【摘要】：可靠性靈敏度可以反映不確定變量分布參數(shù)和可靠性的相互聯(lián)系,為結構可靠性分析和優(yōu)化設計提供指導。本文研究了基于橢球凸集合模型的可靠性靈敏度分析問題,主要包括非概率可靠性指標及其近似求解方法、可靠性靈敏度分析的近似解析法和蒙特卡洛法等,主要研究內(nèi)容如下:1.考慮非概率凸模型和概率模型之間的相似性,研究了橢球模型的非概率可靠性指標及其兩種一階可靠性(FORM)分析方法。研究表明:當極限狀態(tài)函數(shù)為線性時,證明了兩種非概率可靠性指標之間的一致性。當極限狀態(tài)函數(shù)為非線性時,揭示了中心點法中存在的不一致性問題,而且,該現(xiàn)象可以通過設計點法剔除,并且在此基礎上討論了兩種一階可靠性方法。2.研究了非概率可靠性靈敏度的近似解析法。把可靠性靈敏度定義為相應的可靠性指標對區(qū)間中點、半徑和不確定變量相關系數(shù)的偏導數(shù),推導了線性極限狀態(tài)函數(shù)的非概率可靠性靈敏度的解析公式,提出了兩種非線性極限狀態(tài)函數(shù)的非概率可靠性靈敏度的近似解析法:中心點法和設計點法。3.將可靠性靈敏度定義為非概率失效度對區(qū)間中點、半徑和不確定變量相關系數(shù)的偏導數(shù),利用復合函數(shù)求導公式,推導了非概率可靠性靈敏度的計算公式,并提出了可靠性靈敏度分析的蒙特卡洛法,對上述近似解析法的求解精度進行檢驗。
[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.
【學位授予單位】：西安科技大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：TB114.3

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