基于支持向量机的非概率可靠性分析

Non-probabilistic reliability analysis based on support vector machines

针对具有隐式极限状态函数的不确定性结构的非概率可靠性分析,提出一种基于支持向量机回归的不确定性结构非概率可靠性分析方法,并给出了该方法的分析流程.抽取数据样本,优化支持向量机回归参数,使用训练后的支持向量机替代隐式极限状态函数.利用非概率集合理论中的区间分析法,引入尺寸比例因子,构造合适的不确定性结构非概率可靠性指标迭代算法.最后用一个数值算例和一个工程算例来验证该方法.数值算例表明支持向量机回归模型预测精度高,用支持向量机回归模型替代结构隐式极限状态函数进行非概率可靠性分析是可行的.工程算例证明该方法具有可行性、正确性和高精度的优点.因此,该方法具有较好的工程实用价值,并对其它具有隐式极限状态函数的不确定性结构的非概率可靠性分析具有一定的参考价值.

For non-probabilistic reliability analysis of uncertainty structure with implicit limit state function,a method for non-probabilistic reliability analysis of uncertainty structure was presented on the basis of support vector regression,and analysis process of the method was given.Taking data samples and optimizing support vector regression parameters,the support vector machine after training was used to replace implicit limit state function.Using interval analysis method of non-probabilistic set theory and introducing size scale factor,suitable non-probabilistic reliability index iterative algorithm of uncertainty structure was presented.Finally,a numerical example and an engineering example were used to test the presented method.The numerical example shows that support vector regression model forecast precision is high,and using the model instead of implicit limit state function to analyze non-probabilistic reliability is feasible.The engineering example shows that the presented method has three virtues of feasibility,correctness and high accuracy.Therefore,the presented method is of good practical engineering value,and it also has a certain useful value for other uncertainty structure non-probabilistic reliability analysis with implicit limit state function.