基于支持向量机和证据理论的复杂系统可靠性分析方法  

Method of reliability analysis on complex systems based on support vector machine and evidence theory

作　　者：曹亮[1,2] 龚曙光 陈国强[1] 董丽君[1] CAO Liang;GONG Shuguang;CHEN Guoqiang;DONG Lijun(College of Mechanical Engineering,Hunan Institute of Engineering,Xiangtan 411104;College of Mechanical Engineering,Xiangtan University,Xiangtan 411105)

机构地区：[1]湖南工程学院机械工程学院,湖南湘潭411104 [2]湘潭大学机械工程学院,湖南湘潭411105

出　　处：《机械设计》2024年第5期131-137,共7页Journal of Machine Design

基　　金：国家重点研发计划项目(2023YFC2206501);湖南省自然科学基金(2022JJ50112);湘潭大学研究生科研创新项目(XDCX2021B172)。

摘　　要：针对复杂系统中存在极限状态方程为隐式情况及参数为认知不确定性的问题,文中提出了一种基于支持向量机和证据理论的高效可靠性分析方法。首先,基于贝叶斯方法和最大熵原理将焦元上的基本概率分配平均分配到焦元中每一个元素以实现证据体精确化;其次,面对多学科系统中极限状态方程为隐式情况,采用支持向量机(SVM)进行显式化处理。在该方法中提出了SVM训练样本抽取策略,并对SVM通过引入马尔可夫蒙特卡洛模拟法(MCMC)进行改进,使其能适用于多学科系统的隐式极限状态方程小失效概率的求解;最后,通过算例分析,表明该方法的精度和计算效率具有较大优势,相比于MCS,该方法抽样2000个样本点精度相对误差仅为3.05%,为复杂系统的可靠性分析提供了一定的参考价值。This paper presents an efficient reliability analysis method based on support vector machines(SVM)and evi⁃dence theory to address the challenges posed by implicit limit state equations and cognitive uncertainty in complex systems.Firstly,using Bayesian methods and the maximum entropy principle,the basic probability assignment on focal elements is even⁃ly distributed to each element to achieve the refinement of evidence bodies.Secondly,when facing implicit limit state equations in multidisciplinary systems,support vector machines(SVM)are employed to explicitly handle them.In this method,an SVM training sample extraction strategy is proposed,and an improvement is made to the SVM by introducing the Markov Chain Monte Carlo(MCMC)simulation method,enabling it to solve the small failure probability of implicit limit state equations in multidisciplinary systems.Finally,through case studies,the accuracy and computational efficiency of the proposed method are demonstrated,showing significant advantages compared to Monte Carlo simulation(MCS).With a sample size of 2000 points,the proposed method achieves an accuracy error of only 3.05%,providing valuable insights for reliability analysis of complex systems.

关 键 词：支持向量机 证据理论 马尔可夫蒙特卡洛模拟法 复杂系统 

分 类 号：TB114.3[理学—概率论与数理统计]