Random vibration of hysteretic systems under Poisson white noise excitations

doi:10.1007/s10483-023-2941-6

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (2): 207-220.doi: https://doi.org/10.1007/s10483-023-2941-6

Random vibration of hysteretic systems under Poisson white noise excitations

Lincong CHEN^1,2, Zi YUAN¹, Jiamin QIAN¹, J. Q. SUN³

1. College of Civil Engineering, Huaqiao University, Xiamen 361021, Fujian Province, China;
2. Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province, Xiamen 361021, Fujian Province, China;
3. Department of Mechanical Engineering, School of Engineering, University of California, Merced, CA 95343, U.S.A.

收稿日期:2022-07-16 修回日期:2022-09-14 发布日期:2023-02-04
通讯作者: J. Q. SUN, E-mail: jqsun@ucmerced.edu
基金资助:
the National Natural Science Foundation of China (No. 12072118), the Natural Science Funds for Distinguished Young Scholar of Fujian Province of China (No. 2021J06024), and the Project for Youth Innovation Fund of Xiamen of China (No. 3502Z20206005)

Random vibration of hysteretic systems under Poisson white noise excitations

Lincong CHEN^1,2, Zi YUAN¹, Jiamin QIAN¹, J. Q. SUN³

1. College of Civil Engineering, Huaqiao University, Xiamen 361021, Fujian Province, China;
2. Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province, Xiamen 361021, Fujian Province, China;
3. Department of Mechanical Engineering, School of Engineering, University of California, Merced, CA 95343, U.S.A.

Received:2022-07-16 Revised:2022-09-14 Published:2023-02-04
Contact: J. Q. SUN, E-mail: jqsun@ucmerced.edu
Supported by:
the National Natural Science Foundation of China (No. 12072118), the Natural Science Funds for Distinguished Young Scholar of Fujian Province of China (No. 2021J06024), and the Project for Youth Innovation Fund of Xiamen of China (No. 3502Z20206005)

摘要/Abstract

摘要： Hysteresis widely exists in civil structures, and dissipates the mechanical energy of systems. Research on the random vibration of hysteretic systems, however, is still insufficient, particularly when the excitation is non-Gaussian. In this paper, the radial basis function (RBF) neural network (RBF-NN) method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations. The solution to the reduced generalized Fokker-PlanckKolmogorov (GFPK) equation is expressed in terms of the RBF-NNs with the Gaussian activation functions, whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition. A steel fiber reinforced ceramsite concrete (SFRCC) column loaded by the Poisson white noise is studied as an example to illustrate the solution process. The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated, and the obtained results are compared with those obtained by the Monte Carlo simulations (MCSs). The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.

关键词: random vibration, Bouc-Wen hysteresis system, non-Gaussian excitation, Poisson white noise excitation, radial basis function (RBF) neural network (RBF-NN)

Abstract: Hysteresis widely exists in civil structures, and dissipates the mechanical energy of systems. Research on the random vibration of hysteretic systems, however, is still insufficient, particularly when the excitation is non-Gaussian. In this paper, the radial basis function (RBF) neural network (RBF-NN) method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations. The solution to the reduced generalized Fokker-PlanckKolmogorov (GFPK) equation is expressed in terms of the RBF-NNs with the Gaussian activation functions, whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition. A steel fiber reinforced ceramsite concrete (SFRCC) column loaded by the Poisson white noise is studied as an example to illustrate the solution process. The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated, and the obtained results are compared with those obtained by the Monte Carlo simulations (MCSs). The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.

Key words: random vibration, Bouc-Wen hysteresis system, non-Gaussian excitation, Poisson white noise excitation, radial basis function (RBF) neural network (RBF-NN)

中图分类号:

Lincong CHEN, Zi YUAN, Jiamin QIAN, J. Q. SUN. Random vibration of hysteretic systems under Poisson white noise excitations[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(2): 207-220.

参考文献

[1] WANG, T. and ZHU, Z. W. A new type of nonlinear hysteretic model for magnetorheological elastomer and its application. Materials Letters, 301, 130176(2021)
[2] GOODARZ, A. Stochastic earthquake response of structures on sliding foundation. International Journal of Engineering Science, 21(2), 93–102(1983)
[3] SALVATORE, A., CARBONI, B., CHEN, L. Q., and LACARBONARA, W. Nonlinear dynamic response of a wire rope isolator: experiment, identification and validation. Engineering Structures, 238, 112121(2021)
[4] KITAMURA, K. Shape memory properties of Ti-Ni shape memory alloy/shape memory polymer composites using additive manufacturing. Materials Science Forum, 1016, 697–701(2021)
[5] YE, J., YAN, G., LIU, R., XUE, P., and WANG, D. Hysteretic behavior of replaceable steel plate damper for prefabricated joint with earthquake resilience. Journal of Building Engineering, 46, 103714(2022)
[6] ISMAIL, M., IKHOUANE, F., and RODELLAR, J. The hysteresis Bouc-Wen model, a survey. Archives of Computational Methods in Engineering, 16(2), 161–188(2009)
[7] JIANG, K., WEN, J., HAN, Q., and DU, X. Identification of nonlinear hysteretic systems using sequence model-based optimization. Structural Control and Health Monitoring, 27(4), 2500(2020)
[8] YING, Z. Response analysis of randomly excited nonlinear systems with symmetric weighting preisach hysteresis. Acta Mechanica Sinica, 19(4), 365–370(2003)
[9] YING, Z. G., ZHU, W. Q., NI, Y. Q., and KO, J. M. Random response of Preisach hysteretic systems. Journal of Sound and Vibration, 254(1), 37–49(2002)
[10] IWAN, W. D. and LUTES, L. D. Response of the bilinear hysteretic system to stationary random excitation. The Journal of the Acoustical Society of America, 43(3), 545–552(1968)
[11] CAUGHEY, T. K. Random excitation of a system with bilinear hysteresis. Journal of Applied Mechanics, 27(4), 649–652(1960)
[12] WEN, Y. K. Method for random vibration of hysteretic systems. Journal of the Engineering Mechanics Division, 102(2), 249–263(1976)
[13] LIU, J., CHEN, L., and SUN, J. Q. The closed-form solution of steady state response of hysteretic system under stochastic excitation. Chinese Journal of Theoretical and Applied Mechanics, 49(3), 685–692(2017)
[14] GUO, S. S., SHI, Q., and XU, Z. D. Stochastic responses of nonlinear systems to nonstationary non-Gaussian excitations. Mechanical Systems and Signal Processing, 144, 106898(2020)
[15] LIU, W., GUO, Z., and YIN, X. Stochastic averaging for SDOF strongly nonlinear system under combined harmonic and Poisson white noise excitations. International Journal of Non-Linear Mechanics, 126, 103574(2020)
[16] VASTA, M. and LUONGO, A. Dynamic analysis of linear and nonlinear oscillations of a beam under axial and transversal random Poisson pulses. Nonlinear Dynamics, 36(2-4), 421–435(2004)
[17] YANG, G., XU, W., HUANG, D., and HAO, M. Stochastic responses of lightly nonlinear vibroimpact system with inelastic impact subjected to external Poisson white noise excitation. Mathematical Problems in Engineering, 2018, 1–12(2018)
[18] ZHU, H. T., ER, G. K., IU, V. P., and KOU, K. P. Probability density function solution of nonlinear oscillators subjected to multiplicative Poisson pulse excitation on velocity. Journal of Applied Mechanics, 77(3), 1–7(2010)
[19] IWANKIEWICZ, R. and NIELSEN, S. R. K. Dynamic response of hysteretic systems to Poissondistributed pulse trains. Probabilistic Engineering Mechanics, 7(3), 135–148(1992)
[20] ZENG, Y. and LI, G. Stationary response of bilinear hysteretic system driven by Poisson white noise. Probabilistic Engineering Mechanics, 33, 135–143(2013)
[21] LAGARIS, I. E., LIKAS, A. C., and PAPAGEORGIOU, D. G. Neural-network methods for boundary value problems with irregular boundaries. IEEE Transactions on Neural Networks, 11(5), 1041–1049(2000)
[22] LAGARIS, I. E., LIKAS, A., and FOTIADIS, D. I. Artificial neural networks for solving ordinary and partial differential equations. IEEE Transactions on Neural Networks, 9(5), 987–1000(1998)
[23] MEADE, A. J. and FERN, A. A. Solution of nonlinear ordinary differential equations by feedforward neural networks. Mathematical & Computer Modelling, 20(12), 1–25(1994)
[24] LU, L., MENG, X., MAO, Z., and KARNIADAKIS, G. E. DeepXDE: a deep learning library for solving differential equations. SIAM Review, 63(1), 208–228(2021)
[25] RAISSI, M., PERDIKARIS, P., and KARNIADAKIS, G. E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707(2019)
[26] PISCOPO, M. L., SPANNOWSKY, M., and WAITE, P. Solving differential equations with neural networks: applications to the calculation of cosmological phase transitions. Physical Review D, 100(1), 016002(2019)
[27] RAISSI, M. and KARNIADAKIS, G. E. Hidden physics models: machine learning of nonlinear partial differential equations. Journal of Computational Physics, 357, 125–141(2018)
[28] GAO, H., ZAHR, M. J., and WANG, J. X. Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse problems. Computer Methods in Applied Mechanics and Engineering, 390, 114502(2022)
[29] WEINAN, E., HAN, J., and JENTZEN, A. Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning. Nonlinearity, 35(1), 278(2021)
[30] HAN, J., JENTZEN, A., and WEINAN, E. Solving high-dimensional partial differential equations using deep learning. Proceedings of the National Academy of Sciences, 115(34), 8505–8510(2018)
[31] WEINAN, E. and YU, B. The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems. Communications in Mathematics & Statistics, 6(1), 1–12(2018)
[32] ZANG, Y., BAO, G., YE, X., and ZHOU, H. Weak adversarial networks for high-dimensional partial differential equations. Journal of Computational Physics, 411, 109409(2019)
[33] KANSA, E. J. Multiquadrics — a scattered data approximation scheme with applications to computational fluid-dynamics — I surface approximations and partial derivative estimates. Computers & Mathematics with Applications, 19(8), 127–145(1990)
[34] KANSA, E. J. Multiquadrics — a scattered data approximation scheme with applications to computational fluid-dynamics — II solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers & Mathematics with Applications, 19(8), 147–161(1990)
[35] DEHGHAN, M. and MOHAMMADI, V. The numerical solution of Fokker-Planck equation with radial basis functions (RBFs) based on the meshless technique of Kansas approach and Galerkin method. Engineering Analysis with Boundary Elements, 47, 38–63(2014)
[36] GORBACHENKO, V. I. and ZHUKOV, M. V. Solving boundary value problems of mathematical physics using radial basis function networks. Computational Mathematics and Mathematical Physics, 57(1), 145–155(2017)
[37] KAZEM, S., RAD, J. A., and PARAND, K. Radial basis functions methods for solving FokkerPlanck equation. Engineering Analysis with Boundary Elements, 36(2), 181–189(2012)
[38] MIRZAEE, F., REZAEI, S., and SAMADYAR, N. Application of combination schemes based on radial basis functions and finite difference to solve stochastic coupled nonlinear time fractional sine-Gordon equations. Computational and Applied Mathematics, 41(1), 1–16(2022)
[39] WANG, X., JIANG, J., HONG, L., and SUN, J. Q. Random vibration analysis with radial basis function neural networks. International Journal of Dynamics and Control, 10, 1385–1394(2022)
[40] WANG, X., JIANG, J., HONG, L., and SUN, J. Q. First-passage problem in random vibrations with radial basis function neural networks. Journal of Vibration and Acoustics, 44, 051014(2022)
[41] ALQEZWEENI, M. M., GORBACHENKO, V. I., ZHUKOV, M. V., and JAAFAR, M. S. Efficient solving of boundary value problems using radial basis function networks learned by trust region method. International Journal of Mathematics and Mathematical Sciences, 2018, 1–4(2018)
[42] YE, L., LU, X., MA, Q., CHENG, G., SONG, S., MIAO, Z., and PAN, P. Study on the influence of post-yielding stiffness to seismic response of building structures. Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China (2008)
[43] JIA, W. T. and ZHU, W. Q. Stochastic averaging of quasi-partially integrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations. Physica A: Statistical Mechanics and Its Applications, 398, 125–144(2014)

Random vibration of hysteretic systems under Poisson white noise excitations

Random vibration of hysteretic systems under Poisson white noise excitations

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

编辑推荐

Metrics

本文评价

[1]	Lincong CHEN, Haisheng ZHU, J. Q. SUN. Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(12): 1759-1776.
[2]	赵雷;陈虬. AN EQUIVALENT NONLINEARIZATION METHOD FOR ANALYSING RESPONSE OF NONLINEAR SYSTEMS TO RANDOM EXCITATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(6): 551-561.