基于Rényi熵的q-指数分布及其可靠性分析应用  

q-Exponential Distribution Based on Rényi Entropy and Its Application on Reliability Analysis

作　　者：谢暄[1] 王敏夷 白颖利 汪东敏 李西峰[1] 谢永乐[1] XIE Xuan;WANG Min-yi;BAI Yin-li;WANG Dong-min;LI Xi-feng;XIE Yong-le(School of Automation Engineering,University of Electronic Science and Technology of China,Chengdu,611731;Communication Satellite Division,China Academy of Space Technology,Haidian Beijing,100094;Sichuan Huilong Technology LLC,Chengdu,610041)

机构地区：[1]电子科技大学自动化工程学院,成都611731 [2]中国空间技术研究院通信卫星事业部,北京海淀区100094 [3]四川慧龙科技有限责任公司,成都610041

出　　处：《电子科技大学学报》2021年第4期535-543,共9页Journal of University of Electronic Science and Technology of China

基　　金：国家自然科学基金(61701095,61601096,61801089,61971111,62027803);四川省科学技术项目(2020YFG0044,2020YFG0046,2021YFG0200);国防基础科研计划(JCKY2020110C041)。

摘　　要：基于最大Rényi熵原理,在归一化和均值约束下,提出了一种具有封闭表达式的双参数广义指数分布,记为q-指数分布。该文研究了该分布的统计性质,指出可以分别利用极大似然法和信息似然法估计q-指数分布参数,并将该分布用于可靠性分析。利用两个已知的数据集进行了验证,实验结果表明,所提出的q-指数分布比其他常用分布,如韦伯分布和线性失效率分布,能够更好地拟合数据集。此外,锂电池剩余寿命估计实验表明,采用q-指数分布比采用传统指数分布,估计精度至少提高17.857%。We propose a two-parameter generalized exponential distribution with closed-form expression based on the maximum Rényi entropy principle under the normalization and mean constraints,which is referred as the q-exponential distribution.The statistical properties of this distribution are investigated.The maximum likelihood method and information likelihood method are used to estimate the parameters of the proposed distribution,respectively.Two well-known data sets are employed to evaluate the q-exponential distribution,and the experimental results demonstrate that the proposed distribution can fit the data sets better than other well-known distributions,such as Weibull distribution and linear failure rate distribution.Additionally,the experiment results of life estimation of the Li-ion batteries prove that compared with the exponential distribution,the proposed distribution can give more accurate prediction.In the last experiment,the estimation accuracy is improved by at least 17.857%.

关 键 词：指数分布 风险函数 q-指数分布 Rényi熵 韦伯分布 

分 类 号：TP202.1[自动化与计算机技术—检测技术与自动化装置]