A modified method to calculate reliability index using maximum entropy principle  

作　　者：徐志军 郑俊杰 边晓亚 刘勇 

机构地区：[1]School of Civil Engineering & Mechanics, Huazhong University of Science and Technology [2]School of Civil Engineering and Architecture, Henan University of Technology [3]Department of Civil Engineering, National University of Singapore

出　　处：《Journal of Central South University》2013年第4期1058-1063,共6页中南大学学报（英文版）

基　　金：Project(50978112) supported by the National Natural Science Foundation of China

摘　　要：Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.Routine reliability index method, first order second moment （FOSM）, may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy （MaxEnt） principle. To achieve this goal, the complicated iteration of first order second moment （FOSM） method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations （MCS） were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 106, which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment （FOSM） method.

关 键 词：reliability index maximum entropy principle first order second moment Newton iteration Monte Carlo simulation 

分 类 号：O213.2[理学—概率论与数理统计]