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Identification of linear and non-linear systems with Walsh wavelet packets

An algorithm for the identification of the parameters of models, based on the least-squares method and exploiting the properties of the signal wavelet packet analysis, has been proposed. A short introduction to wavelet and wavelet packets’ analysis was presented. It has been shown that the n-th step of the Walsh wavelet packet analysis can yield filtered, smooth forms of the deterministic or randomly disturbed signal and its derivatives, which generally enable the identification of the model parameters being sought. Multipliers needed to determine the actual, discrete values of the signal function and its derivatives have been formulated. The proposed approach to the identification of model parameters has been validated for linear and nonlinear differential equations of the first to fourth order inclusive. It was stated that the Walsh wavelet packet analysis is an efficient and numerically effective tool in parameters identification process of complicated nonlinear problems of mechanics.