Identification of Bouc–Wen type models using multi-objective optimization algorithms

Most of the published literature concerned with the parameter estimation of the Bouc–Wen model of hysteresis via evolutionary algorithms uses a single objective function (the mean square error between the known displacements and the estimated ones) and considers the original Bouc–Wen model of hysteresis (without degradation and pinching) in the identification process. In this paper, a novel method for the identification of the parameters of the Bouc–Wen–Baber–Noori (BWBN) model of hysteresis is presented. The methodology is based on a multi-objective evolutionary optimization algorithm called NSGA-II [39]; therefore, a set of objective functions is employed instead of the traditional single objective function. The proposed methodology identifies the structural system and allows the observation of multi-modality of the BWBN model of hysteresis. The performance of the algorithm is evaluated using simulated and real data.

► A method for the identification of parameters of BW type models is presented.
► It uses the multi-objective evolutionary algorithm NSGA-II proposed by Deb [39].
► The method minimizes errors in the displacements and in the energy.
► The methodology is evaluated with simulated and experimental data with good results.
► The method reveals that very different sets of parameters can fit the data.