基于梯度搜索法的非线性结构可靠性分析方法

doi:10.3969/j.issn.1000-1093.2021.01.020

摘要/Abstract

摘要： 很多工程结构具有非线性特征强且功能函数为隐式的特点，以往方法难以精确、高效地分析其可靠性，为此提出一种基于梯度搜索法的强非线性结构可靠性灵敏度分析方法。根据工程结构的隐式功能函数，利用差分法计算初始抽样点附近的梯度信息；基于验算点梯度搜索法，获得与抽样点对应的距极限状态曲面距离最小的极限状态点，过该点依据Taylor展开法将极限状态曲面线性展开；在线性化的极限状态面上继续确定抽样点，并采用高次梯度搜索法继续寻找极限状态曲面上的对应点；经若干次迭代搜索，获得一组极限状态曲面附近的训练样本，在此基础上采用多项式函数、响应面函数等拟合极限状态方程，计算可靠度及可靠性灵敏度。研究结果表明，与重要抽样法、二次响应面法和经典验算点法比较，新方法具有计算精度高、抽样次数少的优点，适用于强非线性隐式结构的可靠性分析问题。

关键词: 非线性结构, 梯度搜索法, 验算点, Taylor展开法, 可靠性灵敏度分析

Abstract: Many engineering structures have strong nonlinear characteristics and their functions are implicit. It is difficult to analyze the reliability of engineering structures accurately and efficiently. A sensitivity analysis method of strong nonlinear structural reliability based on gradient search method is proposed. Based on the implicit function of engineering structure, the gradient information near the initial sampling point is calculated by using the difference method. Then the gradient search method of checking point is used to obtain the limit state point at the minimum distance from the limit state surface corresponding to the sampling point, through which the limit state surface is linearly expanded by Taylor expansion method. A set of training samples near the limit state surface are obtained through several iterative searches. On this basis, the polynomial function and response surface function are used to fit the limit state equation to calculate the reliability and reliability sensitivity. The numerical and engineering examples show that the proposed method has the advantages of high accuracy and less sampling times compared with the previous methods, and it is suitable for the reliability analysis of strong nonlinear implicit structures.

Key words: nonlinearstructure, gradientsearchmethod, mostprobablepoint, Taylorexpansionmethod, reliabilitysensitivityanalysis

中图分类号:

TB114.33

陈鹏霏，和鹏，于泰龙，刘巧伶. 基于梯度搜索法的非线性结构可靠性分析方法[J]. 兵工学报, 2021, 42(1): 175-184.

CHEN Pengfei, HE Peng, YU Tailong, LIU Qiaoling. An Analysis Method for Nonlinear Structural Reliability Based on Gradient Search Method[J]. Acta Armamentarii, 2021, 42(1): 175-184.

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