可靠性计算的失效区组合逼近方法研究

发布时间：2018-06-13 08:59

本文选题：最大可能失效区 + 局部失效区　；参考：《合肥工业大学》2014年博士论文

【摘要】：高可靠性是提高产品质量和竞争力的重要保证,提高可靠性计算精度是可靠性理论研究的重要课题。迄今为止,可靠性计算的主流方法是一次可靠性方法、二次可靠性方法和蒙特卡洛方法。一次可靠性方法在线性功能函数的情况下才可能获得精确解,二次可靠性方法在非线性功能函数的情况下可以提高可靠性计算的精度,但对计算精度提高的程度仍无法估计,而蒙特卡罗模拟法似乎是一种万能的方法。事实上,一次可靠性方法是用设计点处的一个线性功能函数替代原功能函数,二次可靠性方法是用设计点处的一个二次功能函数替代原功能函数,再进行可靠性的计算。无论是线性功能函数,还是二次功能函数,虽然其可靠性的计算较原功能函数变得简单,但是由于线性功能函数或二次功能函数形成的计算失效区与原功能函数的失效区有所不同,因此必然存在计算误差。显然,用一个简单的线性功能函数或二次功能函数替代原功能函数后,再进行可靠性的计算,无论如何,可靠性的计算精度有时可能不够。若能够用多个线性功能函数或二次功能函数替代原功能函数,且这些线性功能函数或二次功能函数失效区的适当组合充分接近原功能函数的失效区,则计算这些线性功能函数或二次功能函数组合失效区的概率,就可充分接近原失效区的概率,从而提高原功能函数可靠性计算的精度。论文研究的主要内容和创新点如下： (1)逼近函数的获取方法主要针对功能函数的最大可能失效区为凸集的情况,深入研究逼近函数的获取方法。确保逼近函数失效区的组合可高精度地逼近原失效区,为进一步提高可靠性计算精度打下坚实基础。提出用PSO算法求多个设计点,用于建立主线性逼近函数。针对高非线性功能函数,提出建立次线性逼近函数的重要方向法,弥补了现有方法的不足。提出建立次线性逼近函数的改进陈方法、球极坐标法及旋转法,作为必要的补充。提出受功能函数非线性程度影响较小的抛物线法来获取二次逼近函数。同时,提出一步响应面法作为必要的补充。 (2)凸失效或凸安全区可靠性的计算研究利用线性逼近函数失效区获得具有较高计算精度的可靠性计算方法。通过逐次建立等效主逼近平面方法,实现用逼近函数失效区逐次高精度地逼近原失效区。当等效主逼近平面的失效区与原失效区接近时,获得的可靠性值可接近精确值。此外,对现有陈方法的次线性化点的迭代搜索方向进行改进,提高该方法的普适性。通过研究线性逼近函数的失效区的组合方法,提出用线性凸概率积分区的组合对原失效区进行高精度逼近,提出利用线性凸概率积分区计算原失效区可靠性方法——线性凸区法。 (3)非凸失效或非凸安全区可靠性的计算重点研究多个最大可能失效区组成的系统可靠性计算的线性逼近法。首先求出多个设计点和多个最大可能失效区,将结构可靠性计算转化为多个最大可能失效区组成系统的可靠性计算。当设计点为拐点时,提出改进线性凸区法和改进Feng方法构造最大可能失效区的等效主平面。以等效主平面的失效区逼近单个最大可能失效区。将最大可能失效区组成的系统可靠性计算转化为等效主平面失效区组成的系统可靠性计算。提出计算等效主平面失效区系统可靠性的两种方法：逐步累积法和逐次等效法。实现了对现有线性逼近法的进一步完善和发展。 (4)二次逼近可靠性的计算针对具有多个凸峰和凹谷的功能函数的可靠性计算,将原失效区划分若干局部失效区。以原失效区为“顶事件”,局部失效区为“底事件”,利用最小割集将局部失效区进行组合逼近原失效区。重点研究构造若干二次功能函数的失效区组合逼近局部失效区,通过计算二次功能函数失效区组成的系统可靠性获得局部失效区的可靠性,进而以局部失效区组成的系统可靠性估计结构可靠性。 (5)逼近方法的可靠性计算应用以拉杆、螺栓、输出轴及调谐系统振幅的可靠性计算为例,研究逼近方法的工程应用。同时,研究逼近方法在可靠性灵敏度和系统可靠性计算中的应用。
[Abstract]:In fact , the reliability calculation method is a kind of universal method . In fact , the reliability calculation method is a kind of universal method in the case of non - linear function function . In fact , one reliability method is to use a quadratic function function at the design point to replace the original function function .

If a simple linear function or a quadratic function function is used instead of the original function function , the reliability calculation is carried out . In any case , the calculation accuracy of the reliability may not be enough . If a plurality of linear function or quadratic function functions are used instead of the original function function , the probability of the failure area of the linear function or the quadratic function function can be sufficiently close to the failure area of the original function function , so that the accuracy of the reliability calculation of the original function function can be improved .

( 1 ) Method for acquiring approximation function

In order to improve the accuracy of reliability calculation , it is proposed to establish the important direction method of the sub - linear approximation function and to make up for the deficiency of the existing methods .

( 2 ) Calculation of the reliability of convex failure or convex safety zone

In this paper , the reliability calculation method with higher computing accuracy is obtained by using the failure region of linear approximation function . By establishing the equivalent principal approximate plane method one by one , the reliability value obtained is close to the exact value . In addition , the method is improved by studying the iterative search direction of the sub linearization point of the existing method .

( 3 ) Calculation of non - convex failure or non - convex safety zone reliability

This paper focuses on the linear approximation method of system reliability calculation consisting of a plurality of maximum possible failure zones . First , a plurality of design points and a plurality of maximum possible failure regions are obtained , and the reliability calculation of the structure is converted into the equivalent main plane of a plurality of maximum possible failure zones .

( 4 ) Calculation of reliability of quadratic approximation

According to the reliability calculation of the function function with a plurality of convex peaks and valleys , the original failure area is divided into a plurality of local failure areas . The original failure area is a " top event " , the local failure area is a " bottom event " , and the local failure area is combined with the minimum cut set to approximate the original failure area .

( 5 ) Reliability calculation and application of approximation method

Taking the reliability of the amplitude of the pull rod , bolt , output shaft and tuning system as an example , the engineering application of the approximation method is studied . At the same time , the application of the approximation method in the calculation of reliability sensitivity and system reliability is studied .
【学位授予单位】：合肥工业大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TB114.3

【参考文献】