本文選題：時(shí)變可靠性 + 概率方法��； 參考：《湖南大學(xué)》2014年碩士論文

【摘要】：結(jié)構(gòu)的可靠性與機(jī)械產(chǎn)品質(zhì)量密切相關(guān)，近年來(lái)越來(lái)越受到重視。傳統(tǒng)的可靠性分析技術(shù)，通常在不考慮時(shí)變載荷和強(qiáng)度退化的精確模型下處理問(wèn)題，因而得到的可靠度是一個(gè)不變的固定數(shù)值。然而實(shí)際工程問(wèn)題往往很復(fù)雜：1、因材料退化及動(dòng)態(tài)不確定性載荷等引起的時(shí)變特性廣泛存在；2、由于試驗(yàn)條件和成本的限制，有些參數(shù)，例如強(qiáng)度衰減函數(shù)參數(shù)、初始抗力和動(dòng)、靜載荷概率分布參數(shù)等，因試驗(yàn)樣本不足無(wú)法得到精確值。因此，可靠性分析方法應(yīng)夠充分考慮這些問(wèn)題，以更好地滿(mǎn)足工程實(shí)際要求。基于上述想法，本文研究了機(jī)械結(jié)構(gòu)時(shí)變可靠性分析方法，為產(chǎn)品在全生命周期內(nèi)的設(shè)計(jì)提供了分析工具。主要研究?jī)?nèi)容如下： 1、針對(duì)概率分布參數(shù)中存在區(qū)間不確定性的混合不確定問(wèn)題，構(gòu)造了一種含區(qū)間變量的時(shí)變可靠性分析方法。該方法首先將含區(qū)間變量的時(shí)變可靠性分析模型轉(zhuǎn)換為一概率—區(qū)間混合靜態(tài)可靠性問(wèn)題，并采用了一種高效序列迭代格式，最終獲得時(shí)變可靠度的上、下邊界。 2、針對(duì)非線(xiàn)性功能函數(shù)，提出了一種時(shí)變可靠性分析方法。該方法首先將時(shí)變功能函數(shù)中的隨機(jī)過(guò)程進(jìn)行離散，獲得多個(gè)不同時(shí)間段的靜態(tài)功能函數(shù)，，通過(guò)將各功能函數(shù)在最大可能點(diǎn)(Most Probable Point, MPP)處進(jìn)行線(xiàn)性化，并運(yùn)用全概率公式將其化簡(jiǎn)為一新的靜態(tài)可靠度分析模型，最終采用傳統(tǒng)的一次二階矩方法(First Order Reliability Method, FORM)進(jìn)行高效求解。 3、針對(duì)功能函數(shù)非線(xiàn)性且存在任意隨機(jī)變量和隨機(jī)過(guò)程的可靠性分析問(wèn)題，提出了一種基于過(guò)程離散的時(shí)變可靠度分析方法（TRPD）。通過(guò)時(shí)間離散，將隨機(jī)過(guò)程轉(zhuǎn)換為隨機(jī)變量，并將時(shí)變可靠性問(wèn)題轉(zhuǎn)換為常規(guī)的時(shí)不變體系可靠性問(wèn)題。通過(guò)FORM進(jìn)行極限狀態(tài)方程的線(xiàn)性化，并引入一新的隨機(jī)變量，對(duì)轉(zhuǎn)換得到的體系可靠性問(wèn)題進(jìn)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.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：TB114.3

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