Semi-analytical steady-state response prediction for multi-dimensional quasi-Hamiltonian systems  

作　　者：叶文伟 陈林聪 原子 钱佳敏 孙建桥 Wen-Wei Ye;Lin-Cong Chen;Zi Yuan;Jia-Min Qian;Jian-Qiao Sun(College of Civil Engineering,Huaqiao University,Xiamen 361021,China;Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province,Huaqiao University,Xiamen 361021,China;Department of Mechanical Engineering School of Engineering,University of California Merced,CA 95343,USA)

机构地区：[1]College of Civil Engineering,Huaqiao University,Xiamen 361021,China [2]Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province,Huaqiao University,Xiamen 361021,China [3]Department of Mechanical Engineering School of Engineering,University of California Merced,CA 95343,USA

出　　处：《Chinese Physics B》2023年第6期177-186,共10页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No. 12072118);the Natural Science Funds for Distinguished Young Scholar of the Fujian Province, China (Grant No. 2021J06024);the Project for Youth Innovation Fund of Xiamen, China (Grant No. 3502Z20206005)。

摘　　要：The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.

关 键 词：steady-state response quasi-Hamiltonian systems FPK equation RBF neural networks 

分 类 号：O302[理学—力学]