Proximal Gauss-Newton Method for Box-constrained Parameter Identification of a Nonlinear Railway Suspension System
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Published
Sep 17, 2024
Kristian Bredies
Enis Chenchene
Josef Fuchs
Bernd Luber
Abstract
The identification of railway vehicle components’ characteristics from measured data is a challenging task with compelling applications in health monitoring, fault detection, and system prognosis. Usually, though, such systems are highly nonlinear, and naive identification techniques may lead to unstable methods and inaccurate results. In this paper, we show that these issues can be easily tackled with the recently introduced proximal Gauss–Newton method, which we employ to identify the parameters of a railway nonlinear suspension system. In the proposed model, the parameters are subject to safety bounds in form of box constraints, which allows preventing nonphysical solutions. The suspension system we consider is highly nonlinear due to the presence of an airspring in the secondary suspension, which we introduce in a simplified Berg model. Numerical examples, featuring data corrupted by various noise levels, demonstrate the accuracy and efficiency of our proposed method. Comparisons with state-of-the-art approaches are also provided.
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Keywords
Proximal Gauss-Newton method, parameter identification, railway suspension systems, airspring, Fault Detection and Isolation
References
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Bruni, S., Goodall, R., Mei, T. X., & Tsunashima, H. (2007). Control and monitoring for railway vehicle dynamics. Vehicle System Dynamics, 45(7-8), 743–779.
Callejo, A., & de Jalón, J. G. (2015). Vehicle suspension identification via algorithmic computation of state and design sensitivities. Journal of Mechanical Design, 137(2).
Ding, J., Pan, Z., & Chen, L. (2012). Parameter identification of multibody systems based on second-order sensitivity analysis. International Journal of Non-Linear Mechanics, 47(10), 1105–1110.
Eich-Soellner, E., & Führer, C. (1998). Numerical methods in multibody dynamics (1st ed.). Vieweg+Teubner VerlagWiesbaden.
Ferreau, H., Kirches, C., Potschka, A., Bock, H., & Diehl, M. (2014). qpOASES: A parametric active-set algorithm for quadratic programming. Mathematical Programming Computation, 6(4), 327–363.
Gonçalves,M., &Menezes, T. (2020). Gauss–Newton methods with approximate projections for solving constrained nonlinear least squares problems. Journal of Complexity, 58, 101459.
Grewal,M., & Glover, K. (1976). Identifiability of linear and nonlinear dynamical systems. IEEE Transactions on Automatic Control, 21(6), 833–837.
Grupp, F., & Kortüm,W. (1993). Parameter identification of nonlinear descriptor systems. In Advanced multibody system dynamics (pp. 457–462). Springer.
Kraft, S., Puel, G., Aubry, D., & Funfschilling, C. (2016). Parameter identification of multi-body railway vehicle models – application of the adjoint state approach. Mechanical Systems and Signal Processing, 80, 517-532.
Matsumiya, S., Nishioka, S., Nishimura, S., & Suzuki, M. (1969). On the diaphragm air spring “Sumiride”. Sumitomo Search, 2, 86–92.
Mazzola, L., & Berg, M. (2014). Secondary suspension of railway vehicles-air spring modelling: Performance and critical issues. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 228(3), 225–241.
Moheyeldein, M., Abd-El-Tawwab, A. M., El-gwwad, K. A., & Salem, M. (2018). An analytical study of the performance indices of air spring suspensions over the passive suspension. Beni Suef University Journal of Basic and Applied Sciences, 7(4), 525–534.
Oda, N., &Nishimura, S. (1969). Vibration of air suspension bogies and their design. JSME International Journal Series B Fluids and Thermal Engineering, 13, 43–50.
Puel, G., Bourgeteau, B., & Aubry, D. (2013). Parameter identification of nonlinear time-dependent rubber bushings models towards their integration in multibody simulations of a vehicle chassis. Mechanical Systems and Signal Processing, 36(2), 354–369.
Salzo, S., & Villa, S. (2012). Convergence analysis of a proximal Gauss–Newton method. Computational Optimization and Applications, 53(2), 557–589.
Sayyaadi, H., & Shokouhi, N. (2009). A new model in railvehicles dynamics considering nonlinear suspension components behavior. International Journal of Mechanical Sciences, 51(3), 222–232.
Serban, R., & Freeman, J. S. (2001). Identification and identifiability of unknown parameters in multibody dynamic systems. Multibody System Dynamics, 5(4), 335–350.
Strano, S., & Terzo, M. (2019). Review on model-based methods for on-board condition monitoring in railway vehicle dynamics. Advances in Mechanical Engineering, 11(2).
Vyasarayani, C., Uchida, T., Carvalho, A., & McPhee, J. (2012). Parameter identification in dynamic systems using the homotopy optimization approach. Lecture Notes in Control and Information Sciences, 418, 129–145.
Xin-Chun, Z., & Cheng-Jun, G. (2013). Cubature Kalman filters: Derivation and extension. Chinese Physics B, 22(12), 128401.
Zoljic-Beglerovic, S., Luber, B., Stettinger, G., Müller, G., & Horn, M. (2020). Parameter identification for railway suspension systems using cubature Kalman filter. In Advances in dynamics of vehicles on roads and tracks (pp. 128–132). Springer International Publishing.
Zoljic-Beglerovic, S., Stettinger, G., Luber, B., & Horn, M. (2018). Railway suspension system fault diagnosis using cubature Kalman filter techniques. IFACPapersOnLine, 51(24), 1330–1335. (10th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes SAFEPROCESS 2018)
Berg, M. (1997). A model for rubber springs in the dynamic analysis of rail vehicles. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 211(2), 95–108.
Berg, M. (1999). A three–dimensional airspring model with friction and orifice damping. Vehicle System Dynamics, 33(sup1), 528–539.
Bruni, S., Goodall, R., Mei, T. X., & Tsunashima, H. (2007). Control and monitoring for railway vehicle dynamics. Vehicle System Dynamics, 45(7-8), 743–779.
Callejo, A., & de Jalón, J. G. (2015). Vehicle suspension identification via algorithmic computation of state and design sensitivities. Journal of Mechanical Design, 137(2).
Ding, J., Pan, Z., & Chen, L. (2012). Parameter identification of multibody systems based on second-order sensitivity analysis. International Journal of Non-Linear Mechanics, 47(10), 1105–1110.
Eich-Soellner, E., & Führer, C. (1998). Numerical methods in multibody dynamics (1st ed.). Vieweg+Teubner VerlagWiesbaden.
Ferreau, H., Kirches, C., Potschka, A., Bock, H., & Diehl, M. (2014). qpOASES: A parametric active-set algorithm for quadratic programming. Mathematical Programming Computation, 6(4), 327–363.
Gonçalves,M., &Menezes, T. (2020). Gauss–Newton methods with approximate projections for solving constrained nonlinear least squares problems. Journal of Complexity, 58, 101459.
Grewal,M., & Glover, K. (1976). Identifiability of linear and nonlinear dynamical systems. IEEE Transactions on Automatic Control, 21(6), 833–837.
Grupp, F., & Kortüm,W. (1993). Parameter identification of nonlinear descriptor systems. In Advanced multibody system dynamics (pp. 457–462). Springer.
Kraft, S., Puel, G., Aubry, D., & Funfschilling, C. (2016). Parameter identification of multi-body railway vehicle models – application of the adjoint state approach. Mechanical Systems and Signal Processing, 80, 517-532.
Matsumiya, S., Nishioka, S., Nishimura, S., & Suzuki, M. (1969). On the diaphragm air spring “Sumiride”. Sumitomo Search, 2, 86–92.
Mazzola, L., & Berg, M. (2014). Secondary suspension of railway vehicles-air spring modelling: Performance and critical issues. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 228(3), 225–241.
Moheyeldein, M., Abd-El-Tawwab, A. M., El-gwwad, K. A., & Salem, M. (2018). An analytical study of the performance indices of air spring suspensions over the passive suspension. Beni Suef University Journal of Basic and Applied Sciences, 7(4), 525–534.
Oda, N., &Nishimura, S. (1969). Vibration of air suspension bogies and their design. JSME International Journal Series B Fluids and Thermal Engineering, 13, 43–50.
Puel, G., Bourgeteau, B., & Aubry, D. (2013). Parameter identification of nonlinear time-dependent rubber bushings models towards their integration in multibody simulations of a vehicle chassis. Mechanical Systems and Signal Processing, 36(2), 354–369.
Salzo, S., & Villa, S. (2012). Convergence analysis of a proximal Gauss–Newton method. Computational Optimization and Applications, 53(2), 557–589.
Sayyaadi, H., & Shokouhi, N. (2009). A new model in railvehicles dynamics considering nonlinear suspension components behavior. International Journal of Mechanical Sciences, 51(3), 222–232.
Serban, R., & Freeman, J. S. (2001). Identification and identifiability of unknown parameters in multibody dynamic systems. Multibody System Dynamics, 5(4), 335–350.
Strano, S., & Terzo, M. (2019). Review on model-based methods for on-board condition monitoring in railway vehicle dynamics. Advances in Mechanical Engineering, 11(2).
Vyasarayani, C., Uchida, T., Carvalho, A., & McPhee, J. (2012). Parameter identification in dynamic systems using the homotopy optimization approach. Lecture Notes in Control and Information Sciences, 418, 129–145.
Xin-Chun, Z., & Cheng-Jun, G. (2013). Cubature Kalman filters: Derivation and extension. Chinese Physics B, 22(12), 128401.
Zoljic-Beglerovic, S., Luber, B., Stettinger, G., Müller, G., & Horn, M. (2020). Parameter identification for railway suspension systems using cubature Kalman filter. In Advances in dynamics of vehicles on roads and tracks (pp. 128–132). Springer International Publishing.
Zoljic-Beglerovic, S., Stettinger, G., Luber, B., & Horn, M. (2018). Railway suspension system fault diagnosis using cubature Kalman filter techniques. IFACPapersOnLine, 51(24), 1330–1335. (10th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes SAFEPROCESS 2018)
Section
Technical Papers