Recursive Identification for Fractional Order Hammerstein Model Based on ADELS

Abstract

This paper deals with the identification of the fractional order Hammerstein model by using proposed adaptive differential evolution with the Local search strategy (ADELS) algorithm with the steepest descent method and the overparameterization based auxiliary model recursive least squares (OAMRLS) algorithm. The parameters of the static nonlinear block and the dynamic linear block of the model are all unknown, including the fractional order. The initial value of the parameter is obtained by the proposed ADELS algorithm. The main innovation of ADELS is to adaptively generate the next generation based on the fitness function value within the population through scoring rules and introduce Chebyshev mapping into the newly generated population for local search. Based on the steepest descent method, the fractional order identification using initial values is derived. The remaining parameters are derived through the OAMRLS algorithm. With the initial value obtained by ADELS, the identification result of the algorithm is more accurate. The simulation results illustrate the significance of the proposed algorithm.

An efficient conjugate gradient based Cholesky CMA‐ES estimation algorithm for nonlinear systems

“…Equation ( 15) is more computationally cheaper than (16), but it accumulates successive search directions without scaling in the local coordinate system expanded by the eigenvectors. Thus it is difficult to measure correlations accurately in the un-normalized coordinate system.…”

Parameter Identification with a New Recursive Framework for Wiener–Hammerstein-Like System and Its Application

“…Some evaluation indicators are used to check the usefulness of the four estimators, as listed in Table 1. e mean squared error (MSE) and mean of prediction error (PEM) in reference [13], integral square error (ISE), and integral absolute error (IAE) [17] are chosen as evaluation indicators.…”

“…e deterministic method includes recursive structure [9], iterative structure [10], multi-innovation identi cation [11], subspace identi cation [12], two-stage identi cation [13], and experimental tests [14], etc. While nondeterministic method includes the improved PSO [15], hybrid metaheuristic algorithm [16], supervised learning method [17], gravitational search algorithm [18], weighted differential evolution [19], etc.…”

“…Fang et al [8] report an overparameterized method based on the regularization technique for Hammerstein-like system, in which the persistently exciting condition is satisfied by using different input signals. Jin et al [13] used an auxiliary model recursice least square to optimize the parameter values based on the obtained initial values. In reference [25], Krikelis used a recurrent artificial neural network to approximate the Hammerstein-like hysteresis model and introduced a mean squared error method to obtain the system parameter data.…”

“…(2) Parameter estimation error data based on auxiliary filtered variables are obtained, such that the extraction method for the parameter estimation error from the system data is provided. (3) A new parameter estimation estimator using parameter estimation error data is derived, so as to provide an alternative way to design the identification algorithm by using other errors rather than the traditional prediction error [9,13,20].…”