首次超越动力可靠度分析中广义密度全局演化方程的本征漂移系数特性研究  

Property of intrinsic drift coefficients in globally-evolving-based generalized density evolution equation for the first-passage reliability assessment

作　　者：孙婷婷 律梦泽 陈建兵 Tingting Sun;Mengze Lyu;Jianbing Chen(College of Civil Engineering,Tongji University,Shanghai,200092,China;State Key Laboratory of Disaster Reduction in Civil Engineering,Tongji University,Shanghai,200092,China)

机构地区：[1]College of Civil Engineering,Tongji University,Shanghai,200092,China [2]State Key Laboratory of Disaster Reduction in Civil Engineering,Tongji University,Shanghai,200092,China

出　　处：《Acta Mechanica Sinica》2023年第4期109-131,共23页力学学报（英文版）

基　　金：supported by the National Distinguished Youth Fund of the National Natural Science Foundation of China(NSFC)(Grant No.51725804);the NSFC-Guangdong Province Joint Project(Grant No.U1711264);the Fund for State Key Laboratories from Ministry of Science and Technology of China(Grant No.SLDRCE19-B-23);the Shanghai Post-Doctoral Excellence Program(Grant No.2022558).

摘　　要：广义密度全局演化方程(GE-GDEE)是求解随机激励下高维系统中任意感兴趣物理量瞬态概率密度函数的有力工具.对于给定的失效准则,通过引入所感兴趣物理量的吸收边界过程(ABP)并求解其GE-GDEE,可以高效计算首次超越动力可靠度.对ABP的GEGDEE,构造本征漂移系数尤为关键.本文研究了ABP的GE-GDEE中本征漂移系数的特性,特别对线性系统给出其ABP的精确本征漂移系数,对一般系统给出了其形式解析表达.典型分析结果表明,ABP的本征漂移系数在边界附近相对于原物理量的本征漂移系数有明显偏差且趋于零值,而在远离边界的安全域内部则与原物理量的本征漂移系数十分接近.这种偏差在物理上表现为表观阻尼在边界附近的局部折减.因此,采用原物理量的本征漂移系数代替其ABP的本征漂移系数求解首次超越动力可靠度,将导致估计的失效概率结果偏不安全.值得注意的是,数值分析结果表明其数量级与真实解相同,特别是低失效概率问题也是如此,因而可以作为近似解答.本文研究为高维非线性系统首次超越可靠度分析中的GE-GDEE中漂移系数构造提供了指导.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE)provides a promising tool to obtain the instantaneous probability density of any quantity of interest of stochastically excited high-dimensional systems.By introducing an absorbing boundary process(ABP)determined by failure criteria,a corresponding GE-GDEE can be constructed and solved to assess the first-passage reliability.The construction of the intrinsic drift coefficient of the GE-GDEE is the crucial step.In the present paper,the property of the intrinsic drift coefficients of the GE-GDEE for ABPs is studied.In particular,the intrinsic drift coefficients of some linear systems are exactly constructed via analytical solutions.Compared to the GE-GDEE of the original quantity of interest,the intrinsic drift coefficients of GE-GDEE of the corresponding ABP in both linear and nonlinear systems change considerably in the vicinity of the boundary,curving towards zero,but vary very little far away from the boundary.This physically means that the apparent damping is reduced,thus leading to an unconservative estimate of failure probability if the intrinsic drift coefficients of the original quantity of interest rather than those of the ABP are adopted.Interestingly,the failure probability by solving the GE-GDEE of the original quantity of interest is in the same order of magnitude as the true value and thus can be an acceptable approximate result,particularly for low failure probability estimate problems.The findings in the paper provide insightful guidance on constructing the intrinsic drift coefficients of the GE-GDEE of ABPs for the first-passage reliability evaluation of high-dimensional nonlinear systems.

关 键 词：动力可靠度 首次超越 演化方程 典型分析 失效概率 安全域 真实解 线性系统 

分 类 号：O175[理学—数学]