三维路径积分法的积分区间以及子区间数目选取方法研究  

Research on selection of integral interval and number of subintervals for 3D path integral method

作　　者：徐严钢 朱海涛[1,2] 刘治国 Xu Yangang;Zhu Haitao;Liu Zhiguo(School of Civil Engineering and Architecture,Tianjin University,300072,Tianjin,China;Key Laboratory of Coastal Civil Engineering Structure and Safety,Ministry of Education,Tianjin University,300072,Tianjin,China;China North China Institute of Municipal Engineering Design and Research Co.,Ltd.,300074,Tianjin,China)

机构地区：[1]天津大学建筑工程学院,天津300072 [2]天津大学滨海土木工程结构与安全教育部重点实验室,天津300072 [3]中国市政工程华北设计研究总院有限公司,天津300074

出　　处：《应用力学学报》2021年第4期1358-1365,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51478311)。

摘　　要：对基于Gauss-Legendre公式的路径积分法在二维、三维模型上的运用进行了研究。以高斯白噪声激励下的附加集中质量块悬臂梁、单稳态、双稳态、三稳态能量收集器为例,采用路径积分法计算平稳或非平稳响应的概率密度函数解,重点研究了积分区间以及子区间数目的选取对于路径积分法计算精度和效率的影响,采用蒙特卡洛数值模拟法的计算结果作为标准值,与路径积分法计算的结果进行了对比。提出了先对积分区间以及子区间数目进行粗选,再根据粗选结果进行负反馈调节积分区间的方法,提高了路径积分法的计算精度。In this paper, the application of path integration method based on Gauss-Legendre integration formula is used to study the application of two-dimensional and three-dimensional models. Taking Gaussian white noise on the additional concentrated mass cantilever, monostable, bistable, and tristable energy collectors as examples, the path integration method is used to calculate stationary or non-stationary probability density function solutions. This paper focuses on the influence of the selection of the integration interval and the number of sub-intervals on the calculation accuracy and efficiency of the path integration method. Result of the Monte-Carlo numerical simulation method is used as a standard value are compared with the result of the path integration method. A method is proposed to roughly select the integration interval and the number of sub-intervals according to the table, and then adjust the integration interval with negative feedback according to the rough selection result, which improves the calculation accuracy of the path integration method.

关 键 词：路径积分法 概率密度函数 高斯白噪声 积分区间 子区间数目 

分 类 号：TU351[建筑科学—结构工程]