Elasticity index evaluation based on Le Cam divergence and kernel density estimator in PM space

Abstract

This work focuses on the application of Preisach-Mayergoyz (PM) model applied to the evaluation of elastic properties of hysteretic material. In the first part, essential concepts are explained such as material hysteresis, probability density functions of PM space, optimization algorithm used, and phi-divergence measures applied in the PM identification process. Next, two different characterizations of PM space of hysterons based on kernel density estimators are proposed, either for one-dimensional PM space projection or for fully two-dimensional pyramid kernel. Finally, new index of elasticity is built up by means of the squared Le Cam divergence between probability density corresponding to the super-elastic distribution and the probability density found by our optimized PM identification process, respectively. This elasticity index describes ability of the material to absorb mechanical deformation, or alternatively, it gives an evidence about the certain degree of damage of the material. This proposed index of elasticity (IE) is evaluated for the case of experimental data measured on the steel dampers used for the protection against earthquakes.