模糊可靠性研究

【作者】 孙占全；

【导师】 黄洪钟；

【作者基本信息】 大连理工大学 ， 机械设计及理论， 2003， 硕士

【摘要】 可靠性是度量产品质量的重要指标，产品的可靠性问题不仅影响产品性能，而且影响一个国家的国计民生和社会的安全与稳定。努力提高产品的质量可靠性，不仅可以防止故障和事故的发生，尤其是灾难性事故的发生，而且可以避免产品开发时频繁的“事后更改”现象，从而缩短开发周期、节约开发成本、降低维修费用和其他由于可靠性不高而产生的附加费用。因此，可靠性成为各国科研机构和学者致力研究的重点和热点。 随着人们对可靠性研究的不断深入，人们发现许多实际工程问题不仅存在随机性，而且存在广泛的模糊性，特别是在对小样本进行可靠性分析时，模糊性对分析结果起到决定性的影响。因此，人们将模糊理论引入到可靠性的研究中，开展了模糊可靠性的研究。模糊可靠性的研究虽只有20多年的历史，却吸引了国内外众多优秀学者致力于此，并取得了很大的理论成果。但随着可靠性理论的不断发展，模糊可靠性分析的理论和方法还有待于进一步完善和发展。本文基于现有可靠性的研究成果，在以下几方面对模糊可靠性进行了较为深入的研究： (1)深入研究了用广义模糊强度表示的模糊安全状态情况下的模糊可靠度计算形式。提出了一种简单易行的模糊安全事件隶属函数定义方式，完善了模糊可靠度计算理论。建立了以模糊可靠度为约束条件的模糊可靠性优化设计模型，给出了用遗传算法对该模型进行求解的方法。 (2)在目前利用Bayes方法进行模糊可靠性分析研究的基础上，提出了比较完整的模糊Bayes可靠性预测的方法。将神经网络和遗传算法等智能计算和优化方法引入基于Bayes理论的可靠性预测方法中，为模糊可靠性估计的隶属函数的确定提供了有效途径。 (3)把截尾试验中生产者风险和消费者风险定义成模糊数，在确定的可行方案中，利用隶属度来确定最优的截尾方案。提出在对可用语言变量描述的截尾数据进行可靠性分析时，不应把截尾数据看成是无信息数据，而应将模糊截尾数据转换成完全数据，给出了相应的转换方法，并利用Bayes方法进行了模糊可靠性分析。 (4)讨论了材料的模糊S-N曲线和P-S-N曲线的生成方法，克服了常规方法中由于没有考虑试验数据的模糊性而造成的不足。介绍了用极大似然法确定P-S-N曲线的方法。提出了一种利用神经网络模拟P-S-N曲线生成的方法，有效地避免由于试验样本少且离散性太大而产生P-S-N曲线与实际不相符的现象。 模糊可靠性的理论还有很多方面需要完善，本文只从几个方面进行了较为深入的研究，模糊可靠性理论的完善还需要更多的学者的不断努力。更多还原

【Abstract】 Reliability is one of the most important indices to evaluate the quality of product. It has become a most popular research direction. With the development of research, people begin to realize that there exist not only randomness but also fuzziness in practical problems. So people begin to study fuzzy reliability. The theory and method of fuzzy reliability are not perfect. The paper has studied several aspects of fuzzy reliability as follows:For the definition of fuzzy safety state is different, the calculation of fuzzy reliability is different under different condition. A simple and practical method, to define membership function of fuzzy event denoted by generalize fuzzy strength, is developed in the paper. Then fuzzy reliability optimization model is developed. In the model, fuzzy reliability is regarded as constraint and genetic algorithm method is introduced to resolve it.The most efficient means to analyse the reliability of small sample is Bayes method because it takes full use of priori information. The theory of fuzzy Bayes reliability prediction is not perfect. Based on current research results, a systematic method of fuzzy Bayes reliability prediction is developed. Neural network and genetic algorithm are introduced into the method.Censored test plan cannot meet with actual producer risk and customer risk because the censored number must be integer. Producer risk and customer risk are defined as fuzzy numbers and the optimum censored test plan is determined according to the membership grade after determining the feasible region. Fuzzy censored numbers described with linguistic variables are transformed into completed numbers, then fuzzy Bayes reliability method is introduced to analyse them.Fuzzy S-N curve is introduced in the paper. How to create the ideal P-S-N curve with the least test numbers is an important problem to be resolved. A maximum likelihood method to determine P-S-N curve is introduced and a method with neural network simulating P-S-N curve is developed in the paper. The method can avoid the problem that the P-S-N curve doesn’t meet reality when the samples are scattered.更多还原