Data-driven methods for the inverse problem of suspension system excited by jump and diffusion stochastic track excitation

Following a lengthy tenure of service, suspension systems may exhibit inaccurate model parameters due to the presence of complex conditions, which can result in a deterioration of control and the potential for operational failures. It is therefore imperative to estimate the key parameters of suspension systems. This paper introduces two data-driven methods for addressing the inverse problem in suspension systems subjected to stochastic track excitations. By employing physics-informed neural networks (PINNs) and Monte Carlo (MC) simulation, we are able to address the resulting integro-differential equation that arises from stochastic jump processes, thus avoiding the necessity for mesh grids. In order to mitigate the numerical challenges that arise from the system parameters, a residual-based adaptive sampling method is proposed. These methods effectively infer unknown parameters, addressing scenarios where data is directly available as a probability density function (PDF) or only sparse trajectories are given. In the latter case, a novel loss function employing Kullback-Leibler divergence facilitates learning from stochastic trajectories. Both methods successfully obtain solutions to the forward Kolmogorov equation, as validated by numerical experiments testing their robustness against added noise. The results demonstrate accurate parameter estimation under varying noise intensities, highlighting the methods’ robustness.