结构时变可靠度及敏感性分析方法

发布时间：2018-03-22 23:06

本文选题：时变可靠度　切入点：模糊性　出处：《湖南大学》2015年硕士论文　论文类型：学位论文

【摘要】：结构的可靠度与机械产品质量密切相关,近年来越来越受到重视。传统的可靠度分析技术,通常在不考虑强度退化和动态载荷等时变因素的静态模型下处理问题,因而得到的可靠度是一个不变的数值。然而结构所处环境变化、材料性能退化、载荷时变性等引起的时变特性广泛存在。因此,可靠度分析方法应充分考虑这些时变因素,以更好地满足工程实际要求。本文系统研究了机械结构时变可靠度分析方法,主要研究内容如下：1、针对工程结构失效准则不确定性的可靠度问题,构造了一种考虑失效准则模糊性的时变可靠度分析方法。该方法首先将模糊失效准则下的时变功能函数随机过程进行离散,然后应用模糊集基本理论,引入新的随机变量,得到不同时间段的等效功能函数,最终将模糊失效准则下的时变可靠度问题转化为常规的可靠度问题,通过一次二阶矩(FORM)方法求解获得时变可靠度和失效概率。2、针对复杂工程结构中的时变可靠度计算问题,构造了一种新型的跨越率计算方法(sPHI2)。该方法首先将时变功能函数随机过程及随机变量转换至独立标准正态空间,并对转化后的各极限状态函数在最大可能(MPP)点处线性展开,然后应用PHI2方法的基本理论,引入新的参数和随机变量,最终将极限状态方程为复杂非线性功能函数的时变可靠度模型转化为静态的可靠度分析模型,运用FORM方法进行高效求解。3、基于过程离散的时变可靠性模型(TRPD),提出了一种用于复杂工程结构的时变可靠度敏感性分析方法。该方法首先通过时间离散,将随机过程转换为随机变量,并将时变可靠性问题转化为常规的时不变体系可靠性问题。然后采用微分链式法则,将失效概率对任意随机变量和随机过程参数的敏感性转化为可靠度指标对分布参数的一阶微分。之后运用Nataf全概率变换和正交变换,最终获得失效概率对分布参数的一阶导数。该方法大大简化了时变可靠度敏感性分析的求解过程,具有较高的计算效率。
[Abstract]:The reliability of structures is closely related to the quality of mechanical products, and has attracted more and more attention in recent years. Traditional reliability analysis techniques usually deal with problems in static models that do not take into account the time-varying factors such as strength degradation and dynamic loads. Therefore, the reliability obtained is an invariant numerical value. However, the time-varying characteristics caused by the environmental change of the structure, the degradation of material properties and the time-varying of load are widely existed. Therefore, these time-varying factors should be fully taken into account in the reliability analysis method. In order to better meet the practical requirements of engineering, this paper systematically studies the time-varying reliability analysis method of mechanical structures, the main contents of which are as follows: 1, aiming at the reliability problem of uncertainty of failure criteria of engineering structures, In this paper, a time-varying reliability analysis method considering the fuzziness of failure criteria is proposed, in which the time-varying function stochastic processes under the fuzzy failure criteria are first discretized, and then new random variables are introduced by applying the basic theory of fuzzy sets. The equivalent function function of different time periods is obtained. Finally, the time-varying reliability problem under fuzzy failure criterion is transformed into a conventional reliability problem. The time-varying reliability and failure probability of complex engineering structures are obtained by the first-order second-order moment form method. In this paper, a new method for calculating span rate is constructed, in which the stochastic processes and random variables of time-varying function functions are first transformed into independent normal spaces, and the transformed limit state functions are linearly expanded at the maximum possible MPP points. Then, applying the basic theory of PHI2 method and introducing new parameters and random variables, the time-varying reliability model, which the limit state equation is a complex nonlinear function, is transformed into a static reliability analysis model. Based on the time-varying reliability model of process discretization, a time-varying reliability sensitivity analysis method for complex engineering structures is proposed. The stochastic process is transformed into a random variable, and the time-varying reliability problem is transformed into a conventional time-invariant system reliability problem. The sensitivity of failure probability to random variables and parameters of random processes is transformed into the first order differential of reliability index to distributed parameters, and then Nataf full probability transformation and orthogonal transformation are used. Finally, the first derivative of failure probability to distributed parameters is obtained. This method greatly simplifies the calculation process of time-varying reliability sensitivity analysis and has a high computational efficiency.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TH123

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