Parameter identification of Jiles–Atherton model using the chaotic optimization method

Abstract

Purpose The purpose of this paper is to propose a chaotic optimization method for identifying the parameters of the Jiles–Atherton (J-A) hysteresis model. Design/methodology/approach The J-A model has five parameters which are assigned with physical meaning and whose determination is demanding. To determine these parameters, the fitness function, which represents the difference between the measured and the modeled hysteresis loop, is formed. Optimal parameter values are the values that minimize the fitness function. Findings The parameters of J-A model for three magnetic materials are determined. The model with the optimal parameters is validated using measured data and comparison with particle swarm optimization algorithm, genetic algorithm, pattern search and simulated annealing algorithm. The results show that the proposed method provides better agreement between measured and modeled hysteresis loop than other methods used for comparison. The proposed method is also suitable for simultaneous optimization of multiple hysteresis loops. Originality/value Chaotic optimization method is implemented for the first time for J-A model parameter identification. Numerical comparisons with results obtained with other optimization algorithms demonstrate that this method is a suitable alternative in parameters identification of J-A hysteresis model. Furthermore, this method is easy to implement and set up.

Estimation of Single-Diode and Two-Diode Solar Cell Parameters by Using a Chaotic Optimization Approach

“…COA is a very powerful optimization technique that has found numerous scientific applications [59][60][61][62][63]. This approach is based on the theory of chaos, which is, in a mathematical sense, described by ordinary differential equations or by an iterative map [64].…”

“…Different chaotic systems, including the logistic map, lozi map, tent map and Lorenz system, can be found in the literature. In this paper, we will base COA on the logistic map [59][60][61][62][63][64].…”

“…where P is the number of measured I-V pairs from the I-V characteristics, and V t and I t represent the voltage and current value of pair t. Figure 2 presents the search procedure, i.e., the COA flowchart. The detailed description of COA flowchart can be found in [59].…”

“…Recently, COA has been used in solving various optimization problems: parameter identification of Jiles-Atherton hysteresis model [59], single-phase transformer parameter estimation [60], design of PID parameters for automatic voltage regulation of synchronous machine [61], antenna array radiation pattern synthesis [62,63]. The main advantages of COA over other optimization techniques are easy implementation and short execution time [64].…”

“…COA flowchart. Define ranges (upper and lower limits) of unknown parameters (Rs, Rp, Ipv, Io and n for SDM and Rs, Rp, Ipv, Io1, Io2, n1 and n2 for DDM) Define number of iterations (Mg) Define number of COA starting (Ms) Define initial values for logistic mapping In the kth iteration for X(k), calculate the value of OF (Equation (3) for SDM and Equation (4) for DDM) The estimated parameters values are those which minimize the OF over all possible startings and iterations By using logistic mapping, form variables xi(k), k = 1, ..., Mg and i = 1, ..., 5 for SDM, and i = 1, ..., 7 for DDM, as described in[59] …”