非平稳随机激励下高维非线性系统可靠度分析的概率密度全局演化方法  

GE⁃GDEE for reliability analysis of high⁃dimensional nonlinear systems enforced by non⁃stationary stochastic excitations

作　　者：律梦泽 陈建兵[1,2] LÜMeng-ze;CHEN Jian-bing(State Key Laboratory of Disaster Reduction in Civil Engineering,Tongji University,Shanghai 200092,China;College of Civil Engineering,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学土木工程防灾减灾全国重点实验室,上海200092 [2]同济大学土木工程学院,上海200092

出　　处：《振动工程学报》2024年第6期903-914,共12页Journal of Vibration Engineering

基　　金：国家杰出青年科学基金资助项目(51725804)。

摘　　要：实际工程结构遭受的灾害性动力作用(如强风、地震等)往往具有显著的随机性和非平稳性。对复杂随机激励下高维非线性系统的动力可靠度进行精细化分析,对于实际工程结构的抗灾设计和优化具有重要意义。基于一般连续随机过程的降维概率密度演化方程,给出了一类非平稳随机激励下的高维非线性系统动力可靠度分析方法。具体地,若仅针对系统某一感兴趣物理量在给定安全域下的首次超越问题,则可以构造该物理量在安全域内的吸收边界过程,并建立其瞬时概率密度函数满足的二维偏微分方程,即降维概率密度演化方程。方程中的本征漂移系数是驱动概率密度演化的全局性物理驱动力,可以通过对原系统有限次代表性确定性动力分析获取的数据进行数值构造。采用数值方法求解降维概率密度演化方程,即可获得系统的动力可靠度解答。文中通过两个算例验证了该方法的有效性,并讨论了需要进一步研究的问题。Dynamic actions such as strong winds and earthquakes often have significant randomness and non-stationarity,which can have disastrous effects on practical engineering structures.Therefore,accurately evaluating the dynamic reliability of high-dimen⁃sional nonlinear systems under non-stationary stochastic excitations is crucial for the disaster-resistant design and optimization of these structures.This paper presents a numerical method for solving the high-dimensional nonlinear dynamic reliability under nonstationary noises,based on the globally-evolving-based generalized density evolution equation(GE-GDEE)for generic continuous processes.Specifically,if we are concerned with the first-passage reliability of a quantity of interest within a specified safe domain,an absorbing boundary process(ABP)of the quantity of interest can be constructed.This leads to a two-dimensional partial differ⁃ential equation for its transient probability density function(PDF),known as the GE-GDEE for ABPs.The effective drift coeffi⁃cient in the GE-GDEE,which serves as the global physical driving force for evolution of the PDF,can be identified using data from representative deterministic dynamic analyses.The solution for dynamic reliability can be obtained by solving the GE-GDEE.This paper includes two numerical examples to verify the efficiency and accuracy of the proposed method and discusses areas that require further study.

关 键 词：降维概率密度演化方程 高维非线性随机动力系统 非平稳随机激励 动力可靠度分析 物理驱动 

分 类 号：O324[理学—一般力学与力学基础] TU318[理学—力学]