The Use of Uniform Design and Nelder-Mead Simplex Methods to Optimization of Suspension Parameters of a High Speed Railway Vehicle System

Abstract:

This paper has proposed an optimization process with two phases to optimize suspension parameters of a high speed railway vehicle for advancing system’s robustness and performance. The vehicle’s nonlinear coupled differential equations of motion with fourteen degrees of freedom are created based on Kalker’s linear theory and the heuristic nonlinear creep model. The performance measure of the vehicle system is critical hunting speed, which is determined by Lyapunov’s indirect method. The first phase of optimization is to execute a set of experiments which is planned based on uniform design method. The second phase of optimization is to apply the Nelder-Mead Simplex method to exploit the best solution obtained in the first phase. Finally, the presented optimization process can effectively not only advance the performance of the vehicle system but also increase the performance’s robustness.

• Periodical: Advanced Materials Research (Volumes 488-489)
• Pages: 1257-1262
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.488-489.1257
• Online since: March 2012
• Authors: Yung Chang Cheng, Cheng Kang Lee
• Keywords: Critical Hunting Speed, Heuristic Nonlinear Creep Model, Nelder-Mead Simplex Method, Uniform Design

References

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DOI: 10.1115/1.2775515

[3] Y.C. Cheng and C.K. Lee: Integration of Uniform Design and Kriging Interpolation to the Optimization of Suspension Parameters of a High Speed Railway Vehicle. International Conference on Modelling, Identification and Control, Okayama, Japan (2010).

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[1] [2] [3] [4] [5] [6] [1] [1] [2] [3] [5] [7] [10] [2] [2] [4] [6] [10] [3] [9] [3] [3] [6] [9] [4] [10] [8] [4] [4] [8] [1] [9] [6] [7] [5] [5] [10] [4] [3] [2] [6] [6] [6] [1] [7] [8] [9] [5] [7] [7] [3] [10] [2] [5] [4] [8] [8] [5] [2] [7] [1] [3] [9] [9] [7] [5] [1] [8] [2] [10] [10] [9] [8] [6] [4] [1] [11] [11] [11] [11] [11] [11] [11] Table 2 Upper and lower bounds of suspension parameters Bound (N/m) (N/m) (N/m) (N/m) (N-s/m) (N-s/m) Upper 1200000 1200000 150000 150000 150000 150000 Lower 400000 400000 5000 4000 5000 5000 Table 3 The experiments planned based on Exp.

DOI: 10.7717/peerj-cs.805/table-11

[1] 400000 480000 34000 62400 92000 135500.

[2] 480000 640000 77500 135400 34000 121000.

[3] 560000 800000 121000 47800 135500 106500.

[4] 640000 960000 5000 120800 77500 92000.

[5] 720000 1120000 48500 33200 19500 77500.

[6] 800000 400000 92000 106200 121000 63000.

[7] 880000 560000 135500 18600 63000 48500.

[8] 960000 720000 19500 91600 5000 34000.

[9] 1040000 880000 63000 4000 106500 19500.

[10] 1120000 1040000 106500 77000 48500 5000.

[11] 1200000 1200000 150000 150000 150000 150000 Table 4 Results of experiments Exp. V1 (km/h) (l=0. 05) V2(km/h) (l=0. 07) V3(km/h) (l=0. 1) SNR 100/SNR.

DOI: 10.1177/237455680430.n2

[1] [92] [75] [60] 37. 18434 2. 68930.

[2] [88] [74] [61] 37. 13325 2. 69300.

[3] 304 322 286 49. 62695 2. 01503.

[4] 279 297 320 49. 46294 2. 02172.

[5] 278 293 316 49. 38019 2. 02510.

[6] 308 329 316 50. 02986 1. 99881.

[7] 322 336 347 50. 48866 1. 98064.

[8] 304 301 255 49. 06150 2. 03826.

[9] 337 346 350 50. 73630 1. 97098.

[10] 339 325 301 50. 11642 1. 99535.

[11] 273 276 282 48. 84723 2. 04720 Table 5 Optimal solution of suspension parameters (N/m) (N/m) (N/m) (N/m) (N-s/m) (N-s/m) 962031. 9 931072. 4 14363. 58 6947. 386 147128. 9 2455. 388 Table 6 Critical hunting speeds after optimization V1 (km/h) (l=0. 05) V2 (km/h) (l=0. 07) V3 (km/h) (l=0. 1) SNR 100/SNR 370 376 377 51. 46428 1. 9431.