一种针对多峰随机分布的不确定性传播分析方法  

An uncertainty propagation analysis method considering multimodal random distribution

作　　者：谢博群 张哲[1,2] 姜潮[1,2] XIE BoQun;ZHANG Zhe;JIANG Chao(State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha 410082,China;College of Mechanical and Vehicle Engineering,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,长沙410082 [2]湖南大学机械与运载工程学院,长沙410082

出　　处：《中国科学：技术科学》2022年第8期1259-1273,共15页Scientia Sinica(Technologica)

基　　金：国家自然科学基金创新研究群体(批准号:51621004);国家自然科学基金(批准号:51805157);国家杰出青年科学基金(批准号:51725502);国防基础科研项目(编号:JCKY2020110C105)资助。

摘　　要：在实际工程应用中随机变量可能会服从多峰随机分布,如火车减振器在长期使用后的阻尼特性和安全切割试件修复后的疲劳寿命等.传统的不确定性传播方法主要用于处理单峰随机分布问题,而在处理多峰随机分布问题时容易产生较大误差.本研究提出了一种针对多峰随机分布的不确定性传播分析方法.首先,使用高斯混合模型建立多峰随机变量的概率密度函数;其次,发展了一种高效三元降维法计算响应函数的高阶统计矩,该方法可以有效提高不确定传播的计算效率;再次,使用最大熵方法来计算响应的概率密度函数并且通过基于熵值的自适应方法来确定统计矩的最优阶数;最后,使用四个算例验证了提出方法在多峰不确定性传播中的计算精度和效率.In practical engineering applications,random variables may follow a multimodal random distribution,such as damping characteristics of train shock absorber after long-term use and fatigue life of safety cut specimens after repair.Traditional uncertainty propagation analysis methods are mainly used for random variables following a unimodal distribution.Therefore,large errors will be produced when random variables follow a multimodal distribution.In this study,an uncertainty propagation analysis method considering a multimodal random distribution is proposed.First,the probability density function of input multimodal random variables is defined by the Gaussian mixture model;then,the high-order moments of response function are calculated using the efficient trivariate dimension reduction method,which effectively improves the computational efficiency of uncertainty propagation.Once again,the maximum entropy method is used to compute the probability density function of response,whereas an adaptive method based on entropy is used to determine the optimal order of statistical moments.Finally,four numerical examples are demonstrated to analyze the accuracy and efficiency of the proposed method in handling multimodal uncertainty propagation analysis.

关 键 词：不确定性传播 多峰随机分布 高效三元降维法 高阶统计矩 

分 类 号：O211.6[理学—概率论与数理统计]