Convergence of Direct Recursive Algorithm for Identification of Preisach Hysteresis Model with Stochastic Input

Abstract

Abstract. We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. The classical identification algorithm due to Mayergoyz defines explicitly a series of test inputs that allow one to find parameters of the Preisach model with any desired precision provided that (a) such input time series can be implemented and applied; and, (b) the corresponding output data can be accurately measured and recorded. Recursive iterative identification schemes suitable for a number of engineering applications have been recently proposed as an alternative to the classical algorithm. These recursive schemes do not use any input design but rather rely on an input-output data stream resulting from random fluctuations of the input variable. Furthermore, only recent values of the input-output data streams are available for the scheme at any time instant. In this work, we prove exponential convergence of such algorithms, estimate explicitly the convergence rate, and explore which properties of the stochastic input and the algorithm affect the guaranteed convergence rate.

The Devil is in the details: Spectrum and eigenvalue distribution of the discrete Preisach memory model

“…The unique stationary probability distribution for this Markov chain has been described in [1], where the Preisach model with random input was considered 2 . Properties of the stochastic output of the Preisach model under various random inputs have been characterized in [15,26,30,36,37,39] (in the context of this work, the output is the area (measure) of the dark gray region in Fig. 1).…”

Online identification of piezoelectric hysteresis by direct recursive algorithm of Preisach model

“…It has been shown in [2] that, for any initial estimateρ 0 , the mean square distance from the approximationρ k to the target density function ρ,…”

“…ρ k − ρ 2 ≤ c e −λk , where the convergence rate λ is determined by parameters of the stochastic input process and the discretization step 1/L (see [2] for explicit formulas).…”

“…Further, it should be noted that the designed notch filter (2) has been transformed by a standard zero-order hold method into the discrete time domain so as to comply with the real-time implementation of the digital signal processor (DSP).…”

“…Later, an alternative direct recursive method has been proposed in [1]; this method uses the output increment error to update parameters of only those hysteresis operators which are responsible for the instantaneous hysteresis output increment. A rigorous mathematical prove of convergence behavior for this direct recursive method has been recently provided by the authors in [2].…”