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

doi:10.1088/1674-1056/acae7c

中国物理B ›› 2023, Vol. 32 ›› Issue (6): 60506-060506.doi: 10.1088/1674-1056/acae7c

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

Wen-Wei Ye(叶文伟)^1,2, Lin-Cong Chen(陈林聪)^1,2,†, Zi Yuan(原子)^1,2, Jia-Min Qian(钱佳敏)^1,2, and Jian-Qiao Sun(孙建桥)³

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

收稿日期:2022-10-14 修回日期:2022-12-06 接受日期:2022-12-27 出版日期:2023-05-17 发布日期:2023-06-05
通讯作者: Lin-Cong Chen E-mail:lincongchen@hqu.edu.cn
基金资助:
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), and the Project for Youth Innovation Fund of Xiamen, China (Grant No. 3502Z20206005).

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

Wen-Wei Ye(叶文伟)^1,2, Lin-Cong Chen(陈林聪)^1,2,†, Zi Yuan(原子)^1,2, Jia-Min Qian(钱佳敏)^1,2, and Jian-Qiao Sun(孙建桥)³

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

Received:2022-10-14 Revised:2022-12-06 Accepted:2022-12-27 Online:2023-05-17 Published:2023-06-05
Contact: Lin-Cong Chen E-mail:lincongchen@hqu.edu.cn
Supported by:
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), and the Project for Youth Innovation Fund of Xiamen, China (Grant No. 3502Z20206005).

摘要/Abstract

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

Abstract: 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.

Key words: steady-state response, quasi-Hamiltonian systems, FPK equation, RBF neural networks

中图分类号: (Computational methods in statistical physics and nonlinear dynamics)

05.10.-a

05.10.Gg (Stochastic analysis methods) 05.10.Ln (Monte Carlo methods) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)

Wen-Wei Ye(叶文伟), Lin-Cong Chen(陈林聪), Zi Yuan(原子), Jia-Min Qian(钱佳敏), and Jian-Qiao Sun(孙建桥). Semi-analytical steady-state response prediction for multi-dimensional quasi-Hamiltonian systems[J]. 中国物理B, 2023, 32(6): 60506-060506.

参考文献

[1] Xu W, Wang L, Feng J Q, Qian Y and Han P2018 Chin. Phys. B 27 110503
[2] Ghany H A2014 Chin. Phys. Lett. 31 60503
[3] Zhu W Q, Cai G Q and Lin Y K1992 IUTAM Symposium, 1991, Turin, Italy, p. 543
[4] Zhu W Q2006 Appl. Mech. Rev. 59 230
[5] Huang Z L and Jin X L2009 Sci. China Ser. E-Technol. Sci. 52 2424
[6] Zhu W Q and Huang Z L2001 Int. J. Nonlinear Mech. 36 39
[7] Ying Z G and Zhu W Q2000 Int. J. Nonlinear Mech. 35 837
[8] Huang Z L and Zhu W Q2000 J. Sound Vib. 230 709
[9] Zhu W Q and Yang Y Q1996 J. Appl. Mech. 63 493
[10] Zhu W Q and Deng M L2004 J. Sound Vib. 274 1110
[11] Zhu W Q, Huang Z L and Suzuki Y2001 Int. J. Nonlinear Mech. 36 773
[12] Jia W T and Zhu W Q2014 Nonlinear Dynam. 76 1271
[13] Zeng Y and Zhu W Q2010 J. Appl. Mech. 78 021002
[14] Deng M L and Zhu W Q2007 J. Sound Vib. 305 783
[15] Huang Z L and Zhu W Q2004 Probabilist. Eng. Mech. 19 219
[16] Wang J L, Leng X L and Liu X B2021 Chin. Phys. B 30 60501
[17] Sun J Q, Xiong F R, Schütze O and Hernández C2018 Cell mapping methods (Singapore: Springer)
[18] Er G K2000 Int. J. Nonlinear Mech. 35 69
[19] Guo S S, Er G K and Lam C C2014 Nonlinear Dynam. 77 597
[20] Zhang H, Xu Y, Liu Q, Wang X L and Li Y G2022 Nonlinear Dynam. 108 4029
[21] Zhang Y an Yuen K V2022 Int. J. Nonlinear Mech. 147 104202
[22] Xu Y, Zhang H, Li Y G, Zhou K, Liu Q and Kurths J2020 Chaos 30 13133
[23] Zio E2013 Monte carlo simulation: The method (London: Springer) pp. 19-58
[24] Hirvijoki E, Kurki-Suonio T, äkäslompolo S, Varje J, Koskela T and Miettunen J2015 J. Plasma Phys. 81 435810301
[25] Chen L C and Sun J Q2020 Appl. Math. Mech. 41 967
[26] Li J Y, Wang Y, Jin X L and Huang Z L2021 Nonlinear Dynam. 105 1297
[27] Yang J N, Liu J G and Guo Q2018 Acta Phys. Sin. 67 048901 (in Chinese)
[28] Wang X Y, Wang Y, Qin X M, Li R and Eustace J2018 Chin. Phys. B 27 100504
[29] Jin L, Wang X J, Zhang Y and You J W2018 Chin. Phys. B 27 98901
[30] Luo S L, Gong K, Tang C S and Zhou J2017 Acta Phys. Sin. 66 188902 (in Chinese)
[31] Sun J C2016 Chin. Phys. Lett. 33 100503
[32] Fang P J, Zhang D M and He M H2015 Chin. Phys. Lett. 32 88901
[33] Gao S G, Dong H R, Sun X B and Ning B2015 Chin. Phys. B 24 10501
[34] Chen H, Kong L and Leng W J2011 Appl. Soft Comput. 11 855
[35] Mai-Duy N and Tanner R I2005 Int. J. Numer. Meth. Eng. 63 1636
[36] Li J Y, Luo S W, Qi Y J and Huang Y P2003 Neural Netw. 16 729
[37] Wang X, Jiang J, Hong L and Sun J Q2022 J. Vib. Acoust. 144 051014
[38] Wang X, Jiang J, Hong L and Sun J Q2022 Int. J. Dynam. Control 10 1385
[39] Er G K2011 Ann. Phys. 523 247
[40] Nelles O2020 Nonlinear system identification, 2nd edn. (Cham: Springer Nature) pp. 831-891
[41] Chen J B and Li J2008 Int. J. Numer. Meth. Eng. 74 1988
[42] Zhu W Q, Huang Z L and Yang Y Q1997 J. Appl. Mech. 64 975

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

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

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Linghongzhi Lu(陆凌弘志), Yang Li(李扬), and Xianbin Liu(刘先斌). Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise[J]. 中国物理B, 2023, 32(5): 50501-050501.
[2]	Yun-Yun Yang(杨云云), Biao Feng(冯彪), Liao Zhang(张辽), Shu-Hong Xue(薛舒红), Xin-Lin Xie(谢新林), and Jian-Rong Wang(王建荣). Robustness measurement of scale-free networks based on motif entropy[J]. 中国物理B, 2022, 31(8): 80201-080201.
[3]	Yong Huang(黄勇) and Yang Li(李扬). Data-driven modeling of a four-dimensional stochastic projectile system[J]. 中国物理B, 2022, 31(7): 70501-070501.
[4]	Meili Liu(刘美丽), Xiaogang Qi(齐小刚), and Hao Pan(潘浩). Multifractal analysis of the software evolution in software networks[J]. 中国物理B, 2022, 31(3): 30501-030501.
[5]	Ru-Qi Li(李汝琦), Yu-Rong Song(宋玉蓉), and Guo-Ping Jiang(蒋国平). Prediction of epidemics dynamics on networks with partial differential equations: A case study for COVID-19 in China[J]. 中国物理B, 2021, 30(12): 120202-120202.
[6]	Dongli Duan(段东立), Tao Chai(柴涛), Xixi Wu(武茜茜), Chengxing Wu(吴成星), Shubin Si(司书宾), and Genqing Bian(边根庆). Identification of unstable individuals in dynamic networks[J]. 中国物理B, 2021, 30(9): 90501-090501.
[7]	Xiaodong Liu(柳晓东) and Lipo Mo(莫立坡). Consensus problems on networks with free protocol[J]. 中国物理B, 2021, 30(7): 70701-070701.
[8]	Jian-Long Wang(王剑龙), Xiao-Lei Leng(冷小磊), and Xian-Bin Liu(刘先斌). Stationary response of colored noise excited vibro-impact system[J]. 中国物理B, 2021, 30(6): 60501-060501.
[9]	Zi-Wei Yuan(袁紫薇), Chang-Chun Lv(吕长春), Shu-Bin Si(司书宾), and Dong-Li Duan(段东立). Dynamical robustness of networks based on betweenness against multi-node attack[J]. 中国物理B, 2021, 30(5): 50501-050501.
[10]	. [J]. 中国物理B, 2021, 30(3): 38901-.
[11]	陈侠, 尹立远, 刘永泰, 刘皓. Hybrid-triggered consensus for multi-agent systems with time-delays, uncertain switching topologies, and stochastic cyber-attacks[J]. 中国物理B, 2019, 28(9): 90701-090701.
[12]	方木云, 周灿灿, 黄鑫, 李晓, 周建平. H_∞ couple-group consensus of stochastic multi-agent systems with fixed and Markovian switching communication topologies[J]. 中国物理B, 2019, 28(1): 10703-010703.
[13]	刘晓, 王进法, 景薇, Menno de Jong, Jeroen S Tummers, 赵海. Evolution of the Internet AS-level topology:From nodes and edges to components[J]. 中国物理B, 2018, 27(12): 120501-120501.
[14]	徐伟, 王亮, 冯进钤, 乔艳, 韩平. Some new advance on the research of stochastic non-smooth systems[J]. 中国物理B, 2018, 27(11): 110503-110503.
[15]	王兴元, 王宇, 秦小蒙, 李睿, Justine Eustace. Detecting overlapping communities based on vital nodes in complex networks[J]. 中国物理B, 2018, 27(10): 100504-100504.