Dynamic response uncertainty analysis of vehicle-track coupling system with fuzzy variables

다국어 초록 (Multilingual Abstract)

Dynamic analysis of a vehicle-track coupling system is important to structural design, damage detection and condition assessment of the structural system. Deterministic analysis of the vehicle-track coupling system has been extensively studied in the past, however, the structural parameters of the coupling system have uncertainties in engineering practices. It is essential to treat the parameters of the vehicle-track coupling system with consideration of uncertainties. In this paper, a method for predicting the bounds of the vehicle-track coupling system responses with uncertain parameters is presented. The uncertain system parameters are modeled as fuzzy variables instead of conventional random variables with known probability distributions. Then, the dynamic response functions of the coupling system are transformed into a component function based on the high dimensional representation approximation. The Lagrange interpolation method is used to approximate the component function. Finally, the bounds of the system’s dynamic responses can be predicted by using Monte Carlo method for the interpolation polynomials of the Lagrange interpolation function. A numerical example is introduced to illustrate the ability of the proposed method to predict the bounds of the system’s dynamic responses, and the results are compared with the direct Monte Carlo method. The results show that the proposed method is effective and efficient to predict the bounds of the system’s dynamic responses with fuzzy variables.

참고문헌 (Reference)

1 Sobol, I. M., "Theorems and examples on high dimensional model representation" 79 (79): 187-193, 2003

2 Hua-Peng Chen, "Symptom-based reliability analyses and performance assessment of corroded reinforced concrete structures" 국제구조공학회 53 (53): 1183-1200, 2015

3 Chen, H. P., "Structural Health Monitoring of Large Civil Engineering Structures" John Wiley and Sons 2018

4 Hua-Peng Chen, "Stochastic modelling fatigue crack evolution and optimum maintenance strategy for composite blades of wind turbines" 국제구조공학회 63 (63): 703-712, 2017

5 Tannert, T., "Probabilistic models for structural performance of rounded dovetail joints" 139 (139): 1479-1488, 2013

6 Wang, X. J., "Probabilistic damage identification of structures with uncertainty based on dynamic responses" 27 (27): 172-180, 2014

7 Zou, Q., "Predicting the bounds of vehicle-induced bridge responses using the interval analysis method" 21 (21): 04016046-, 2016

8 Ye, L., "Parameter identification of vehicle-track coupling system based on sensitivity analysis" 36 (36): 154-160, 2019

9 Li, X., "On product of positive L-R fuzzy numbers and its application to multi-period portfolio selection problems" 19 : 53-79, 2020

10 Wang, C., "Novel model calibration method via non-probabilistic interval characterization and Bayesian theory" 183 : 84-92, 2019

11 Liu, N., "Interval dynamic response analysis of vehicle-bridge interaction system with uncertainty" 332 (332): 3218-3231, 2013

12 Moore, R. E., "Interval Analysis" Prentice-Hall 1966

13 Degrauwe, D., "Improving interval analysis in finite element calculations by means of affine arithmetic" 88 (88): 247-254, 2010

14 Ma, Y., "Hybird uncertainty quantification for probabilistic corrosion damage prediction for aging RC bridges" 27 (27): 04014152-, 2014

15 Li, G., "High dimensional model representations" 105 (105): 7765-7777, 2001

16 Adhikari, S., "High dimensional model representation method for fuzzy structure dynamics" 330 (330): 1516-1529, 2011

17 Chowdhury, R., "High dimensional model representation for piece wise continuous function approximation" 24 (24): 1587-1609, 2008

18 Balu, A. S., "High dimensional model representation based formulations for fuzzy finite element analysis of structures" 50 : 217-230, 2012

19 Farkas, L., "Fuzzy finite element analysis based on reanalysis technique" 32 (32): 442-448, 2010

20 Wang, C., "Fuzzy finite difference method for heat conduction analysis with uncertain parameters" 30 : 383-390, 2014

21 Qiu, Z. P., "Eigenvalue bounds of structures with uncertain-but-bounded parameters" 282 (282): 297-312, 2005

22 Alis, O. F., "Efficient implementation of high dimensional model representations" 29 (29): 127-142, 2001

23 Deng, L., "Development of dynamic impact factor for performance evaluation of existing multi-girder concrete bridges" 32 (32): 21-31, 2010

24 Hinke, L., "Component mode synthesis as a framework for uncertainty analysis" 324 (324): 161-178, 2009

25 Obrien, E. J., "Characteristic dynamic increment for extreme traffic loading events on short and medium span highway bridges" 32 (32): 3827-3835, 2010

26 Manson, G., "Calculating frequency response functions for uncertain systems using complex affine analysis" 288 (288): 487-521, 2005

27 De, M. M., "An efficient response surface based optimization method for non-deterministic harmonic and transient dynamic analysis" 47 (47): 119-166, 2009

28 De, M. M., "A response surface based optimization algorithm for the calculation of fuzzy envelope frfs of models with uncertain properties" 86 (86): 1080-1092, 2008

29 Doan, L. T. T., "A comprehensive reverse supply chain model using an interactive fuzzy approach-A case study on the Vietnamese electronics industry" 76 : 87-108, 2019