基于场变换的非高斯随机过程快速算法  

Fast algorithm for non-Gaussian stochastic processes based on translation processes

作　　者：刘晋铭 谭星 陈卫婷 何欢[1,2] LIU Jinming;TAN Xing;CHEN Weiting;HE Huan(State Key Laboratory of Mechanics and Control for Aerospace Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;Institute of Vibration Engineering Research,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]南京航空航天大学航空航天结构力学及控制全国重点实验室,南京210016 [2]南京航空航天大学振动工程研究所,南京210016

出　　处：《航空学报》2024年第18期192-204,共13页Acta Aeronautica et Astronautica Sinica

摘　　要：在非高斯平稳随机振动环境试验技术中,基于概率密度函数的试验技术更能精确地还原试验环境。但现有基于概率密度函数的随机信号仿真算法存在效率问题,难以在工程上应用。本文基于随机过程的场变换理论,提出了一种非高斯平稳随机过程仿真的快速算法。针对场变换理论中关键二重积分计算困难、计算速度慢的问题,对2个随机过程的相关系数函数进行级数展开,将一个含有隐式函数的复杂二重积分问题转换成一个简单的定积分问题,并利用Gauss-Hermite求积规则进行了快速求解。数值仿真验证了该方法能够在不影响仿真精度的前提下,提高非高斯平稳随机过程仿真的效率,满足了随机振动环境试验对于随机信号生成的实时性需求。In the non-Gaussian stationary random vibration environment testing technology, testing techniques based on probability density functions can more accurately reproduce the test environment. However, existing simulation algorithms based on probability density functions suffer from efficiency issues, making it challenging to apply them to engineering. A fast algorithm for simulating non-Gaussian stationary stochastic processes is proposed in this paper based on the translation process theory of stochastic processes. To address the difficulties and slow computation speed in critical double integral calculations of the field transformation theory, we expand the correlation coefficient functions of two random processes in series. This approach transforms a complicated double integral with an implicit function into a simple definite integral, which is efficiently solved using the Gauss-Hermite quadrature rule. Numerical simulations validate that this method can improve the efficiency of simulating non-Gaussian stationary random processes without compromising simulation accuracy, meeting the real-time requirement for generating random signals in the context of random vibration environment experiments.

关 键 词：随机振动环境试验 非高斯平稳随机过程 随机信号仿真 场变换理论 概率密度函数 

分 类 号：V216[航空宇航科学与技术—航空宇航推进理论与工程] O324[理学—一般力学与力学基础]