基于Copula函数的多元加速退化试验方法研究

发布时间：2018-06-14 22:55

本文选题：多元性能参数 + 加速退化试验　；参考：《浙江理工大学》2014年硕士论文

【摘要】：随着科学技术的发展和加工工艺的不断提高，许多产品都具有高可靠、长寿命的特点，造成基于失效数据的可靠性评估和寿命预测愈加困难，加速退化试验能利用性能退化数据的信息，从而为解决这些产品可靠性评估和寿命预测提供有效手段。目前关于性能退化试验的研究大多数针对单个性能参数展开，但在实际工程中，许多复杂产品已不能以单一的性能参数来判断其是否满足正常工作需求，而且产品多个性能参数退化数据间存在一定的相关性，需要合理的建立其相关模式。Copula函数作为一种灵活、稳健的相关性分析工具，在分析变量间相关性时具有诸多的优点。因此，本文基于Copula函数对多性能参数产品的可靠性建模、数据统计分析方法、可靠性评估和寿命预测展开研究。论文主要工作如下：首先，简要阐述了论文的研究背景、目的及意义；综述了加速退化试验的发展历史、国内外研究现状、存在的问题及发展趋势；概述了Copula函数的发展及其在可靠性领域的研究现状。其次，给出了产品可靠性的度量指标和性能退化的相关概念；基于Copula函数建立了多性能参数产品的可靠性模型；并介绍了Copula函数的定义、性质、相关性度量、参数估计及Copula函数选择等基本理论；为多元加速退化试验数据统计分析及多性能参数产品的可靠性评估奠定了基础。第三，分析了加速退化数据的特点，总结了退化量分布、退化轨迹和加速方程的一般形式，建立了多元加速退化试验数据的统计模型；提出了退化数据分布选择、分布参数估计、退化轨迹拟合、Copula函数参数估计及选择、产品可靠性评估和寿命预测方法，从而建立了基于Copula函数的多元加速退化试验数据统计分析的一般方法；并通过数值仿真实例，验证了该方法的可行性。第四，，分析了贮存条件下电液伺服机构用丁腈橡胶O型密封圈的失效机理，建立了其性能参数退化轨迹和加速方程；以温度为加速因子，压缩永久变形和压缩应力松弛为O型密封圈退化性能参数，设计了O型密封圈加速退化试验方案；利用基于Copula函数的多元加速退化试验数据统计分析方法对O型密封圈加速退化数据进行了统计分析，得到了正常温度下O型密封圈的可靠度曲线及中位寿命。最后，总结了全文研究的内容，并指出了多元加速退化试验方法进一步研究的内容。
[Abstract]:With the development of science and technology and the continuous improvement of processing technology, many products have the characteristics of high reliability and long life, which makes reliability assessment and life prediction based on failure data more difficult. The accelerated degradation test can utilize the information of the performance degradation data, thus providing an effective means to solve the reliability evaluation and life prediction of these products. At present, most of the researches on performance degradation test focus on single performance parameter, but in practical engineering, many complex products can not judge whether they meet the normal working requirements with a single performance parameter. Moreover, there is a certain correlation between the degradation data of multiple performance parameters. It is necessary to reasonably establish its correlation mode. Copula function is a flexible and robust tool for correlation analysis, which has many advantages in analyzing the correlation between variables. Therefore, based on Copula function, the reliability modeling, data statistical analysis, reliability evaluation and life prediction of multi-performance parameter products are studied in this paper. The main work of this paper is as follows: firstly, the research background, purpose and significance of the thesis are briefly described, and the development history, domestic and foreign research status, existing problems and development trend of accelerated degradation test are summarized. This paper summarizes the development of Copula function and its research status in the field of reliability. Secondly, the measurement index of product reliability and the related concepts of performance degradation are given, the reliability model of multi-performance parameter product is established based on Copula function, and the definition, property, correlation measure of Copula function are introduced. The basic theory of parameter estimation and Copula function selection lays a foundation for statistical analysis of multivariate accelerated degradation test data and reliability evaluation of multi-performance parametric products. Thirdly, the characteristics of accelerated degradation data are analyzed, the general forms of degradation quantity distribution, degradation trajectory and acceleration equation are summarized, the statistical model of multivariate accelerated degradation test data is established, and the selection of degradation data distribution is proposed. Distribution parameter estimation, parameter estimation and selection of Copula function, product reliability evaluation and life prediction method, and a general method for statistical analysis of multivariate accelerated degradation test data based on Copula function are established. The feasibility of the method is verified by numerical simulation. Fourthly, the failure mechanism of nitrile-butadiene rubber O-type seal ring for electro-hydraulic servo mechanism under storage condition is analyzed, and the degradation track and acceleration equation of its performance parameters are established. The compression permanent deformation and compression stress relaxation are the degradation performance parameters of O-type seal ring, and the accelerated degradation test scheme of O-type seal ring is designed. Based on Copula function, the accelerated degradation data of O type seal ring is analyzed by using the statistical analysis method of multivariate accelerated degradation test data. The reliability curve and median life of O type seal ring at normal temperature are obtained. Finally, the contents of this paper are summarized, and the further research contents of multivariate accelerated degradation test method are pointed out.
【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114.3

【参考文献】