基于支持向量机和蒙特卡洛的结构可靠性 分析方法及应用

Structural reliability analysis method based on support vector machines and Monte Carlo and its application

关键词:  支持向量机  蒙特卡洛方法  极限状态函数重构  结构可靠性分析  自升式平台

Key words:  support vector machines (SVM)  Monte Carlo method  reconstruction of limit state function  structural reliability analysis  Jack-up platform

摘要:

将支持向量机作为极限状态函数重构的工具引人结构可靠性分析问题中，并结合蒙特卡洛方法,分别给出了 模式识别型和涵数回归型两种支持向量机(SVM)模型应用于结构可靠性分析的计算流程图。结合数值算例,对两 种支持向量机模型在结构可靠性问题的应用方面进行了对比,并研究了训练样本数目、核函数类型、模型参数的取 值以及随机变量数目等因素对可靠性分析结果的影响。最后以某自升式平台为工程对象,进行了考虑多个随机变 量的结构可靠性评估。结果表明:在应用支持向量机方法进行极限状态函数重构时，无论是模式识别型SVM模型还 是函数回归型SVM模型均可取得良好的效果,前者对模型参数的敏感程度大于后者;支持向量机理论作为极限状态 函数重构工具与蒙特卡洛方法相结合，可有效解决大型复杂工程结构可靠性分析精度和效率问题。

Abstract:

Support vector machines( SVM) was introduced to structural reliability analysis as a tool for reconstruction of limit state function. Combined with Monte Carlo method, two computation flow diagrams applied to structural reliability analysis were given based on support vector classifier and support vector regress. TTie two models were numerically compared from the application of structural reliability. The effects of several factors including count of sampling, type of kernel function，value of model parameter and number of random variable on the reliability analysis were analyzed. Structural reliability considering multiple random variables was evaluated for a Jack-up platform by the presented approach. The results show that both support vector classifier and support vector regress can be effectively used to the reconstruction of limit state function, and the former is more sensible to the model parameter than the latter. The approach is effective on improving computational efficiency and accuracy of structural reliability analysis for large and complicated engineering structures.