Large scale structural identification by multi civilization genetic algorithm approach

Acknowledgments I would like to thank all those who helped me through this research, without whom I could not have accomplished it Special thanks go to the following people: • Prof Koh Chan Ghee and Assoc Prof Liaw Chih Young, for their guidance and support throughout this study Their extensive knowledge, serious research attitude, constructive suggestions and encouragement were extremely valuable to me • Assoc Prof Wang Quan (currently at University of Central Florida), and Prof Zhang Linmin (at Nanjing University of Aeronautics & Astronautics), for their valuable suggestions and guidance on system identification and control theory • My fellow research students in the department of Civil Engineering of NUS, and in particular, Hong Bo, Chen Yuefeng, Zhao Shuliang, Zhang jing, Cui Zhe, Shen Lijun, Wang Shenying, etc, for their encouragement and helpful assistance when problems were encountered • My friend Xu Zhijie for his righteous character and trust; and Yi Fan, Qiu Wenjie, Esther Chang, for their faithful prayer for my thesis • My family, my wife, parents and sister for their eternal love and supports Finally, the financial support from National University of Singapore is highly appreciated I CONTENT ACKNOWLEDGMENTS .I CONTENT II SUMMARY IV LIST OF TABLES VI LIST OF FIGURES VII CHAPTER INTRODUCTION 1.1 BACKGROUND 1.2 LITERATURE REVIEW 10 1.2.1 Conventional Methods 11 1.2.2 Unconventional Methods 13 1.3 OBJECTIVE AND SCOPE OF STUDY 18 1.4 ORGANIZATION OF THE THESIS 19 CHAPTER GA, GA-LS AND PGA 22 2.1 INTRODUCTION 22 2.2 GENETIC ALGORITHM (GA) 22 2.3 GA-LS METHOD (GA-LS) 26 2.4 PARALLEL GENETIC ALGORITHM (PGA) 27 2.5 NUMERICAL STUDY 30 2.6 CONCLUDING REMARKS 33 CHAPTER DISTRIBUTED COMPUTING FOR SINGLE-POPULATION AND MULTI-POPULATION PGA 47 3.1 INTRODUCTION 47 3.2 CHOICE OF COMPUTING PLATFORMS 47 3.3 SINGLE-POPULATION PGA 48 3.3.1 Server-Client Communication Model 49 II 3.3.2 Program Structure for Single-Population GA 52 3.3.3 Interfaces to link different languages 56 3.3.4 Data Security Mechanism 58 3.3.5 Resetting Mechanism 60 3.3.6 Load Balance Mechanism 61 3.4 MULTI-POPULATION PGA 63 3.4.1 Migration Server 63 3.4.2 Migration Client 65 3.5 NUMERICAL EXPERIMENTS 65 3.5.1 Computation and Communication Times 66 3.5.2 Relationship between Speed-up Rate and Computer Number 67 3.5.3 Single-Population PGA 69 3.5.4 Multi-Population PGA 71 3.6 CONCLUDING REMARKS 72 CHAPTER MULTI-CIVILIZATION GENETIC ALGORITHM 80 4.1 INTRODUCTION 80 4.2 INNOVATIVE IDEAS IN MCGA 81 4.3 STRATEGIES OF MCGA 82 4.3.1 Population Strategy 83 4.3.2 Topology Strategy 85 4.3.3 Strategy for Crossover and Mutation 86 4.3.4 Strategy for Local Search 88 4.3.5 Multiple Criteria Strategy 90 4.3.6 Migration Strategy 92 4.4 NUMERICAL EXPERIMENTS 96 4.5 CONCLUDING REMARKS 99 CHAPTER CONCLUSIONS AND RECOMMENDATIONS 112 5.1 CONCLUSIONS 112 5.2 RECOMMENDATION FOR FUTURE STUDY 114 REFERENCES 116 III Summary The approach of Genetic algorithm (GA) has been proven to be a relatively robust search and optimization method over the years It has recently been applied to parameter identification of structural systems, with encouraging results, in particular when it is combined with suitable local search operator However, for realistic problems, which involve large number of unknown parameters and degrees of freedom, the total trial number increases substantially and the forward analysis becomes very time-consuming Thus the total search time increases dramatically, and the expensive computational cost makes the GA approach infeasible Meanwhile, the identified results deteriorate even when the trial number is greatly increased, since the search is more likely to fall in local optimum when there are a large number of unknown parameters To tackle this problem, the sequential algorithm should be changed into parallel model correspondingly In this study, a distributed computing method based on JAVA language is proposed to meet the above requirements Satisfactory speed-up rate is achieved because of the high computation-communication ratio There is virtually no limit on the number of computers that could run simultaneously via this method The proposed distributed computing method in this study reduces the simulation time from half a month to half a day, by using available networked computers during off-peak hours In addition, inspired from the observation of the virtues of existing multi-culture societies in the world, a multi-civilization genetic algorithm (MCGA) is presented in this thesis MCGA executes a set of special population strategies, selection strategies, IV migration strategies and local search strategies etc Numerical simulation results in this study show that this innovative approach significantly improves the identified results of common parallel genetic algorithm (PGA) Keywords: System Identification (SI); Structural System Identification; Structural Health Monitoring; Genetic Algorithms (GA); Local Search (LS); Parallel Genetic Algorithm (PGA); Distributed Computing V List of Tables Table 1-1 Comparison of Evolutionary Algorithms 20 Table 2-1 Control Parameters List 34 Table 2-2 Exact Parameters of the 10-DOF LMS 34 Table 2-3 Identification Results of Case without I/O noise 35 Table 2-4 Identification Results of Case & 36 Table 2-5 Case Identification Result by GA - LS 37 Table 2-6 Sequential GA & GA-LS 38 Table 3-1 Speed-up rate by distributed computing method 73 Table 4-1 LS Control Parameters in MCGA 100 Table 4-2 Case 1: GA-LS Control Parameters in Common PGA 101 Table 4-3 Case 2, and GA-LS Parameter Used in MCGA 101 VI List of figures Figure 1-1 Procedure of System Identification 21 Figure 2-1 The Flow Chart of Sequent GA 39 Figure 2-2 Illustrate of Crossover Operator 40 Figure 2-3 Flow Chart of Local Search Operator 41 Figure 2-4 Classification of Parallel Genetic Algorithm 42 Figure 2-5 Results from Chen, Y.F (2001) M.Eng Thesis (Search Range: +30%) 43 Figure 2-6 Identification Result by GA+LS for 50-DOF LMS without noise (Search Range: ±50%) 44 Figure 2-7 Identification Result by GA+LS for 50 DOF LMS With 5% Noise (Search Range: ±50%) 45 Figure 2-8 Identification Result by GA+LS for 50 DOF LMS With 10% Noise (Search Range: ±50%) 46 Figure 3-1 Flow Chart of Server-Client Model 74 Figure 3-2 Program Structure for Single-Population GA 75 Figure 3-3 Comparison of Active Server Method and Passive Server Method 76 Figure 3-4 Program Structure for Multi-Population GA 77 Figure 3-5 Proportion of Computer Times for Evaluation, Communication & Other GA Operations 78 Figure 3-6 Relationship between speed-up rate and No of participating worker machines 79 VII Figure 4-1 (a) Classification of Topology and (b) MCGA Topology 102 Figure 4-2 Jump-Out-Effect of Local Search 103 Figure 4-3 Illustration of Sensitivity of Evaluation Error to Individual Parameter 104 Figure 4-4 Identification Results Based on Common PGA 105 Figure 4-5 Identification Results Based on MCGA for 102 Unknowns without Noise (200 generations) 106 Figure 4-6 Identification Results Based on MCGA for 102 Unknowns without Noise (300 generations) 107 Figure 4-7 Identification Results Based on MCGA for 102 Unknowns without Noise (400 generations) 108 Figure 4-8 Identification Results Based on MCGA for 102 Unknowns with 5% Noise (200 generations) 109 Figure 4-9 Identification Results Based on MCGA for 102 Unknowns with 10% Noise (200 generations) 110 Figure 4-10 Improvement of Evolution Error of Best Individual due to migration (migration rate 20% & interval 20 generations) 111 VIII Chapter Introduction 1.1 Background In the field of civil engineering, the nature of analysis can be broadly categorized as direct analysis and inverse analysis (Bekey, 1970) In direct analysis, system parameters (such as stiffness, mass and damping ratio) are known and the responses (output) of the system under a certain excitation (input) can be calculated by various methods In inverse analysis, the response is known and the unknown system parameters can be determined through polynomial times of direct analysis (forward analysis) In general, the process of determining parameters (e.g stiffness, mass) of a structural system based on given input and output (I/O) information is called structural identification (Figure 1-1) Structural identification (SI) can be applied to determine the actual values of parameters, which can be used instead of relying on assumed or estimated values in structural analysis Consequently, a better prediction of structural response under environmental excitations can be obtained Structural identification is also the core process of Structural Health Monitoring, Damage Detection and Safety Assessment But for real world problems, three factors in particular make structural identification difficult: • Generally speaking, the problem contains many unknown parameters, which makes the solution space large (with high dimensions) As a result, the computational time required for SI is normally too long for any practical purpose • Individual parameters collectively affect the response and there is no obvious rule that could be used to guide the search • It is difficult to accurately measure response Input and output (I/O) data are always contaminated by noise because of electronic interference, resolution of sensors and ambient vibration Correspondingly, a good optimization strategy generally should perform well in three aspects Firstly, the computational strategy should minimize the execution time without losing the ability in optimization Secondly, the objective function to determine the fitness between estimated responses and actual responses should actually reflect the influence of parameters on the response Thirdly, the identification strategy should not be too sensitive to I/O noise 1.2 Literature Review Generally speaking, structure identification methods can be classified into two categories i.e conventional methods and unconventional methods Least Square Method, Kalman Filter Method and Maximum Likelihood Method are representatives of conventional methods They perform point-to-point search strategy Hence they often prematurely converge to the local optima rather than the global optima These methods are not suitable for large-scale structural system identification problems due to the ill-conditioned nature of inverse analysis Moreover, they normally involve gradient or higher-order derivatives of the objective function Some of them even need good initial guess of unknown parameter in order for the methods to work These drawbacks of conventional methods make them very difficult, if not impossible, to 10 Figure 4-6 Identification Results Based on MCGA for 102 Unknowns without Noise (300 generations) 107 Figure 4-7 Identification Results Based on MCGA for 102 Unknowns without Noise (400 generations) 108 Figure 4-8 Identification Results Based on MCGA for 102 Unknowns with 5% Noise (200 generations) 109 Figure 4-9 Identification Results Based on MCGA for 102 Unknowns with 10% Noise (200 generations) 110 Figure 4-10 Improvement of Evolution Error of Best Individual due to migration (migration rate 20% & interval 20 generations) 111 Chapter Conclusions and Recommendations 5.1 Conclusions Parameter identification of large-scale structural systems is a very challenging task that requires efficient and accurate search algorithm Classical system identification methods are mostly suitable for simple systems with few unknown parameters due to the ill-conditioned nature of inverse analysis Some non-classical system identification methods offer an attractive alternative that avoids such inverse analysis Among them, the genetic algorithm (GA) approach that has shown its potential in previous research works is adopted in this study Nevertheless, the GA approach has its limitations It carries out global search and is relatively not efficient in local fine-tuning Hence a local search method is integrated to improve the fine-tuning capability The GA-LS method successfully solves the system with 52 unknown parameters But for real-world problems that may have more than 100 unknown parameters, this sequential approach on single computer is not good enough Firstly, thousands of loops of evaluation or local search operations, which involves very time-consuming calculation, make computational time unaffordable Secondly it tends to converge in local optimum value with the significant increase of probable combinations of unknown parameters In order to reduce the computational time, the intrinsic parallelism of GA has been made use of As evaluation and local search operations, are independent, the simplest method is to parallelize them This level of parallelism does not change the 112 GA in nature and the identification results are the same as those of sequential GA By using server-client environment in JAVA, the proposed distributed computing method successfully expedites the computational task for large-scale structural identification through the use of PC network The method has following advantages: No additional hardware is required through using existing PCs available on the network “Worker” computers can be hooked on/off during the running time The speed-up effect is generally above 50% based on numerical experiments conducted in this study For the problems considered, the distributed computing strategy provides a solution in about 10-12 hours to the time-consuming large-scale structural identification problem, which would have taken weeks using a personal computer This means that structural identification task can be done without much interruption to daytime application, taking advantage of idle times of networked computers during off-office hours Furthermore, in order to improve the accuracy of solutions, a higher level of parallelism is implemented Several populations simultaneously evolve and exchange genetic information according to preset migration rate and interval But unfortunately numerical experiments show that multi-population PGA is still limited in its capability to obtain accurate solution for large problems studied Consequently, an innovative MCGA method is formulated, inspired by observation of development of human societies Six computational strategies have been designed to achieve the precise balance between convergence and diversity, 113 thereby obtaining more accurate solutions The method divides the initial population into a mainstream civilization and several fringe civilizations (two in this study) Essentially, the diversity of the mainstream civilization benefits from taking in immigrants selectively from fringe civilizations The method allows flexibility in implementation since different parameters and strategies can be adopted in various civilizations Involving the use of a total of 52 PCs for distributed computing, the numerical study shows that the parameter identification is feasible for as many as 102 unknown parameters and good identification results are obtained 5.2 Recommendation for Future Study By speed-up of the computation and design of MCGA, a breakthrough has taken place in identifying large structural systems not attempted before But there still exist some issues that can be further studied in order to maximize the potential of the proposed MCGA Firstly for the distributed computing method, the server does not record any information of the worker machines No active management happens at the end of servers Moreover, for installation and maintenance, client-end program has to be downloaded and installed manually in advance In case there is any change of the source code, re-installation of new source has to be done on every client Hence, the proposed program should be upgraded to the JAVA Remote Invocation (RMI), which allows the server machine to automatically install the updated client-end program at remote worker machines Secondly an Object-Oriented GA with a new principle deserves future investigation Under the object-oriented principle, the “subroutine”, “program block” 114 and “operators”, which appear commonly at structural programming idea, are all designed and used as a set of “ministries” with different functions At the same time, those population and sub-population that originally appear as an outlook of a whole generation now appear as a group of independent “human being” that have their own willingness It is suggested that the algorithm that has been controlled and driven by “selection pressure” be allowed to evolve along two routes: • “Society” is managed under various authority “ministries”, which guide the direction and step of the evolution • Each “person”, as an individual with “self-conscious ability”, exploits to the best of the existing various “ministry” to fulfill the goal of survival and reproduction GA imitates the natural world and realizes the procedure via computer simulation, under the “the fittest of survival” rule MCGA imitates the 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of the second International Conference on Genetic Algorithms, (pp 177-183) Hillsdale, NJ: Lawrence Erlbaum Associates Tanese, R (1989a) “Distributed Genetic Algorithms” In Schaffer, J.D (Ed.), Proceedings of the third International Conference on Genetic Algorithms (pp 434-439) San Mateo, CA: Morgan Kaufmann Tanese, R (1989b) “Distributed Genetic Algorithms for function optimization” Doctoral Dissertation, University of Michigan, Ann Arbor 120 Zhao S L (2002) “Hybrid algorithms for structural identification and sensitivity study” M.Eng Thesis, Department of Civil Engineering, National University of Singapore 121 [...]...identify structural systems with large number of unknowns Therefore, unconventional methods, e.g Neural Network, Simulated Annealing and Evolutionary Algorithms, are more feasible alternatives for large- scale system identification problems 1.2.1 Conventional Methods Least Square Method The least square method identifies the parameters of a given structural identification problem by minimizing... experiments By analyzing those results, the limitation of genetic algorithm is revealed Local search operation is hence added to GA in order to strengthen the fine-tuning and convergence capabilities This chapter provides some numerical experiment cases to demonstrate the robustness and effect of GA and hybrid GA for structural identification problem 2.2 Genetic Algorithm (GA) Genetic Algorithm is... optimization algorithm that combines the genetic algorithm and a recently proposed global optimization algorithm called the nested partitions method to maximize the market share of the producer Koh et al (2003) proposed a multi- variate (MV) LS method (GA-LS method) to identify a fairly large system with 52 unknown parameters By means of many control rules and peak-depot, Zhao S L (2002) proposed a LS algorithm. .. thesis aims to formulate an effective genetic algorithm approach to identify large- scale systems with many unknown parameters, taking advantage of the intrinsic parallelism of GA 18 Firstly, the performance of sequential GA (including GA with local search) and single-population GA are examined The purpose is to reveal their respective potential for large- scale system identification But the expensive computational... network to fit a class of practical problems Moreover, if the structural systems are complex, a large amount of training data is required by neural networks in order to obtain good identification results This drawback makes neural networks difficult to apply in structural identification, where the large amount of training data required by neural networks are very difficult to obtain owing to the difficulty... parallelizes the multi- population method at higher level with single population PGA at low level Manderick and Spiessens (1989) proposed this algorithm as an extension to the conventional fine-grained algorithms that they examined Stepping Stone Model Genetic Algorithm While island model migration method allows individuals migrate to arbitrary sub-populations, as another migration genetic algorithm, stepping... simple and million times of trial-&-error is feasible But for structural identification problems, because of the complex process of evaluation, simulated annealing becomes infeasible due to the exponential increase of time required by the problem size Evolutionary Algorithms Evolutionary Algorithms are a group of search methods inspired by natural evolution Its philosophy is based on the evolution... are construction scheduling, structural optimization and structural identification Friswell (1998) applied GA to the problem of damage detection using vibration data to identify the position of one or more damage sites in a structure, and to estimate the extent of the damage at these sites Leu et al (1999) employed GA to solve construction-scheduling problem by using a multi- criteria optimal model... (GA-LS) The random nature of genetic algorithm results in poor searching efficiency or even worse: the search leave correct region It is because that common genetic algorithm may still evolve too slowly to find out the right value though the searching has reached the correct region To avoid this problem and enhance the searching efficiency, a local search strategy as proposed by Koh et al (2003) is adopted... much larger populations than common population size This type of algorithm better simulates the local selection and mating that occur in natural populations (Manderick and Spiessens, 1989) 28 Coarse-grained Genetic Algorithm Coarse-grained GA divides the initial population into several sub-populations At selected time, intervals single individuals may move from one sub-population to another The GA multi- population ... Distributed Genetic Algorithm Multiple Population Genetic Algorithm Single Population Genetic Algorithm Master-Slave Distributed Genetic Algorithm Synchronous Master-Slave GA Fine-Grained Genetic Algorithm. .. innovative approach significantly improves the identified results of common parallel genetic algorithm (PGA) Keywords: System Identification (SI); Structural System Identification; Structural. .. demonstrate the robustness and effect of GA and hybrid GA for structural identification problem 2.2 Genetic Algorithm (GA) Genetic Algorithm is a probabilistic search technique Different from