臺灣博碩士論文加值系統

基於模擬退火之全域最佳化方法及其於結構工程之應用
研 究 生：莫兆松
指導教授：江達雲
本研究提出一個基於模擬退火而發展出的全域最佳化方法，稱為區間縮減模擬退火法。它是在全域最佳值出現之機率較高的區間進行群體搜尋，並且不斷地刪除全域最佳值出現之機率較低的區間，以加速搜尋，直到滿足收斂條件為止。本文引入累積機率分佈函數、穩態能量等觀念，使得模擬退火法中初始溫度之選擇及平衡狀態的判定變得容易而有效。藉由一組標準測試函數的檢驗，本法可應用在一般函數最佳化問題上，求得有效的全域最佳解。
本文並將所發展的區間縮減模擬退火法應用於結構設計最佳化與結構損傷偵測兩個結構工程相關的領域。關於結構設計最佳化的問題，結合區間縮減模擬退火法與外部懲罰函數法可有效地求解全域最佳值。藉由一個十桿桁架設計最佳化的例子，顯現出本法的可行性。在結構損傷偵測部份，本文提出一個結合模型修正法與區間縮減模擬退火法優點的多階段損傷偵測法，可降低逆向分析中參數可識別性的問題。藉由數值模擬多種不同的損傷情況，本文分析結果顯示在適度的量測雜訊影響下，本法仍可有效地解決結構損傷偵測的問題。

A Global Optimization Method Based on Simulated Annealing
and Its Applications in Structural Engineering
Student: Jau-Sung Moh
Advisor: Dar-Yun Chiang
ABSTRACT
A robust global optimization algorithm based on simulated annealing is proposed. The algorithm is called the Region-Reduction Simulated Annealing (RRSA) method because it locates the optimum by successively eliminating the regions with low probability of containing the global optimum. By introducing the ideas of probability cumulative distribution function and stable energy, the selection of initial temperature and equilibrium criterion in the process of simulated annealing becomes easy and effective. Numerical studies using a set of standard test functions show that the approach is effective and robust in solving function optimization problems.
For applications of proposed RRSA method, we consider optimum structural design and structural damage detection problems. By combining the exterior penalty function method, RRSA algorithm may solve the optimum structural design problem successfully. A design example of ten-bar truss is studied to show that the approach is effective and robust. A multi-stage structural damage detection method is also proposed, which combines the characteristics of the model updating method and the advantage of RRSA method. Numerical studies involving various damage conditions show that the proposed approach is effective in solving structural damage detection problems under moderately noisy conditions.
第二章 改良型模擬退火法
第三章 區間縮減模擬退火法於函數最佳化之驗證
第四章 區間縮減模擬退火法於結構最佳設計之應用
第五章 區間縮減模擬退火法於結構損傷偵測之應用
第六章 結論

封面
ABSTRACT
CONTENTS
LIST OF TABLES
LIST OF FIGURES
NOMENCLATURE
CHAPTER 1 INTRODUCTION
1.1 Motivation
1.2 Literature Review
1.2.1 Global Optimization Methods Based on Simulated Annealing
1.2.2 Optimum Structural Design
1.2.3 Damge Detection by Model Modification
1.3 Thesis Outline
2. MODIFIED SIMULATED ANNEALING METHOD
2.1 Introduction
2.2 The Metropolis Algorithm
2.3 The Simulated Annealng Algorithm
2.4 Cncept and Procedures of RRSA
2.4.1 Equilibrium criterion
2.4.2 Convergent condition
2.4.3 Stopping criterion
2.4.4 Neighborhood structure
2.4.5 Reliability
2.4.6 Exchanging of information and retaining the best
2.4.7 Multiple optima
2.4.8 RRSA procedure
2.5 Conclusions
3 NUMERICAL EXPERIMENTS OF RRSA FOR FUNCTION OPTIMIZATION
3.1 Parametric Study
3.1.1 Temperature decreasing ratio Tr
3.1.2 Thenumber of candidates in a population Np
3.1.3 Frequency of information exchange Nf
3.2 Effect of Stable Energy
3.3 Numerical Experiments for function Optimization
3.4 Comparison with Other Optimization Methods
3.5 Conclusions
4. APPLICATINS OF RRSA IN OPTIMUM STRUCTURAL DESIGN
4.1 Optimum structural Design
4.2 RRSA in Optimm Structural Design
4.3 Ten-bar Truss Example
4.4 Conclusions
5 APPLICATIONS OF RRSA IN STRUCTURAL DAMAGE DETETION
5.1 Introduction
5.2 Structural Damage Detection
5.3 Multi-stage Damage Detection method
5.4 Numerical Simulation
5.5 Damage Detection under Noisy Conditions
5.6 Conclusions
6 SUMMARY AND CONCLUSION
REFFERENCES
PUBLICATION LIST
VITA

REFERENCES
Aarts, E. and Korst, J., Simulated Annealing and Boltzmann Machines, J. Wiley & Sons, 1989.
Aluffi-Pentini, Parisi, F. V. and Zirilli, F., “Global Optimization and Stochastic Differential Equations,” Journal of Optimization Theory & Applications, 47, (1), 1985, pp.1-17.
Atiqullah, M. M., and Rao, S. S., “Parallel Processing in Optimal Structural Design Using Simulated Annealing,” AIAA Journal, Vol. 33, No. 12, 1995, pp.2386-2392.
Balling, R. J., “Optimal Steel Frame Design by Simulated Annealing,” Journal Structure Engineering, 117, 1991, pp.1780-1795.
Baruch, M., and Bar Itzhack, I. Y., “Optimum Weighted Orthogonalization of Measured Modes,” AIAA Journal, Vol. 16, No. 4, 1978, pp.346-351.
Baruch, H. and Ratan, S., “Damage Detection in Flexible Structures,” Journal of Sound and Vibration, Vol. 166, No. 1, 1993, pp.21-30.
Belegundu, A. D., and Arora, J. S., “A Computational Study of Transformation Methods for Optimal Design,” AIAA Journal, Vol. 22, No. 4, 1984, pp.535-542.
Berman, A., and Flannelly, W. G., “Theory of Incomplete Models of Dynamic Structures,” AIAA Journal, Vol. 9, No. 8, 1971, pp.1481-1487.
Binder, K., Monte Carlo Method in Statistical Physics, Springer-Verlag, New York, 1978.
Bohachevsky, I. O., Johnson, M. E. and Stein, M. L., “Generalized Simulated Annealing for Function Optimization,” Technometrics, Vol. 28, No. 3, 1986, pp.209-218,
Boseniuk, T. and Ebeling, W., “Optimization of NP-Complete Problems by Boltzmann-Darwin Strategies Including Life Cycles,” Europhysics Letters, Vol. 6, No. 2, 1988, pp.107-112.
Brooks, K. H., “A Discussion of Random Methods of Seeking Optima,” Operations Research, Vol. 6, 1958, pp.244-251.
Cerny, V., “Thermodynamical Approach to the Traveling Salesman Problem: An efficient simulation algorithm,” Journal of Optimization Theory and Application, 45, 1985, pp.41-51.
Chen, G-S., Bruno, R. J., and Salama, M., “Optimal Placement of Active/Passive Members in Truss Structures Using Simulated Annealing,“ AIAA Journal, 29, 1991, pp.1327-1334.
Chiang, D. Y. and Huang, S. T., “Modal Parameter Identification Using Simulated Evolution,” AIAA Journal, Vol. 35, No. 7, 1997, pp.1204-1208.
Chiang, D. Y., and Lai, W. Y., “A Two-stepped Structural Damage Detection Method,” Trans. of the Aeronautical and Astronautical Society of the R. O. C., Vol. 30, No. 1, 1998, pp.19-26.
Corana, A., M. Marchesi, C. Martini, and S. Ridella, “Minimizing Multimodal Functions of Continuous Variables with the Simulated Annealing Algorithm,” ACM Trans. On Mathimatical Software, 13, 1987, pp.262-280.
Davis, L. and Ritter, F., “Schedule Optimization with Probabilistic Search,” in Proc. 3 rd IEEE Conf. Art. Intell., 1987, pp.231-236.
Fabio, S. “Stochastic Techniques for Global Optimization: A Survey of Recent Advances,” Journal of Global Optimization, Vol. 1, 1991, pp.207-228.
Fogel, L. J., Owens, A. J., and Walsh, M. J., Artificial Intelligence Through Simulated Evolution, Wiley Publishing, New York, 1966.
Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Reading, MA, 1989.
Hajek, B., “Cooling Schedules for Optimal Annealing,” Mathematics of Operations Research, 13, 1988, pp.311-329.
Hajela, P., “Genetic Search-An Approach to the Nonconvex Optimization problem,” AIAA Journal, Vol. 28, No. 7, 1990, pp.1205-1210.
Hajela, P., and Soeiro, F., “Recent Developments in Damage Detection Based on System Identification Methods,” Structural Optimization, Vol. 2, 1990, pp.1-10.
Hajela, P., and Yoo, J., “Constraint Handling in Genetic Search Using Expression Strategies,” AIAA Journal, Vol. 34, No. 12, 1996, pp.2414-2420.
Jaynes, E. T., “Information Theory and Statistical Mechanics,” Physical Reviews, Vol. 106, 1957, pp.620-630.
Jenkins, W. M., “Towards Structural Optimization via the Genetic Algorithm,” Computer & Structures, Vol. 40, No. 5, 1991, pp.1321-1327.
Junjiro, O., and Yoji, H., “Actuator Placement Optimization by Genetic and Improved Simulated Annealing Algorithms,” AIAA Journal, Vol. 31, No. 6, 1992, pp.1167-1169.
Kabe, A M., “Stiffness Matrix Adjustment Using Mode Data,” AIAA Journal, Vol. 23, No. 9, 1985, pp.1431-1436.
Kammer, D. C., “Optimum Approximation for Residual Stiffness in Linear System Identification,” AIAA Journal, Vol. 26. No. 1, 1988, pp.104-112.
Kirkpatrick, S., Gelatt, C. D, and Vecchi, M. P., “Optimization by Simulated Annealing,” Science, Vol. 220, 1983, pp.671-680.
Kirsch, U., Optimum Structural Design, McGraw-Hill, 1981, Chap. 6.
Le Riche, R., and Haftka, R. T., “Optimization of Laminate Stacking Sequence for Buckling Load Maximization by Genetic Algorithm,” AIAA Journal, Vol. 31, No. 5, 1993, pp.951-956.
Lee, J. B. and Lee, B. C., “A global Optimization Algorithm Based on the New Filled Function Method and the Genetic Algorithm,” Engineering Optimization. 27, 1996, pp.1-20.
Levy, A. V. and Gomez, S., “The Tunneling Method Applied to Global Optimization,” Numerical Optimization 1984 ,edited by P. T. Boggs, R.H. Byrd, and R. B. Schnabel, Society for Industrial and Applied Mathematics, Philadelphia, PA,1985, pp213-244.
Levy, A. V. and Montalvo, A., “The Tunneling Algorithm for the Global Minimization of Function,” SIAM. J. Sci. Statist. Comput., 6, (1), 1985, pp.15-29.
Lin, C. S., “Location of Modeling Errors Using Modal Test Data,” AIAA Journal, Vol. 28, No. 9, 1990, pp.1650-1654.
Lin, C. Y., and Hajela, P., “Design Optimization with Advanced Genetic Search Strategies,” Advances in Engineering Software, Vol. 21, No. 3, 1994, pp.179-189.
Lin, C. Y. and J. F. Jiang, “Nonconvex and Discrete Optimal Design Optimization Using Multistage Simulated Annealing,” Structural Optimization, Vol. 14, 1997, pp. 121-128.
Lucidi, S. and Piccioni, M., “Random Tunneling by Means of Acceptance-Rejection Sampling for Global Optimization,” Journal of Optimization Theory & Applications, Vol. 62, No. 2, 1989, pp.255-277.
Metropolis, N., A. Rosenbluth., A. Teller, and E. Teller., “Equation of State Calculations by Fast Computing Machines,” Journal of Chemical Physics, 21, 1953, pp.1087-1092.
Mitra, D., Romeo, F., and A. L. Sangiovanni-Vincentelli, “Convergence and Finite-time Behavior of Simulated Annealing,” Advances in Applied Probability, 18, 1986, pp.747-771.
Nagendra, S., Jestin, D., Gurdal, Z., Haftka, R. T., and Watson, L. T., “Improved Genetic Algorithm for the Design of Stiffened Composite Panels,” Computer and Structures, Vol. 58, No. 3, 1996, pp.543-555.
Riche, R. L., and Haftka, R. T., “Optimization of Laminate Stacking Sequence for Buckling Load Maximization by Genetic Algorithm,” AIAA Journal, Vol. 31, No. 5, 1993, pp.951-956.
Ricles, J. M. and Kosmatka, J. B., “Damage Detection in Elastic Structures Using Vibratory Residual Forces and A Weighted Sensitivity,” AIAA J., Vol. 30, 1992, pp.2310-2316.
Rinnoy, Kan, A. H. G. and Timmer, G. T., “Stochastic Global Optimization Methods. Part I: Clustering Methods, and Part II: Multi Level Methods,” Mathematical Programming, 39, 1987, pp.27-78.
Rodden, W. P., “A Method for Deriving Structural Influence Coefficients from Ground Vibration Tests,” AIAA Journal, Vol. 5, No. 5, 1967, pp.991-1000
Romeo, F. and and Sangiovanni-Vincentelli, A., “A Theoretical Framework for Simulated Annealing,” Algorithmica, 6, 1991, pp.346-366,
Rose, J., Klebsch, W. and Wolf, J., “Temperature Measurement and Equilibrium Dynamics of Simulated Annealing Placements,” IEEE Trans. On Computer Aided Design, 9, 1990, pp.253-259.
Rozvany, G. I. N., Structural Design via Optimal Criteria: The Prager Approach to Structural Optimization, 1st ed., Kluwer, Dordrecht, The Netherlands, 1989, pp.1-20.
Schoen F., “Stochastic Techniques for Global Optimization: A Survey of Recent Advances,” Journal of Global Optimization, 1, 1991, pp.207-228.
Snyman, J. A., and stander, N., “New Successive Approximation Method for Optimum Structural Design,” AIAA Journal, Vol. 32, No. 6, 1994, pp.1310-1315.
Solis, F. J. and Wets, R. J.-B., “Minimization by Random Search Techniques,” Mathematics of Operations Research, Vol. 6, 1981, pp.19-30.
Sorkin, G. B., ”Efficient Simulated Annealing on Fractal Energy Landscapes,” Algorithmica, 6, 1991, pp.302-345
Srichander, R., “Aircraft Controller Synthesis by Solving a Non-convex Optimization Problem,” AIAA Journal of Guidance, Control & Dynamics, 1995, 18, No. 1.
Srichander, R., “Efficient Schedules for Simulated Annealing,” Engineering Optimization, Vol. 24, 1995, pp.161-176.
Strenski, P. N. and Kirkpatrick, S., “Analysis of Finite Length Annealing Schedules,” Algorithmica, 6, 1991, pp.346-366.
Toda, M., Kubo, R., and Saito, N., Statistical Physics, Springer-Verlag, Berlin, 1983.
Vanderbilt, D., and S. G. Louie, “A Monte-Carlo Simulated Annealing Approach to Optimization over Continuous Variables,” Journal of Computational Physics, 36, 1984, pp.259-271.
Vanderplaats, G. N., and Moses, F., “Structural Optimization by Methods of Feasible Directions,” Computers and Structures, Vol. 3, No. 4, 1973, pp.739-755.
Yip, P. P. C., and Pao, Y. H., “Combinatorial Optimization with Use of Guided Evolutionary Simulated Annealing,” IEEE Transactions on Neural Networks, Vol. 6, No. 2, 1995, pp.290-295.
Zabinsky, Z. B., Smith, R. L., McDonald, J. F., Romeijn, H. E., and Kaufman, D. E., “Improving Hit-and-Run for Global Optimization,” Journal of Global Optimization, Vol. 3, No. 2, 1993, pp.171-192.
Zabinsky, Z. B., “Global Optimization for Composite Structural Design,” Proceedings of the AIAA/ASME/ASCE/AHS/ASC 35th Structures, Structural Dynamics,, and Materials Conference, Vol 3, AIAA, Wanshington, DC, 1994, pp1406-1412.
Zimmerman, D. C., and Kaouk, M., “Structural Damage Detection Using a Minimum Rank Update Theory,” Journal of Vibration and Acoustics, Vol. 116, 1994, pp.222-230.