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工程力学  2014 

基于等概率近似变换的向量型层递响应面法分析结构可靠度

, PP. 185-191

Keywords: 结构可靠度,层递响应面法,非高斯分布,正交变换,等概率近似变换

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Abstract:

基于正交变换和等概率近似变换,研究建立了随机变量为非高斯互相关的工程结构可靠度分析的向量型层递响应面法。首先利用正交变换将非高斯互相关随机变量变换为互不相关的非高斯标准随机变量,建立结构总体刚度矩阵和荷载列阵,据此定义预处理器并形成预处理随机Krylov子空间,进而利用该空间的层递基向量将结构总体节点位移向量近似展开,建立关于互不相关非高斯标准随机变量的层递响应面;然后根据等概率近似变换,将独立标准正态空间的样本点转换为层递响应面在非高斯空间中的概率配点;最后通过回归分析确定层递响应面待定系数,并利用层递响应面建立极限状态方程求解结构可靠度。分析表明:该文提出的等概率近似变换方法不仅成功地将层递响应面法拓展到非高斯互相关随机变量下的结构可靠度分析,而且方法简便、适用范围广、计算精度和效率较高,具有良好的全域性。

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