Abstract
Estimating parameters for nonlinear dynamic systems is a significant challenge across numerous research areas and practical applications. This paper introduces a novel two-step approach for estimating parameters that control the lateral dynamics of a vehicle, acknowledging the limitations and noise within the data. The methodology merges spline smoothing of system observations with a Bayesian framework for parameter estimation. The initial phase involves applying spline smoothing to the system state variable observations, effectively filtering out noise and achieving precise estimates of the state variables’ derivatives. Consequently, this technique allows for the direct estimation of parameters from the differential equations characterizing the system’s dynamics, bypassing the need for labor-intensive integration procedures. The subsequent phase focuses on parameter estimation from the differential equation residuals, utilizing a Bayesian method known as likelihood-free ABC-SMC. This Bayesian strategy offers multiple advantages: it mitigates the impact of data scarcity by incorporating prior knowledge regarding the vehicle’s physical properties and enhances interpretability through the provision of a posterior distribution for the parameters likely responsible for the observed data. Employing this innovative method facilitates the robust estimation of parameters governing vehicle lateral dynamics, even in the presence of limited and noisy data.
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References
Sinha, N.K.: System identification - theory for the user : Lennart ljung. Autom 25(3), 475–476 (1989)
Biegler, L.T., Damiano, J.J., Blau, G.E.: Nonlinear parameter estimation: a case study comparison. AIChE J. 32(1), 29–45 (1986)
Wang, S., Xu, X.: Parameter estimation of internal thermal mass of building dynamic models using genetic algorithm. Energy Convers. Manage. 47(13), 1927–1941 (2006)
Gutowski, N., Schang, D., Camp, O., Abraham, P.: A novel multi-objective medical feature selection compass method for binary classification. Artif. Intell. Med. 127, 102277 (2022)
Eftaxias, A., Font, J., Fortuny, A., Fabregat, A., Stüber, F.: Nonlinear kinetic parameter estimation using simulated annealing. Comput. Chem. Eng. 26(12), 1725–1733 (2002)
Schwaab, M., Biscaia, E.C., Jr., Monteiro, J.L., Pinto, J.C.: Nonlinear parameter estimation through particle swarm optimization. Chem. Eng. Sci. 63(6), 1542–1552 (2008)
Ascher, U.M., Petzold, L.R.: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, 1st edn. Society for Industrial and Applied Mathematics, USA (1998)
Raissi, M., Perdikaris, P., Karniadakis, G.: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019)
Barber, D., Wang, Y.: Gaussian processes for Bayesian estimation in ordinary differential equations. In: International Conference on Machine Learning (2014)
Calderhead, B., Girolami, M., Lawrence, N.: Accelerating bayesian inference over nonlinear differential equations with gaussian processes. In: Advances in Neural Information Processing Systems, vol. 21. Curran Associates, Inc. (2008)
Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning, MIT Press, Cambridge (2006)
Chib, S., Greenberg, E.: Understanding the metropolis-hastings algorithm. Am. Stat. 49(4), 327–335 (1995)
Casella, G., George, E.I.: Explaining the Gibbs sampler. Am. Stat. 46(3), 167–174 (1992)
Marin, J.-M., Pudlo, P., Robert, C.P., Ryder, R.J.: Approximate Bayesian computational methods. Stat. Comput. 22, 1167–1180 (2012)
Toni, T., Welch, D., Strelkowa, N., Ipsen, A., Stumpf, M.P.: Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6, 187–202 (2009)
Liepe, J., Kirk, P., Filippi, S., Toni, T., Barnes, C.P., Stumpf, M.P.H.: A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat. Protoc. 9(2), 439–456 (2014)
Secrier, M., Toni, T., Stumpf, M.P.H.: The ABC of reverse engineering biological signalling systems. Mol. BioSyst. 5, 1925–1935 (2009)
Lillacci, G., Khammash, M.: Parameter estimation and model selection in computational biology. PLOS Comput. Biol. (2010)
Pacejka, H. Bakker, E., Pacejka, W., Hans, B., Afsar, M.: Tyre and Vehicle Dynamics. Elsevier Science (2006)
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This research is financially supported by the Ministry of Defense through the Defense Innovation Agency (AID) and by the National Institute for Research in Computer Science and Automation (INRIA).
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Lionti, F., Gutowski, N., Aubin, S., Martinet, P. (2024). Bayesian Approach for Parameter Estimation in Vehicle Lateral Dynamics. In: Appice, A., Azzag, H., Hacid, MS., Hadjali, A., Ras, Z. (eds) Foundations of Intelligent Systems. ISMIS 2024. Lecture Notes in Computer Science(), vol 14670. Springer, Cham. https://doi.org/10.1007/978-3-031-62700-2_22
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