Training of nonlinear neural networks to model nonlinear vehicle dynamics was undertaken to convergence of the weights, not error convergence, to ensure the nonlinear dynamic modelling ability of the nonlinear neural networks was assessed fairly. An error measure was introduced which allowed comparison of the performance of trained nonlinear neural networks over the full required range of vehicle operating conditions. For off-line training of a two layer nonlinear neural network to model nonlinear vehicle dynamics: As the number of neurons in the nonlinear layer increases, the modelling error of a network with converged weights reduces asymptotically towards a constant error level. Networks of the same number of nonlinear neurons, but with different random initial weights, will have different error levels. As the number of neurons in the nonlinear layer increases, the variation in error due to the initial weights decreases. The size of the nonlinear neural network used to model vehicle dynamics must be chosen to ensure the variation in accuracy due to random initial weights is within the desired range of model error. When modelling the nonlinear vehicle dynamics used in this paper 16 nonlinear neurons allows a low and consistent error level. As the number of nonlinear neurons increases to ten, the number of training steps to convergence of weights increases. For networks of size greater than ten nonlinear neurons, the number of training steps to convergence of weights is approximately constant. Varying convergence times can be expected for nonlinear neural networks of the same size with different sets of random initial weights. The variation in convergence time due to different sets of random initial weights cannot be controlled by selecting the nonlinear neural network size. Considering a three layer structure, results showed no significant improvement over the two layer structure in modelling error or time to convergence of weights. Results of online training indicate it can be equally as successful as off-line training, with a greater computational cost. This indicates it should be possible to use neural networks for online identification and control of nonlinear vehicle models.


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    Titel :

    Modelling nonlinear vehicle dynamics with neural networks


    Beteiligte:

    Erschienen in:

    Erscheinungsdatum :

    2010


    Format / Umfang :

    28 Seiten, 16 Bilder, 2 Tabellen, 43 Quellen




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Print


    Sprache :

    Englisch




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