Model structures with wavelet basis functions

The paper addresses formalization of discrete model structures in a simulation/ predictive framework with generalized basis functions and in particular with wavelet basis functions. In deviation from traditional methods that develop models in terms of sampled data, the model directly relates wavelet projections of data thereby effectively utilizing the benefits offered by wavelet basis functions. Nonlinear estimate of output from sparse representation in wavelet domain is synthesized by alternate projection that converges to minimum norm solution. Two industry applications are discussed - one pertaining to the problem of modeling Liquid Zone Control System (LZCS) in a large Pressurized Heavy Water Reactor (PHWR) and the other for identifying an inverse map for defect profile estimation from magnetic flux leakage signal. In both these studies, sub-band linear time invariant or time varying models are identified using the method of consistent output estimation. The resulting models exhibit remarkable estimation capabilities and highlight the advantages of using consistent estimation for identification.