有限实验数据下工程结构概率建模及随机响应分析

Probabilistic modeling and stochastic response analysis of engineering structures with experimental data

为了研究实验数据下工程结构输入参数的概率建模以及依据所建模型的响应分析的问题,本文提出了一种实验数据下工程结构概率建模及随机响应求解的方法。依据Karhunen-Loeve展开和任意多项式混沌(aPC)展开理论,提出了一种基于核密度估计的新型随机模型;发展了结构随机响应的求解技术,并提出了用于随机响应aPC系数估计的D-optimal加权插值方法,实现了结构响应的高精度求解。研究表明:本文的研究为实验数据下工程结构的合理随机建模和高效响应分析提供了一个有效的框架,本文方法有效。

In our quest to understand the probabilistic modeling of engineering structure inputs from experimental data and the associated response analysis of the constructed model,we have developed a new method that involves the construction of a nonGaussian random model using experimental data,followed by a random response analysis.First,we introduced an innovative random model that utilizes both Karhunen-Loeve expansion and arbitrary polyno-mial chaos(aPC)expansion.We then expanded on this by developing a technique for solving structural random responses based on this stochastic model.Ultimately,we developed the D-optimal weighted interpolation method for estimating the aPC coefficient of the random response,resulting in a highly precise solution for the structural re-sponse.The research indicates that our proposed method offers a practical framework for creating accurate random models and conducting efficient response analyses of engineering systems.These systems,which rely on real-life experimental data,can greatly benefit from our approach.