基于对偶神经网络的动力方程精细积分法  

A precise integration method for dynamic equations based on dual neural networks

作　　者：杨永 李海滨[1,2] YANG Yong;LI Haibin(School of Science,Inner Mongolia University of Technology,Hohhot 010051,China;Engineering Training Center,Inner Mongolia University of Technology,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051 [2]内蒙古工业大学工程训练教学部,呼和浩特010051

出　　处：《振动与冲击》2022年第16期188-193,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(11962021);内蒙古自然科学基金(2019MS05063);内蒙古自然科学基金(2021MS05020)。

摘　　要：针对一般动力学方程,提出了一种用于求解具有任意非齐次项动力学方程的对偶神经网络精细积分算法。在时间域内,对动力学非齐次方程求解中涉及到的积分运算,选用一组神经网络同时逼近被积函数和原函数,然后通过牛顿莱布尼茨公式实现积分项的求解。该方法利用神经网络的函数拟合优势,具有对时间步长不敏感,不需要对矩阵求逆,不对非齐次项进行假设等优点。通过算例与精细积分法、威尔逊-θ、广义精细积分法等方法进行比较,计算结果表明该方法精度较高、适用范围广。For dynamics equations,the existing common solution method is the precise integration method,but the result of the equation given by the precise integration method contains complex integrals,which is difficult to solve by the traditional numerical integration method.In this work,an integration algorithm was proposed based on neural networks.The algorithm builds two neural networks,one is used to approximate the integral function and the other is used to approximate the original function.The two neural networks are trained at the same time.The result of the integration can then be obtained by the Newton Leibniz function.The algorithm of this work takes advantage of the function fitting of the neural network,which is insensitive to the selected time step during the solution of the kinetic equations,does not require the inverse of matrix,and does not require inhomogeneous term assumpution.With computational examples,the proposed algorithmwas compared with a variety of existing commonly used methods.Results show that the method has high accuracy and wide applicability.

关 键 词：精细积分法 对偶神经网络 动力方程 直接积分 

分 类 号：O321[理学—一般力学与力学基础]