work. We are deeply indebted to Prof. Dr. Fathalla

ElNahhas, Ain Shams University, whose help, stimulating suggestions and

encouragement helped us floating the boat.

We would also like to express our sincere gratitude and appreciation to Gen. Eng.

ElHosseiny Abdel-Salamm and Dr. Ashraf AbuKreisha, Egyptian Tunneling Society/

National Authority of Tunnels NAT, for providing us with their support at all levels.

11 REFERENCES

[1] Baecher, G.B. And Chritian, J.T., 2003. Reliability and Statistics in GeotechnicalEngineering, John Wiley and Sons.

[2] Elkateb, T., 2003, "Quantification of Soil Heterogeneity", Ph.D. Thesis,Edmonton, Alberta, Canada.


17/17

[3] El-Ramly, H., 2001. Probabilistic Analyses of Landslide Hazards and Risks:Bridging Theory and Practice. Ph.D. Thesis, the Faculty of Graduate Studies and

Research, Edmonton, Alberta, Canada.

[4] Goh, Anthony T. C. and Kulhawy, F. H., 2003. Neural Network Approach ToModel The Limit State Surface For Reliability Analysis. Can. J. Geotech., Rev.

Can. Geotech. 40(6): 1235-1244

[5] Hamza Associates, 1997. Greater Cairo Metro Line 2 Phase 2, Phase 3 TunnelMonitoring, Lot 42 (El-Dokki/ El-Gezira). Monitoring Report.

[6] Jaksa, M. B., 1995, "The Influence of Spatial Variability on the GeotechnicalDesign Properties of A Stiff, Overconsolidated Clay", Ph.D. Thesis, Faculty of

Engineering, University of Adelaide.

[7] Koza, J. R., 1992, Programming: On the Programming of Computers by Meansof Natural Selection, Cambridge MA: MIT Press, ISBN 0-262-11170-5.

[8] Laso, E., Sagrario, M., Lera, G., and Alarcon, E., 1995. A Level II ReliabilityApproach to Tunnel Support Design. Appl. Math. Modeling 1995, Vol. 19.

[9] Noureldin, S.M. 2003. Neuronet Prediction of Settlement Associated with SoftGround Tunneling. M.Sc. Thesis, Ain Shams University, Faculty of Engineering,

Cairo, Egypt.

[10] Noureldin, S.M. 2006. Reliability-Based Tunneling Design: An Overview.International Symposium on Utilization of Underground Space in Urban Areas,

November 2006, Sharm El Sheikh Egypt.

[11] Shahin, M.A., Jaksa, M.B. & Maier, H.R., 2003. Neurofuzzy Networks AppliedTo Settlement Of Shallow Foundations on Granular Soils. Applications ofStatistics and Probability in Civil Engineering, Der Kiureghian, Madanat &

Pestana (EDS), Millpress, Rotterdam, ISBN 90-5966- 004-8.

[12] Shaw, D., Miles, J., and Gray, A., 2004, Genetic Programming Within CivilEngineering, Organization of the Adaptive Computing in Design and

Manufacture 2004 Conference, Engineers House, Clifton, Bristol, UK.

Non-Deterministic Tunneling Analysis Using a.I. Based Techniques Genetic Programming vs ANNs

Documents

Transcript of Non-Deterministic Tunneling Analysis Using a.I. Based Techniques Genetic Programming vs ANNs