A Neural Network-Augmented Bayesian Approach to Uncertain Parameter Estimation in Nonlinear Dynamic Systems

Many engineered and physical systems contain uncertain parameters and knowing their accurate value is essential to system analysis and design. In this paper, we propose a new approach that combines an artificial neural network with a Bayesian algorithm to achieve better computational efficiency in estimating an unknown parameter of a dynamic system. We utilize neural networks (NN) to start the Particle Markov Chain Monte Carlo (PMCMC) algorithm from a better initial guess of the unknown parameters which is closer to the target value of the parameter. The neural network that is trained on kinematic data are used to provide a rough initial estimate of the unknown parameter. This rough estimate is then used as the initial guess for the Particle Markov Chain Monte Carlo (PMCMC) method. The effectiveness of the new algorithm is first evaluated on a nonlinear benchmark problem — the Van der Pol oscillator. In estimating the damping factor using the NN estimate as the initial guess, the number of iterations required by the PMCMC is shown to reduce by 40% as compared to initializing the algorithm with a random guess. The new methodology was then applied to determine the unknown joint torques of a 7-DOF research robot based on the known joint position and velocities. Multiple neural networks based on different combinations of join position and velocities were trained and used to estimate the initial guess for the PMCMC algorithm. In each of the cases, there was a reduction in the number of iterations required for the PMCMC algorithm to converge as compared to a random initial guess with an average reduction around 30%.