2018/04/19 by Jeremy G. Stoddard, Stoddard, Jeremy G., James S. Welsh +1
Engineering · #Control Systems and Identification #Structural Health Monitoring Techniques #Hydraulic and Pneumatic Systems
paper · pdf · doi:10.48550/arxiv.1804.07429
The Volterra series is a powerful tool in modelling a broad range of\nnonlinear dynamic systems. However, due to its nonparametric nature, the number\nof parameters in the series increases rapidly with memory length and series\norder, with the uncertainty in resulting model estimates increasing\naccordingly. In this paper, we propose an identification method where the\nVolterra kernels are estimated indirectly through orthonormal basis function\nexpansions, with regularization applied directly to the expansion coefficients\nto reduce variance in the final model estimate and provide access to useful\nmodels at previously unfeasible series orders. The higher dimensional kernel\nexpansions are regularized using a method that allows smoothness and decay to\nbe imposed on the entire hyper-surface. Numerical examples demonstrate improved\nVolterra series estimation up to the 4th order using the regularized basis\nfunction method.\n