基于椭球凸模型的可靠性灵敏度研究
发布时间：2018-12-12 10:00
【摘要】：可靠性灵敏度可以反映不确定变量分布参数和可靠性的相互联系,为结构可靠性分析和优化设计提供指导。本文研究了基于椭球凸集合模型的可靠性灵敏度分析问题,主要包括非概率可靠性指标及其近似求解方法、可靠性灵敏度分析的近似解析法和蒙特卡洛法等,主要研究内容如下:1.考虑非概率凸模型和概率模型之间的相似性,研究了椭球模型的非概率可靠性指标及其两种一阶可靠性(FORM)分析方法。研究表明:当极限状态函数为线性时,证明了两种非概率可靠性指标之间的一致性。当极限状态函数为非线性时,揭示了中心点法中存在的不一致性问题,而且,该现象可以通过设计点法剔除,并且在此基础上讨论了两种一阶可靠性方法。2.研究了非概率可靠性灵敏度的近似解析法。把可靠性灵敏度定义为相应的可靠性指标对区间中点、半径和不确定变量相关系数的偏导数,推导了线性极限状态函数的非概率可靠性灵敏度的解析公式,提出了两种非线性极限状态函数的非概率可靠性灵敏度的近似解析法:中心点法和设计点法。3.将可靠性灵敏度定义为非概率失效度对区间中点、半径和不确定变量相关系数的偏导数,利用复合函数求导公式,推导了非概率可靠性灵敏度的计算公式,并提出了可靠性灵敏度分析的蒙特卡洛法,对上述近似解析法的求解精度进行检验。
[Abstract]:The reliability sensitivity can reflect the relationship between the distribution parameters of uncertain variables and the reliability, and provide guidance for structural reliability analysis and optimization design. In this paper, the problem of reliability sensitivity analysis based on ellipsoid convex set model is studied, including non-probabilistic reliability index and its approximate solution, approximate analytical method of reliability sensitivity analysis and Monte Carlo method, etc. The main contents are as follows: 1. Considering the similarity between the non-probabilistic convex model and the probabilistic model, the non-probabilistic reliability index of the ellipsoidal model and its two first-order reliability (FORM) analysis methods are studied. It is shown that when the limit state function is linear, the consistency between the two non-probabilistic reliability indices is proved. When the limit state function is nonlinear, the inconsistency problem in the center point method is revealed. Moreover, the phenomenon can be eliminated by the design point method. On this basis, two first order reliability methods are discussed. 2. The approximate analytical method of non-probabilistic reliability sensitivity is studied. The reliability sensitivity is defined as the partial derivative of the corresponding reliability index to the correlation coefficient of the interval midpoint, radius and uncertain variables, and the analytical formula of the non-probabilistic reliability sensitivity of the linear limit state function is derived. Two approximate analytical methods of non-probabilistic reliability sensitivity of nonlinear limit state functions are presented: the center point method and the design point method. The reliability sensitivity is defined as the partial derivative of the non-probabilistic failure degree to the correlation coefficient of the interval midpoint, radius and uncertain variables. The formula for calculating the non-probabilistic reliability sensitivity is derived by using the compound function derivation formula. The Monte Carlo method for reliability sensitivity analysis is proposed, and the accuracy of the above approximate analytical method is tested.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TB114.3
本文编号：2374370
[Abstract]:The reliability sensitivity can reflect the relationship between the distribution parameters of uncertain variables and the reliability, and provide guidance for structural reliability analysis and optimization design. In this paper, the problem of reliability sensitivity analysis based on ellipsoid convex set model is studied, including non-probabilistic reliability index and its approximate solution, approximate analytical method of reliability sensitivity analysis and Monte Carlo method, etc. The main contents are as follows: 1. Considering the similarity between the non-probabilistic convex model and the probabilistic model, the non-probabilistic reliability index of the ellipsoidal model and its two first-order reliability (FORM) analysis methods are studied. It is shown that when the limit state function is linear, the consistency between the two non-probabilistic reliability indices is proved. When the limit state function is nonlinear, the inconsistency problem in the center point method is revealed. Moreover, the phenomenon can be eliminated by the design point method. On this basis, two first order reliability methods are discussed. 2. The approximate analytical method of non-probabilistic reliability sensitivity is studied. The reliability sensitivity is defined as the partial derivative of the corresponding reliability index to the correlation coefficient of the interval midpoint, radius and uncertain variables, and the analytical formula of the non-probabilistic reliability sensitivity of the linear limit state function is derived. Two approximate analytical methods of non-probabilistic reliability sensitivity of nonlinear limit state functions are presented: the center point method and the design point method. The reliability sensitivity is defined as the partial derivative of the non-probabilistic failure degree to the correlation coefficient of the interval midpoint, radius and uncertain variables. The formula for calculating the non-probabilistic reliability sensitivity is derived by using the compound function derivation formula. The Monte Carlo method for reliability sensitivity analysis is proposed, and the accuracy of the above approximate analytical method is tested.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TB114.3
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