基于脉冲暂态混沌神经网络的可靠度分析方法
收稿日期: 2013-04-27
修回日期: 2013-09-06
网络出版日期: 2013-09-19
基金资助
国家“973”计划（2013CB733000）
Pulse Transiently Chaotic Neural Network for the Analysis Method of Reliability
Received date: 2013-04-27
Revised date: 2013-09-06
Online published: 2013-09-19
Supported by
National Basic Research Program of China (2013CB733000)
工程中计算结构可靠度系数β可以看做一个优化问题。考虑极限状态函数的非线性程度很高且存在非凸失效域时，传统的求解非线性优化方法，如序列二次规划（SQP）法、罚函数法和梯度投影法等都有其使用范围和局限性，无法解决局部极小解问题。如何避免局部极小解问题并且兼顾计算精度和效率目前仍很难处理。提出一种新的可靠度计算方法：将求解转化为带有约束条件的非线性规划问题，利用罚函数法转化成无约束条件的非线性规划问题，引入脉冲暂态混沌神经网络（PTCNN）模型快速有效地进行全局寻优，从而解决具有局部极小解的约束非线性规划问题。最后采用不同类型的非线性极限状态函数算例进行算法验证，验证该方法在处理高维、高非线性、不可微、非凸失效域问题时具有可行性、高效性。
关键词： 脉冲暂态混沌神经网络; 非线性规划; 高非线性; 非凸失效域; 可靠度系数
王丕东 , 张建国 , 马志毅 , 孙京 , 高鹏 . 基于脉冲暂态混沌神经网络的可靠度分析方法[J]. 航空学报, 2014 , 35(2) : 469 -477 . DOI: 10.7527/S1000-6893.2013.0382
The structural reliability index β can be solved as an optimization problem in engineering design. However, when the limited state function is high nonlinearity with concave failure domain, the classic methods of solving nonlinear programming such as sequential quadratic programming (SQP) method, penalty function method, and gradient projection method etc, have disadvantages in solving the local minimum solution. It is still difficult to deal with how to solve local minimum solution taking into account the calculation accuracy and efficiency. This paper presents a new method of reliability that the problem for solving reliability indexes is transformed into the nonlinear programming problem with constraint condition. Penalty function method is used to convert the problem into unconstrained nonlinear programming one. Pulse transiently chaotic neural network (PTCNN) is introduced to optimize globally so as to solve constrained nonlinear programming problems with local minimum solution quickly and efficiently. Finally the examples of different types of non-linear limit state functions are presented to prove that this method is feasible and efficient to address the problem with high dimension, highly nonlinear, non-differentiable and non-convex failure domain.
[1] Hasofer A M, Lind N C. Exact and invariant second moment code format[J]. Journal of the Engineering Mechanics Division, 1974, 100(1): 111-121.
[2] Low B K, Tang W H. Reliability analysis of reinforced embankments on soft ground[J]. Canadian Geotechnical Journal, 1997, 34(5): 672-685.
[3] Nadim F. Probabilistic methods for geohazard problems: state-of-the-art[M]. Essen: Verlag Gluckauf, 2002: 333-350.
[4] Ang H S, Tang W H. Probability concepts in engineering planning and design[M]. New York: John Wiley & Sons, 1984: 20-21.
[5] Madsen H O, Krenk S, Lind N C. Methods of structural safety[M]. Englewood Cliffs: Prentice Hall, 1986: 37-38.
[6] Moses F. System reliability developments in structural engineering[J]. Structural Safety, 1982, 1(1): 3-13.
[7] Zhao G F, Li Y G, Wang H D. Forth moment method for structural reliability analysis based on maximum entropy theory[C]//The Sixth Workshop on Concrete Model Code for Asia, 1996.
[8] Zhao Y Q, Ono T. Moment methods for structural reliability[J]. Structural Safety, 2001, 23(1): 47-75.
[9] Lee S H, Kwak B M. Response surface augmented moment method for efficient reliability analysis[J]. Structural safety, 2006, 28(1): 261-272.
[10] Liu C L, Lu Z Z, Response surface combinaion improved by high order term for structural reliability analysis[J]. Acta Aeronautica et Astronautica Sinica, 2013, 27(4):594-599. (in Chinese) 刘成立, 吕震宙. 结构可靠性分析中考虑高次项修正的组合响应面法[J]. 航空学报, 2013, 27(4): 594-599.
[11] Gong Q, Zhang J G, Tan C L, et al. Neural networks combined with importance sampling techniques for reliability evaluation of explosive initiating device[J]. Chinese Journal of Aeronautics, 2012, 25(2): 208-215.
[12] Liu Z, Zhang J G, Wang C C, et al. Hybrid structure reliability method combining optimized Kriging model and importance sampling[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(6): 1347-1355. (in Chinese) 刘瞻, 张建国, 王灿灿, 等. 基于优化Kriging模型和重要度抽样法的结构可靠度混合算法[J]. 航空学报, 2013, 34(6): 1347-1355.
[13] Huang J S, Griffiths D V. Observations on FORM in a simple geomechanics example[J]. Structural Safety, 2001, 33(1): 115-119.
[14] Papadrakakis M, Lagaros N D. Reliability-based structural optimization using neural networks and Monte Carlo simulation[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191(32): 3491-3507.
[15] Tolson B A, Maier H R, Simpson A R, et al. Genetic algorithms for reliability-based optimization of water distribution systems[J]. Journal of Water Resources Planning and Management, 2004, 130(1): 63-72.
[16] Long B, An W G, Jiang X W. Structural reliability anal ysis based on genetic simulated annealing algorithm[J]. Journal of Haerbin Engineering University, 2005, 26(6): 753-757. (in Chinese) 龙兵, 安伟光, 姜兴渭. 基于遗传模拟退火算法的结构可靠性分析[J]. 哈尔滨工程大学学报, 2005, 26(6): 753-757.
[17] Burton S A, Hajela P. A variable-complexity approach to second-order reliability-based optimization[J]. Structural and Multidisciplinary Optimization, 2003, 25(4): 237-250.
[18] Du X P, Chen W. Sequential optimization and reliability assessment method for efficient probabilistic design[J]. Journal of Mechanical Design, 2004, 126(2): 225-233.
[19] Youn B D, Choi K K. A new response surface methodology for reliability-based design optimization[J]. Computers Structural, 2004, 82(2-3): 241-256.
[20] Lv Z Z, Song S F, Li H S, et al. Analysis of structure reliability and reliability sensitivity[M]. Beijing: Science Press, 2009: 21-22.(in Chinese) 吕震宙, 宋述芳, 李洪双, 等, 结构机构可靠性及可靠性灵敏度分析[M]. 北京: 科学出版社, 2009: 21-22.
[21] Li H, Cao H D. Pulse transiently chaotic neural network for layout optimization[J]. Chinese Journal of Computational Mechanics, 2005, 22(5): 623-628. (in Chinese) 李昊, 曹宏铎. 基于PTCNN的结构布局优化问题研究[J]. 计算力学学报, 2005, 22(5): 623-628.
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