Pseudo Analytical Method for Nonlinear Structural Reliability

非线性结构可靠性的伪解析方法

基本信息

批准号：
10650470
负责人：
MASARU Hoshiya
金额：
$ 2.18万
依托单位：
Musashi Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

In random vibration, probability of an event that system performance function becomes negative during the time duration is a means to discuss the system safety. This probability is well known as first excursion probability. Presently, how to develop the evaluation method for nonlinear systems has been a major concern among many researchers.The most powerful tool available for the analysis of the response of nonlinear systems to random loading is the Markovian vector approach. In this case the joint probability density of the state vector components is governed by Fokker-Plank equation. Unfortunately, only very few closed-form solutions are known. Even for the SDOF case only some stationary solutions are available. This means that for more general cases approximated methods such as equivalent linearization have to be utilized.In this context, this research also proposes a method to evaluate the probability for nonlinear SDOF systems under a class of stochastic excitations. The method is a hybrid analytical procedure with the help of numerically simulated response data, namely Pseudo Analytical. This method is a class of linearization approaches that linearize approximately a nonlinear state vector equation to a discrete Gaussian and Markovian state vector equation, and the optimal state vector and covariances at times k and k+1 are estimated by the Kalman Filter algorithm with a set of numerically obtained response data. In this way, the probability of performance may be evaluated. Finally, a numerical example of a nonlinear structural system is demonstrated in order to examine the efficiency of the method.

在随机振动中，系统性能函数在一段时间内变为负值的事件概率是讨论系统安全性的一种手段。该概率被称为首次偏移概率。目前，如何开发非线性系统的评估方法已成为许多研究者关注的焦点。分析非线性系统对随机载荷响应的最有力的工具是马尔可夫矢量方法。在这种情况下，状态向量分量的联合概率密度由 Fokker-Plank 方程控制。不幸的是，已知的封闭式解决方案非常少。即使对于单自由度情况，也只有一些固定解决方案可用。这意味着对于更一般的情况，必须使用等效线性化等近似方法。在此背景下，本研究还提出了一种评估一类随机激励下非线性单自由度系统概率的方法。该方法是借助数值模拟响应数据的混合分析程序，即伪分析。该方法是一类线性化方法，将非线性状态向量方程近似线性化为离散高斯和马尔可夫状态向量方程，并通过卡尔曼滤波器算法估计k和k+1时刻的最优状态向量和协方差，其中一组数值获得的响应数据。通过这种方式，可以评估性能的概率。最后，演示了非线性结构系统的数值例子，以检验该方法的效率。