Suspension parameter identification method for rail transit vehicles using an AO-GRBF surrogate model and non-dominated sorting genetic algorithm

Abstract

The suspension systems of rail transit vehicles are crucial components that connect the vehicle body to the wheelsets, designed to reduce vibrations and shocks induced by track irregularities. During extended service periods, suspension parameters such as stiffness and damping coefficients are inevitably altered due to material aging and temperature fluctuations, rendering vehicle control strategies based on original design values ineffective. This leads to increased vibrations, hunting instability, and potential safety hazards during operation. Therefore, a suspension parameter identification method is proposed that combines an adaptively optimized Gaussian radial basis function (AO-GRBF) surrogate model with the non-dominated sorting genetic algorithm II (NSGA-II) to address these challenges. First, a mechanism- and data-driven AO-GRBF model is constructed to approximate the nonlinear relationship between suspension parameters and vehicle vibration responses, thereby overcoming the high computational cost associated with conventional multibody dynamics models. Then, the NSGA-II algorithm is employed to identify optimal suspension parameters by minimizing the deviation between AO-GRBF surrogate predictions and field-measured responses. Validation using field measurements indicates that the proposed method outperforms existing approaches, such as the radial basis function-high-dimensional model representation (RBF-HDMR) method and the long short-term memory (LSTM) method, in terms of correlation and error metrics related to lateral and vertical vibration accelerations.

Keywords

Multiobjective optimization / parameter identification / rail transit suspension systems / surrogate modeling / genetic algorithm

References

[1] Na J.,Huang Y.,Wu X.,Liu Y. J.,Li Y.,Li G.. Active suspension control of quarter-car system with experimental validation IEEE Trans. Syst. Man Cybern. Syst. 2022 52 4714 26

[2] Bai R.,Wang H. B.. Robust optimal control for the vehicle suspension system with uncertainties IEEE Trans. Cybern. 2022 52 9263 73

[3] Pan Y.,Sun Y.,Li Z.,Gardoni P.. Machine learning approaches to estimate suspension parameters for performance degradation assessment using accurate dynamic simulations Reliab. Eng. Syst. Saf. 2023 230 108950

[4] Jiang X.,Xu X.,Shi T.,Atindana V. A.. Nonlinear characteristic analysis of gas-interconnected quasi-zero stiffness pneumatic suspension system: a theoretical and experimental study Chin. J. Mech. Eng. 2024 37 58

[5] Liu J.,Du D.,He J.,Zhang C.. Prediction of remaining useful life of railway tracks based on DMGDCC-GRU hybrid model and transfer learning IEEE Trans. Veh. Technol. 2024 73 7561 75

[6] Zhang Y. W.,Zhao Y.,Zhang Y. H.,Lin J. H.,He X. W.. Riding comfort optimization of railway trains based on pseudo-excitation method and symplectic method J. Sound Vib. 2013 332 5255 70

[7] Bruni S.,Meijaard J. P.,Rill G.,Schwab A. L.. State-of-the-art and challenges of railway and road vehicle dynamics with multibody dynamics approaches Multibody Syst. Dyn. 2020 49 1 32

[8] Kraft S.,Puel G.,Aubry D.,Fünfśchilling C.. Parameter identification of multi-body railway vehicle models - application of the adjoint state approach Mech. Syst. Signal Process. 2016 80 517 32

[9] Yang Y.,Zeng W.,Qiu W. S.,Wang T.. Optimization of the suspension parameters of a rail vehicle based on a virtual prototype Kriging surrogate model Proc. Inst. Mech. Eng. 2016 230 1890 8

[10] Chen G.,Zhang K.,Xue X..et al. A radial basis function surrogate model assisted evolutionary algorithm for high-dimensional expensive optimization problems Appl. Soft Comput. 2022 116 108353

[11] Ni P.,Li J.,Hao H.,Zhou H.. Reliability based design optimization of bridges considering bridge-vehicle interaction by Kriging surrogate model Eng. Struct. 2021 246 112989

[12] Wei F. F.,Chen W. N.,Mao W.,Hu X. M.,Zhang J.. An efficient two-stage surrogate-assisted differential evolution for expensive inequality constrained optimization IEEE Trans. Syst. Man Cybern. Syst. 2023 53 7769 82

[13] Chen Q.,Zhang H.,Zhou H.,Sun J.,Tian Y.. Adaptive design of experiments for fault injection testing of highly automated vehicles IEEE Intell. Transp. Syst. Mag. 2024 16 35 52

[14] Zhang L.,Li T.,Zhang J.,Piao R.. Optimization on the crosswind stability of trains using neural network surrogate model Chin. J. Mech. Eng. 2021 34 86

[15] Zhang C.,Wang Y.,He J.. Suspension parameter estimation method for heavy-duty freight trains based on deep learning Big Data Cogn. Comput. 2024 8 181

[16] Jiang R.,Jin Z.,Liu D.,Wang D.. Multi-objective lightweight optimization of parameterized suspension components based on NSGA-II algorithm coupling with surrogate model Machines 2021 9 107

[17] Gu J.,Hua W.,Yu W.,Zhang Z.,Zhang H.. Surrogate model-based multiobjective optimization of high-speed permanent magnet synchronous machine: construction and comparison IEEE Trans. Transp. Electr. 2023 9 678 88

[18] Liu C.,Wan Z.,Liu Y.,Li X.,Liu D.. Trust-region based adaptive radial basis function algorithm for global optimization of expensive constrained black-box problems Appl. Soft Comput. 2021 105 107233

[19] Ye N.,Long T.,Shi R.,Wu Y.. Radial basis function-assisted adaptive differential evolution using cooperative dual-phase sampling for high-dimensional expensive optimization problems Struct. Multidiscip. Optim. 2022 65 241

[20] Yao Y.,Chen X.,Li H.,Li G.. Suspension parameters design for robust and adaptive lateral stability of high-speed train Veh. Syst. Dyn. 2023 61 943 67

[21] Tsattalios S.,Tsoukalas I.,Dimas P.,Kossieris P.,Efstratiadis A.,Makropoulos C.. Advancing surrogate-based optimization of time-expensive environmental problems through adaptive multi-model search Environ. Model. Softw. 2023 162 105639

[22] Hua C.,Jiang C.,Niu R..et al. Double neural networks enhanced global mobility prediction model for unmanned ground vehicles in off-road environments IEEE Trans. Veh. Technol. 2024 73 7547 60

[23] Tong H.,Huang C.,Minku L. L.,Yao X.. Surrogate models in evolutionary single-objective optimization: a new taxonomy and experimental study Inform. Sci. 2021 562 414 37

[24] Flores P.,Ambrósio J.,Lankarani H. M.. Contact-impact events with friction in multibody dynamics: back to basics Mech. Mach. Theory 2023 184 105305

[25] Millan P.,Pagaimo J.,Magalhães H.,Ambrósio J.. Clearance joints and friction models for the modelling of friction damped railway freight vehicles Multibody Syst. Dyn. 2023 58 21 45

[26] Zhou Y.,Mei T. X.,Freear S.. Real-time modeling of wheel-rail contact laws with system-on-chip IEEE Trans. Parallel Distrib. Syst. 2010 21 672 84

[27] Liu B.,Bruni S.. Comparison of wheel-rail contact models in the context of multibody system simulation: Hertzian versus non-Hertzian Veh. Syst. Dyn. 2022 60 1076 96

[28] Wu H.,Zeng X. H.,Lai J.,Yu Y.. Nonlinear hunting stability of high-speed railway vehicle on a curved track under steady aerodynamic load Veh. Syst. Dyn. 2020 58 175 97

[29] Sun J.,Meli E.,Song X.,Chi M.,Jiao W.,Jiang Y.. A novel measuring system for high-speed railway vehicles hunting monitoring able to predict wheelset motion and wheel/rail contact characteristics Veh. Syst. Dyn. 2023 61 1621 43

[30] Chen X.,Huang J.,Yi M.. Cost estimation for general aviation aircrafts using regression models and variable importance in projection analysis J. Clean. Prod. 2020 256 120648

[31] Zheng W.,Doerr B.. Approximation guarantees for the non-dominated sorting genetic algorithm II (NSGA-II) IEEE Trans. Evol. Comput. 2024 891 905

[32] Zhang D.,Li C.,Luo S..et al. Multi-objective control of residential HVAC loads for balancing the user's comfort with the frequency regulation performance IEEE Trans. Smart Grid 2022 13 3546 57

[33] Ma Y.,Xiao Y.,Wang J.,Zhou L.. Multicriteria optimal Latin hypercube design-based surrogate-assisted design optimization for a permanent-magnet vernier machine IEEE Trans. Magn. 2021 58 1 5

[34] Yuan Z.,Kong L.,Gao D..et al. Multi-objective approach to optimize cure process for thick composite based on multi-field coupled model with radial basis function surrogate model Compos. Commun. 2021 24 100671

[35] Li G.,Yao Y.,Shen L.,Deng X.,Zhong W.. Influence of yaw damper layouts on locomotive lateral dynamics performance: Pareto optimization and parameter analysis J. Zhejiang Univ. Sci. A 2023 24 450 64

[36] Zhao Z.,Chen W.,Wu X.,Chen P. C. Y.,Liu J.. LSTM network: a deep learning approach for short-term traffic forecast IET Intell. Trans. Syst. 2017 11 68 75

[37] Yao H. Y.,Wan W. G.,Li X.. End-to-end pedestrian trajectory forecasting with transformer network ISPRS Int. J. Geo Inf. 2022 11 44

[38] Suawa P.F.,Halbinger A.,Jongmanns M.,Reichenbach M.. Noise-robust machine learning models for predictive maintenance applications IEEE Sens. J. 2023 23 15081 92

[39] Fares A.,Bani Younes A.. Online reinforcement learning-based control of an active suspension system using the actor critic approach Appl. Sci. 2020 10 8060