基于支持向量机回归的结构系统可靠性及灵敏度分析方法

提出了一种基于支持向量机回归近似极限状态方程的系统可靠性分析方法,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参数灵敏度.与线性展开和响应面法近似极限状态方程相比,文中方法由于采用了基于结构风险最小化原理的支持向量机回归,因而在拟合非线性极限状态方程上表现优越,计算精度高.与直接蒙特卡洛模拟相比,由于该方法采用较少的样本即可近似出概率等价的显式极限状态方程,因而计算效率大幅提高.工程实例表明:所提方法可以处理串联、并联和混合系统的可靠性与可靠性灵敏度分析,具有工程运用价值.

STRUCTURAL SYSTEM RELIABILITY AND SENSITIVITY ANALYSIS BASED ON SUPPORT VECTOR MACHINE REGRESSION

Based on the support vector machine regression approximating the limit state function,a procedure is presented to analyze the reliability and corresponding sensitivity of the structural system.In the presented procedure,the complicated or implicit limit state functions of the system failure modes are firstly fitted by the support vector machine regression,then according to the system logicality,the methods for the system with explicit limit state function can be employed to estimate the reliability and corresponding sensitivity.Compared with the linear expansion polynomial and the response surface method,the support vector machine regression can match the limit state function better due to its underlying structural risk minimization inference rule,the support vector machine regression is more accurate therefore.Since the presented procedure constructs the surrogate of the implicit or the complicated limit state function by a small quantity of samples,its efficiency is much higher than that of Monte Carlo simulation.The presented procedure can treat the reliability and corresponding sensitivity analysis of the series,parallel and mixed systems,and it has wide applicability in engineering problem,which have been demonstrated by two engineering examples.