Wavelet based Steglitz Mc-Bride algorithm for Identification of Multiscale Output-Error Models

Abstract

Identification of output-error models for systems with multiple time scales is known to be a challenging problem due to the spread of dynamics across a wide range of time scales. The wide separation in time constants of the system forces one to deal with unusually fast sampling rates for slow dynamics. In general, output-error model identification of multiscale systems using prediction-error minimization suffers whenever they are initialized with auto-regressive exogenous (ARX) model parameter estimates owing to the sensitivity of ARX models at fast sampling. In the present work, it is observed that the classical Steglitz Mc-Bride (SM) algorithm can serve as an excellent alternative for identification of simple multiscale systems. Despite its advantages, it is seen to yield unstable models at times (related to the sensitivity of ARX estimation) and sometimes converges to a secondary optima. In this work, a multiscale SM algorithm, which respects the multiscale nature of data generating process, is proposed in order to reduce the sensitivity issues arising due to fast sampling. The proposed methodology is observed to yield good results for multiscale systems in terms of obtaining stable models and faster convergence. The performance of the proposed method is demonstrated on three simulation examples and the results are compared with traditional methods.