结构可靠性若干专题研究

【作者】 马超；

【导师】 吕震宙；

【作者基本信息】 西北工业大学 ， 飞行器设计， 2007， 硕士

【摘要】 结构可靠性的基本理论和方法逐渐趋于完善，但可靠性相关计算方法在实际工程中遇到了许多问题，如非正态随机变量处理不准确，相关可靠性分析方法计算量偏大，计算精度不高等，本文针对若干问题，结合近年来最新的数学理论方法，如模拟退火全局优化算法，统计学习理论，马尔可夫链模拟，凸集模型等，发展了一系列计算效率高，计算精度好的适于工程运用的可靠性分析方法。具体研究内容如下： (1) 提出了基于等价正态三参数变换和模拟退火全局优化的失效概率计算方法，阐明了所提方法的理论基础和实施过程。由于采用了基于模拟退火的全局优化使得等价正态的三个参数更加准确，从而降低了计算失效概率的误差；与Monte-Carlo法相比，所提算法计算效率高且误差小，适于工程应用。 (2) 针对结构隐式极限状态函数的可靠性分析，提出了一种支持向量机分类迭代算法。该算法以支持向量机分类来替代隐式极限状态方程，通过构造合理的迭代格式，使得分类支持向量机在对失效概率贡献大的区域收敛于真实的极限状态方程，从而提高了可靠性分析的精度。 (3) 提出了两种快速高效的可靠性参数灵敏度分析方法——半解析法和快速数值模拟法。两种方法均基于重要抽样马尔可夫链模拟，半解析法只要在重要抽样法计算失效概率的结果中增加非常小的工作量，即可以快速得到可靠性参数灵敏度；快速数值模拟法未引入线性假设，可以较好地考虑极限状态方程非线性对可靠性灵敏度的影响。 (4) 提出了一种基于支持向量机回归近似极限状态方程的多馍式结构系统可靠性和可靠性灵敏度分析方法，所提方法首先由支持向量机拟合系统各失效模式的极限状态方程，将复杂或隐式极限状态方程近似等价为显式极限状态方程，然后根据系统各个失效模式的逻辑结构，由高精度的显式极限状态方程方法计算系统的失效概率和可靠性参数灵敏度。由于支持向量机回归具有良好的小样本学习能力和推广泛化性能，因而其在拟合非线性极限状态方程上表现优越，计算精更多还原

【Abstract】 Although the structure reliability theory and analysis methods are gradually well established, the application of reliability methods encounters many problems in engineering, such as imprecision of transforming non-normal randon variables into normal randon variables, unacceptable computional cost and low accuracy, etc. For the problems, the thesis presented a series of reliability methods combining with new mathematic theory, such as simulated annealing optimization, statistical learning theory, Markov chain simulation, convex model, etc. These presented methods listed as follows possess high precision and efficiency in the application.(1) On the basis of the equivalent normal distribution with three parameters and the simulated annealing optimization, an algorithm to calculate the failure probability is proposed for the structure with non-normal variables. The relative formulae are derived, and the implementation of the presented algorithm is demonstrated. The error of the failure probability calculation by this method is decreased due to the precise three parameters sought by the simulated annealing, which has global optimization property. Comparing with Monte-Carlo simulation, the computational effort of the presented algorithm is smaller, therefore it is more suitable for engineering application than Monte-Carlo simulation.(2) For reliability analysis of structure with implicit limit state function, an iterative algorithm is presented on the basis of support vector classification machine. In the presented method, the support vector classification machine is employed to construct surrogate of the implicit limit state function. By use of the rational iteration, the constructed support vector classification machine can converge to the actual limit state function in the important region, which contributes to the failure probability significantly, thus the precision of the reliability analysis is improved.(3) Two reliability parameter sensitivity analysis methods are presented, which are semi-analytical method and fast numerical simulation method. The two methods are both based on importance sampling Markov Chain simulation. The remarkable advantage of the semi-analytical method is its high efficiency. By increasing very limited computational effort in the presented semi-analytical method, the reliability更多还原