基于降维积分的结构系统可靠性分析研究

RESEARCH ON THE METHOD FOR RELIABILITY ANALYSIS OF STRUCTURAL SYSTEMS BASED ON THE DIMENSIONAL-REDUCTION INTEGRATION

复杂结构系统一般具有多个失效模式.传统系统可靠性分析模型是在假设各失效模式相互独立的条件下建立的.而在工程实际问题中,由于结构系统的组成单元之间紧密联系,系统的失效模式大多是相互耦合的.简单地在失效模式相互独立的假设条件下进行系统可靠性分析与评价常常会导致过大的误差,甚至得出错误的结论.提出一种相关失效模式结构系统可靠性分析方法.利用降维法和Gauss--Hermite数值积分技术计算随机参数结构系统极限状态函数的统计矩,采用极限状态函数的前四阶累积量拟合其累积量生成函数,通过鞍点逼近方法拟合结构系统极限状态函数的概率密度函数和累积分布函数,进而获取结构系统的可靠度(或失效概率).数值算例表明该方法具有较高的计算精度和效率,通用性强.

There are usually several failure models in a complex structural system. The conventional model for system analysis is built under the condition that all failure models are independent with each other. However, in engineering practice, failure models in a system are mostly dependent due to the fact that the elements of a structural system are closely interrelated. System reliability analysis and evaluation simply conducted under the condition that all failure models are independent with each other often result in excessive errors or even wrong conclusion. This paper proposes a method for reliability analysis of engineering structural systems with dependent failure models. The dimensional reduction method and Gauss-Herrnite quadrature are applied to compute the statistic moments of the limit state functions of structural systems with random parameters. The first four cumulants of the limit state functions are used to approximate cumulant generating functions. The probability density function and cumulative distribution function of the limit state functions of the structural systems are fitted through saddlepoint approximation. And then the reliability （or failure probability） of the structural system is obtained. Finally, the practicality and efficiency of the proposed method are demonstrated by a numerical example.