Research Papers

Global Sensitivity Analysis for Vehicle–Track Interactions: Special Attention on Track Irregularities

[+] Author and Article Information
Lei Xu

Train and Track Research Institute,
Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu 610031, China;
Section of Railway Engineering,
Delft University of Technology,
Delft 2628LV, The Netherlands

Wanming Zhai

Train and Track Research Institute,
Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu 610031, China
e-mail: wmzhai@swjtu.edu.cn

Jianmin Gao

Train and Track Research Institute,
Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu 610031, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 6, 2017; final manuscript received December 12, 2017; published online January 10, 2018. Assoc. Editor: Xiaobo Yang.

J. Comput. Nonlinear Dynam 13(3), 031007 (Jan 10, 2018) (12 pages) Paper No: CND-17-1407; doi: 10.1115/1.4038820 History: Received September 06, 2017; Revised December 12, 2017

The dynamic vehicle–track interactions are complex processes due to the highly nonlinear terms and spatially varying excitations in vehicle design, track maintenance, dynamic prediction, etc. Therefore, it is of importance to clarify the key factors affecting the dynamic behaviors of system components. In this paper, a comprehensive model is presented, which is capable of analyzing the global sensitivity of vehicle–track interactions. In this model, the vehicle–track interactions considering the nonlinear wheel–rail contact geometries are depicted in three-dimensional (3D) space, and then the approaches for global sensitivity analysis (GSA) and time–frequency analysis are combined with the dynamic model. In comparison to the local sensitivity analysis, the proposed model has accounted for the coupling contributions of various factors. Thus, it is far more accurate and reliable to evaluate the critical factors dominating the vehicle–track interactions. Based on the methods developed in the present study, numerical examples have been conducted to draw the following marks: track irregularities possess the dominant role in guiding the dynamic performance of vehicle–track systems, besides, the vertical stiffness of primary suspension and rail pads also shows significant influence on vertical acceleration of the car body and the wheel–rail vertical force, respectively. Finally, a method is developed to precisely extract the characteristic wavelengths and amplitude limits of track irregularities.

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Zhai, W. , and Sun, X. , 1993, “Analysis and Design of Vertical Dynamic Parameters of Wheel/Rail System With Low Dynamic Interactions,” J. China Railway Soc., 15(3), pp. 1–10.
Zhai, W. , and Sun, X. , 1994, “A Detailed Model for Investigating Vertical Interaction Between Railway Vehicle and Track,” Veh. Syst. Dyn., 23(Suppl. 1), pp. 603–615. [CrossRef]
Kaewunruen, S. , and Remennikov, A. M. , 2006, “Sensitivity Analysis of Free Vibration Characteristics of an In Situ Railway Concrete Sleeper to Variations of Rail Pad Parameters,” J. Sound Vib., 298, pp. 453–461. [CrossRef]
Ilias, H. , 1999, “The Influence of Railpad Stiffness on Wheelset/Track Interaction and Corrugation Growth,” J. Sound Vib., 227, pp. 935–948. [CrossRef]
Kumaran, G. , Menon, D. , and Krishman Nair, K. , 2003, “Dynamic Studies of Railtrack Sleepers in a Track Structure System,” J. Sound Vib., 268, pp. 485–501. [CrossRef]
Suarez, B. , Felez, J. , Maroto, J. , and Rodriguez, P. , 2013, “Sensitivity Analysis to Assess the Influence of the Inertial Properties of Railway Vehicle Bodies on the Vehicle's Dynamic Behavior,” Veh. Syst. Dyn., 51(2), pp. 251–279. [CrossRef]
Zakeri, J. A. , Feizi, M. M. , Shadfar , M. , and Naeimi , M. , 2017, “Sensitivity Analysis on Dynamic Response of Railway Vehicle and Rid Index Over Curved Bridges,” Proc. Inst. Mech. Eng. Part K, 231(1), pp. 266–277.
Ferrara, R. , Leonardi, G. , and Jourdan, F. , 2013, “A Contact-Area Model for Rail-Pads Connections in 2-D Simulations: Sensitivity Analysis of Train-Induced Vibrations,” Veh. Syst. Dyn., 51(9), pp. 1342–1362. [CrossRef]
Haug, E. J. , Wehager, R. , and Bannan, N. C. , 1981, “Design Sensitivity Analysis of Planar Mechanism and Dynamics,” ASEM J. Mech. Des., 103, pp. 560–570. [CrossRef]
Eberhard, P. , and Dignath, F. , 2000, “Control Optimization of Multibody Systems Using Point- and Piecewise Defined Optimization Criteria,” Eng. Optim., 32(4), pp. 417–438.
Iman, R. L. , and Hora, S. C. , 1990, “A Robust Measure of Uncertainty Importance for Use in Fault Tree System Analysis,” Risk Anal., 10, pp. 401–406. [CrossRef]
Morris, M. D. , 1991, “Factorial Sampling Plans for Preliminary Computational Experiments,” Technometrics, 33, pp. 161–174. [CrossRef]
McKay, M. D. , 1996, “Variance-Based Methods for Assessing Uncertainty Importance,” Los Alamos National Laboratory, Los Alamos, NM, Report No. LA-UR-96-2695.
Sobol′, I. M. , 2001, “Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates,” Math. Comput. Simul., 55(1–3), pp. 271–280. [CrossRef]
Saltelli, A. , Tarantola, S. , and Chan, K. P.-S. , 1999, “A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output,” Technometrics, 41(1), pp. 39–56. [CrossRef]
Zhang, Y. , Zhang, W. , Ma, T. , and Tang, T. , 2015, “Optimization Design Method of Non-Linear Complex System Based on Global Sensitivity Analysis and Dynamic Moetamodel,” J. Mech. Eng., 51(4), pp. 126–131. [CrossRef]
Tian, W. , 2013, “A Review of Sensitivity Analysis Methods in Building Energy Analysis,” Renewable Sustainable Energy Rev., 20, pp. 411–419. [CrossRef]
Kiparissides, A. , Kucherenko, S. S. , Mantalaris, A. , and Pistikopoulos, E. N. , 2009, “Global Sensitivity Analysis Challenges in Biological Systems Modeling,” Ind. Eng. Chem. Res., 48(15), pp. 7168–7180. [CrossRef]
Centeno Drehmer, L. R. , Paucar Casas, W. J. , and Gomes, H. M. , 2015, “Parameters Optimization of a Vehicle Suspension System Using a Particle Swarm Optimization Algorithm,” Veh. Syst. Dyn., 53(4), pp. 449–474. [CrossRef]
Xu, L. , and Zhai, W. , 2017, “Stochastic Analysis Model for Vehicle-Track Coupled Systems Subject to Earthquakes and Track Random Irregularities,” J. Sound Vib., 407, pp. 209–225. [CrossRef]
Perrin, G. , Soize, C. , Duhamel, D. , and Funfschilling, C. , 2015, “Quantification of the Influence of the Track Geometry Variability on the Train Dynamics,” Mech. Syst. Signal Process., 60–61, pp. 945–957. [CrossRef]
Li, Z. , Zhao, X. , and Dollevoet, R. , 2017, “An Approach to Determine a Critical Size for Rolling Contact Fatigue Initiating From Rail Surface Defects,” Int. J. Rail Transp., 5(1), pp. 16–37. [CrossRef]
Wei, Z. , Li, Z. , Qian, Z. , Chen, R. , and Dollevoet, R. , 2016, “3D FE Modelling and Validation of Frictional Contact With Partial Slip in Compression-Shift-Rolling Evolution,” Int. J. Rail Transp., 4(1), pp. 20–36. [CrossRef]
Zhai, W. , 2015, Vehicle-Track Coupled Dynamics, 4th ed., Science Press, Beijing, China.
Xu, L. , and Zhai, W. , 2017, “A New Model for Temporal-Spatial Stochastic Analysis of Vehicle-Track Coupled Systems,” Veh. Syst. Dyn., 55(3), pp. 427–448. [CrossRef]
Xu, L. , and Zhai, W. , 2017, “A Novel Model for Determining the Amplitude-Wavelength Limits of Track Irregularities Accompanied by a Reliability Assessment in Railway Vehicle-Track Dynamics,” Mech. Syst. Signal Process., 86, pp. 260–277. [CrossRef]
Zeng, Q. Y. , 2000, “The Principle of a Stationary Value of Total Potential Energy of Dynamic System,” J. Huazhong Univ. Sci. Technol., 28(1), pp. 1–3. http://en.cnki.com.cn/Article_en/CJFDTOTAL-HZLG200001000.htm
Shen, Z. Y. , Hedrick, J. K. , and Elkins, J. A. , 1983, “A Comparison of Alternative Creep Force Models for Rail Vehicle Dynamic Analysis,” Eighth IAVSD Symposium, Cambridge, MA, Aug. 15–19, pp. 591–605.
Chen, G. , and Zhai, W. M. , 2004, “A New Wheel/Rail Spatially Dynamic Coupling Model and Its Verification,” Veh. Syst. Dyn., 41(4), pp. 301–322. [CrossRef]
Cukier, R. I. , Fortuin, C. M. , Shuler, K. E. , Petschek, A. G. , and Schaibly, J. H. , 1973, “Study of the Sensitivity of Coupled Reaction Systems to Uncertainties in Rate Coefficients. I. Theory,” J. Chem. Phys., 59(8), pp. 3873–3878. [CrossRef]
Schaibly, J. H. , and Shuler, K. E. , 1973, “Study of the Sensitivity of Coupled Reaction Systems to Uncertainties in Rate Coefficients: Part II—Applications,” J. Chem. Phys., 59, pp. 3879–3888. [CrossRef]
Wely, H. , 1938, “Mean Motion,” Am. J. Math., 60, pp. 89–896.
Saltelli, A. , Annoni, P. , Azzini, I. , Campolongo, F. , Ratto, M. , and Tarantola, S. , 2010, “Variance Based Sensitivity Analysis of Model Output. Design and Estimator for the Total Sensitivity Index,” Comput. Phys. Commun., 181, pp. 259–270. [CrossRef]
Xu, L. , Zhai, W. , and Gao, J. , 2017, “A Probabilistic Model for Track Random Irregularities in Vehicle/Track Coupled Dynamics,” Appl. Math. Modell., 51, pp. 145–158. [CrossRef]
Xu, L. , and Chen, X. , 2014, “Analysis on Track Characteristic Irregularity Based on Wavelet and Wigner-Hough Transform,” J. China Railway Soc., 36(5), pp. 88–95.
Wang, M. , and Shao, M. , 1997, Finite Element Method: Basic Principle and Numerical Method, 2nd ed., Tsinghua University Press, Beijing, China.


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Fig. 1

3D vehicle–slab track coupled model: (a) side view and (b) end view. 1—car body; 2—bogie frame; 3—wheelset; 4—rail irregularities; 5—rails; 6—rail pads; 7—track slabs; 8—CA mortar; and 9—subgrade; ξi, i=1,2,3,4, denotes the distance between the ith wheel/rail contact point and the left node of the rail beam element.

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Fig. 2

Wheel–rail coupling model with consideration of rail vibrations. ORspatial contact point; B—center of the rolling circle; A—intersection point between normal line of contact point and wheel central line; Oworigin of the wheelset coordinate system; OR′,B′,A′, and Ow′ represent the projective points of OR, B, A, and Ow at O-X-Y-Z plane; and Ow″ is the projective point of Ow′ at O-Y axis.

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Fig. 3

Representation of track irregularities [34]

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Fig. 4

Illustrative framework for GSA of vehicle–track interactions

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Fig. 5

Sensitivity indices of input factors with regard to wheel–rail vertical force: (a) FOSI against time, (b) average FOSI, and (c) average total effect index

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Fig. 6

Sensitivity indices of input factors with regard to wheel–rail lateral force: (a) FOSI against time, (b) average FOSI, and (c) average total effect index

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Fig. 7

Average sensitivity indices for different dynamic indices: (a) lateral acceleration of the car body, (b) vertical acceleration of the car body, (c) railpad lateral force, and (d) railpad vertical force. Abscissa description: 1 − γ1, 2 − γ2, 3 − γ3, 4 − γ4, 5 − kpy, 6 − kpz, 7 − krp,y, and 8 − krp,z.

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Fig. 8

Key information for wheel–rail vertical force: (a) assemblage of dynamic responses, (b) the FOSI with respect to the maximum wheel–rail vertical force, and (c) track vertical profile irregularity including the local irregularities inducing the maximum response

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Fig. 9

Abstraction of the characteristic wavelength for the fourth-order detail signal after wavelet decomposition: (a) Wigner–Hough transform and (b) Wavelet–Wigner distribution

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Fig. 10

The relations between the maximum irregularity amplitude and the wheel–rail vertical force




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