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Hysteresis is a natural phenomenon that widely exists in structural and mechanical systems. The characteristics of structural hysteretic behaviors are complicated. Therefore, numerous methods have been developed to describe hysteresis. In this paper, a review of the available hysteretic modeling methods is carried out. Such methods are divided into: a) model-driven and b) data-driven methods. The model-driven method uses parameter identification to determine parameters. Three types of parametric models are introduced including polynomial models, differential based models, and operator based models. Four algorithms as least mean square error algorithm, Kalman filter algorithm, metaheuristic algorithms, and Bayesian estimation are presented to realize parameter identification. The data-driven method utilizes universal mathematical models to describe hysteretic behavior. Regression model, artificial neural network, least square support vector machine, and deep learning are introduced in turn as the classical data-driven methods. Model-data driven hybrid methods are also discussed to make up for the shortcomings of the two methods. Based on a multi-dimensional evaluation, the existing problems and open challenges of different hysteresis modeling methods are discussed. Some possible research directions about hysteresis description are given in the final section. [ABSTRACT FROM AUTHOR]

[Display omitted] • The enhanced design of an array of the piezoelectric harvester was introduced. • (α) manage the problem of lowering the power between the resonance frequencies of the array. • The working bandwidth broadened by a factor of 26 compared to the conventional design. • The output power increased by a factor of 31 compared to the conventional design. • The effect of harvester parameters on the broadband was investigated. Converting the wasted ambient vibration to electric power, using a piezoelectric energy harvester, is a promising strategy for powering a sensor network for medical and industrial applications. The designed harvester must satisfy the wideband natural frequency of ambient vibration. Conventional array harvester generates peak power at the cantilever's resonance frequencies and low power between them. This challenge can be managed by controlling the inclination angle of the tip masses (α). It is observed that the range of α from 45 ° to 53.3 ° generates an output power of 2 - 3 m W in the frequency range of 1 9 to 29 H z. For the second mode shape, the output power has been measured to be 9 m W in the frequency range from 290 to 330 Hz. Comparing the proposed design with conventional designs, the working bandwidth broadband is increased by a factor of 26, and the output power is increased by a factor of 31. The proposed approach is modeled using finite element analysis and analytical methods. The FEM model is validated by experimental results. [ABSTRACT FROM AUTHOR]