机械结构时变可靠性分析方法及应用

发布时间：2018-06-16 03:39

本文选题：时变可靠性 + 概率方法　；参考：《湖南大学》2014年硕士论文

【摘要】：结构的可靠性与机械产品质量密切相关，近年来越来越受到重视。传统的可靠性分析技术，通常在不考虑时变载荷和强度退化的精确模型下处理问题，因而得到的可靠度是一个不变的固定数值。然而实际工程问题往往很复杂：1、因材料退化及动态不确定性载荷等引起的时变特性广泛存在；2、由于试验条件和成本的限制，有些参数，例如强度衰减函数参数、初始抗力和动、静载荷概率分布参数等，因试验样本不足无法得到精确值。因此，可靠性分析方法应够充分考虑这些问题，以更好地满足工程实际要求。基于上述想法，本文研究了机械结构时变可靠性分析方法，为产品在全生命周期内的设计提供了分析工具。主要研究内容如下： 1、针对概率分布参数中存在区间不确定性的混合不确定问题，构造了一种含区间变量的时变可靠性分析方法。该方法首先将含区间变量的时变可靠性分析模型转换为一概率—区间混合静态可靠性问题，并采用了一种高效序列迭代格式，最终获得时变可靠度的上、下边界。 2、针对非线性功能函数，提出了一种时变可靠性分析方法。该方法首先将时变功能函数中的随机过程进行离散，获得多个不同时间段的静态功能函数，，通过将各功能函数在最大可能点(Most Probable Point, MPP)处进行线性化，并运用全概率公式将其化简为一新的静态可靠度分析模型，最终采用传统的一次二阶矩方法(First Order Reliability Method, FORM)进行高效求解。 3、针对功能函数非线性且存在任意随机变量和随机过程的可靠性分析问题，提出了一种基于过程离散的时变可靠度分析方法（TRPD）。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换为常规的时不变体系可靠性问题。通过FORM进行极限状态方程的线性化，并引入一新的随机变量，对转换得到的体系可靠性问题进行高效求解。
[Abstract]:The reliability of structure is closely related to the quality of mechanical products, and has been paid more and more attention in recent years. The traditional reliability analysis technique usually deals with the problem without considering the time-varying load and the degradation of the strength, so the reliability obtained is an invariant fixed value. However, the practical engineering problems are often very complicated, and the time-varying characteristics caused by material degradation and dynamic uncertain loads are widespread. Due to the limitation of test conditions and costs, some parameters, such as the strength attenuation function parameters, are obtained. The initial resistance, dynamic and static load probability distribution parameters can not be obtained because of the shortage of test samples. Therefore, the reliability analysis method should fully consider these problems in order to better meet the practical requirements of engineering. Based on the above ideas, the time-varying reliability analysis method of mechanical structures is studied in this paper, which provides an analytical tool for product design in the whole life cycle. The main research contents are as follows: 1. A time-varying reliability analysis method with interval variables is proposed to solve the mixed uncertainty problem with interval uncertainty in the parameters of probability distribution. In this method, the time-varying reliability analysis model with interval variables is first transformed into a probabilistic and interval-mixed static reliability problem, and an efficient sequential iterative scheme is used to obtain the upper time-varying reliability. Second, a time-varying reliability analysis method is proposed for nonlinear functional functions. In this method, the random processes in the time-varying function are discretized, and the static function is obtained at different time intervals. By linearizing each function at the maximum possible point, the function can be linearized at the most likely point of most potential point (MPP). The whole probability formula is used to simplify it into a new static reliability analysis model. Finally, the first order Reliability method (FORM) is used to solve this problem efficiently. 3. For the reliability analysis problems of nonlinear functional functions with arbitrary random variables and stochastic processes, the first order Reliability method (FORM) is used to solve the problem. A time-varying reliability analysis method based on process discretization is presented in this paper. By time discretization, 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 limit state equation is linearized by form and a new random variable is introduced to solve the system reliability problem efficiently.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114.3

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