基于最小样本空间的Johnson分布拟合方法  

Johnson Distribution Fitting Method Based on Minimum Sample Space

作　　者：张琪 吴义忠[2] 刘鑫[2] 乔平[2] ZHANG Qi;WU Yizhong;LIU Xin;QIAO Ping(National NC System Engineering Research Center of Huazhong University of Science&Technology,Wuhan,430074;Research Center for National CAD Support Software Engineering and Technology of Huazhong University of Science&Technology,Wuhan,430074)

机构地区：[1]华中科技大学国家数控系统工程技术研究中心,武汉430074 [2]华中科技大学国家企业信息化应用支撑软件工程技术研究中心,武汉430074

出　　处：《中国机械工程》2019年第21期2560-2566,2576,共8页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(61575205)

摘　　要：基于应力强度干涉模型计算可靠度指标时,常使用统计方法获得应力和强度的概率分布,然而,在复杂机电产品的设计过程中,每一个样本值的获取都是一次昂贵估值,大量样本值的获取面临耗时严重等问题。针对该问题,采用参数化的Johnson分布拟合概率分布,研究基于最小样本空间的Johnson分布拟合方法。采用百分位数配比法求解Johnson分布族函数的参数,并基于假设检验原理确定满足拟合精度要求的最小样本空间,同时通过K-S拟合检验法对总体真实分布与拟合分布进行一致性分析,保证拟合精度符合要求。工程应用结果表明,该方法基于少量的昂贵估值样本可快速得到样本的总体分布,为可靠度指标的快速计算奠定了基础。When calculating the reliability index based on the stress-strength interference model,statistical methods were used to obtain the probability distribution of stress and strength.However,in the design processes of complex electromechanical products,the acquisition of each sample values was an expensive evaluation,so,the acquisition of a large number of sample values would be confronted with serious problems such as time consuming.Aiming at this problem,the parameterized Johnson distribution family function was introduced to fit the probability distribution,and the Johnson distribution fitting method was studied based on the minimum sample space.The parameters of the Johnson distribution family function were solved by percentile matching method and the minimum sample space was determined based on the hypothesis testing principle.To ensure the fitting accuracy,K-S test was introduced to analyze the consistency between the real distribution and the fitted distribution.The results of engineering applications show that the method may quickly obtain the distribution of samples based on a small number of expensive evaluation samples,which lays a foundation for the rapid calculation of reliability index.

关 键 词：Johnson分布族函数 假设检验 最小样本空间 一致性分析 

分 类 号：TH122[机械工程—机械设计及理论]