Spline Wavelets for System Identification

Abstract

The paper introduces spline wavelets as a modelling tool for system identification and proposes the technique of consistent output prediction using wavelets for estimating system parameters. It suggests that direct weighted summation of projections in approximation space could be used for deriving consistent output prediction in case model structure is built with spline wavelets. This can be viewed as identification using prefiltered input and output. The prefiltering is motivated to decorrelate samples such that local fit can be considered as a possible solution. An iterative algorithm, alternately projecting the solution in time and wavelet domain for penalized minimization of local error in wavelet coefficients could be designed for estimating system parameters. The algorithm is computationally efficient and exhibits excellent performance in cross validation. As a case study, the paper addresses the problem of modelling Liquid Zone Control System (LZCS) in a large Pressurized Heavy Water Reactor (PHWR). In this work, an identification scheme of a single input single output (SISO) linear time invariant (LTI) model of the LZCS system is studied. Excellent approximation is achieved by modelling with Biorthogonal spline wavelets used for deriving consistent output prediction of the LZCS process.