A stochastic surrogate model for time-variant reliability analysis of flexible multibody system
Linjie Kan1, Jianguo Zhang2, Qian Wang3
Science and Technology on Reliability and Environmental Engineering Laboratory, Beihang University, Beijing, P. R. China
E-mail: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
Abstract. The dynamic model of the flexible multibody systems (FMS) is usually the differential equations with time-variant, high nonlinear and strong coupling characteristics. The traditional reliability models are inefficient to solve these problems. And the reliability model is poor in accuracy and computational efficiency. Based on this point, a new stochastic surrogate model for time-variant reliability analysis of FMS is proposed. Combined model order reduction with generalized polynomial chaos, the stochastic surrogate model is established and the statistical characteristics of system responses are obtained. The calculation method of kinematic time-variant reliability is given. Finally, the effectiveness of the method is verified by a rotating flexible beam. The results show that this method has high computational accuracy compared with Monte Carlo method.
Keywords: flexible multibody system, time-variant reliability analysis, stochastic surrogate model, generalized polynomial chaos, model order reduction.
 Sandu A., Sandu C., Ahmadian M. Modeling multibody systems with uncertainties. Part I: Theoretical and computational aspects. Multibody System Dynamics, Vol. 15, Issue 4, 2006, p. 369‑391.
 Xu W., Zhang Q. Probabilistic analysis and Monte Carlo simulation of the kinematic error in a spatial linkage. Mechanism and Machine Theory, Vol. 24, Issue 1, 1989, p. 19‑27.
 Wang J., Zhang J., Du X.P. Hybrid dimension reduction for mechanism reliability analysis with random joint clearances. Mechanism and Machine Theory, Vol. 46, Issue 10, 2011, p. 1396‑1410.
 Hu Z., Du X. P. Time-dependent reliability analysis with joint upcrossing rates. Structural and Multidisciplinary Optimization, Vol. 48, Issue 5, 2013, p. 893‑907.
 Hu Z., Du X. P. First order reliability method for time-variant problems using series expansions. Structural and Multidisciplinary Optimization, Vol. 51, Issue 1, 2015, p. 1‑21.
 Zhang C. Y., Bai G. C. Extremum response surface method of reliability analysis on two-link flexible robot manipulator. Journal of Central South University, Vol. 18, Issue 1, 2012, p. 101‑107.
 Xiao J., He L., Huang H. Z., Zhang X., Wang Z. Reliability analysis of elastic link mechanism based on BP neural network. International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering, Chengdu, China, 2012, p. 286‑289.
 Ke X. W., Hou J., Chen T. F. Reliability analysis for link mechanism under influence of multiple factors based on support vector machine. Advanced Materials Research, Vol. 753, Issue 755, 2013, p. 2904‑2907.
 Shi W. S., Guo J. B., Zeng S. K., Ma J. M. A mechanism reliability analysis method based on polynomial chaos expansion. 9th International Conference on Reliability, Maintainability and Safety, Guiyang, China, 2011, p. 110‑115.
 Xiu D. B., Karniadakis G. E. The Wiener-Askey polynomial chaos for stochastic differential equations. Society for Industrial and Applied Mathematics, Vol. 24, Issue 2, 2002, p. 619‑644.
 Wu J. L., Luo Z., Zhang N., Zhang Y. Q. Dynamic computation of flexible multibody system with uncertain material properties. Nonlinear Dynamics, Vol. 85, Issue 2, 2016, p. 1231‑1254.
 Guo J. B., Wang Y., Zeng S. K. Nonintrusive-polynomial-chaos-based kinematic reliability analysis for mechanisms with mixed uncertainty. Advances in Mechanical Engineering, Vol. 10, 2014, p. 1‑12.
 Wu L., Tiso P. Nonlinear model order reduction for flexible multibody dynamics: a modal derivatives approach. Multibody System Dynamics, Vol. 36, Issue 4, 2016, p. 405‑425.
 Holzwarth P., Eberhard P. SVD-based improvements for component mode synthesis in elastic multibody systems. European Journal of Mechanics A/Solids, Vol. 49, 2015, p. 408‑418.
 Sarsri D., Azrar L., Jebbouri A., Hami A. E. Component mode synthesis and polynomial chaos expansions for stochastic frequency functions of large linear FE models. Computers and Structures, Vol. 89, Issue 3, 2011, p. 346‑356.
 Mejri M., Cazuguel M., Cognard J. Y. A time-variant reliability approach for ageing marine structures with non-linear behavior. Computers and Structures, Vol. 89, Issues 19‑20, 2011, p. 1743‑1753.
Cite this article
Kan Linjie, Zhang Jianguo, Wang Qian A stochastic surrogate model for time‑variant reliability analysis of flexible multibody system. Vibroengineering PROCEDIA, Vol. 14, 2017, p. 340‑346.
© JVE International Ltd. Vibroengineering PROCEDIA. Oct 2017, Vol. 14. ISSN 2345-0533