Machine Learning for Mathematical Modelling of Piezo Hysteresis

In the mathematical modeling of piezo elements and general actuators and sensors with hysteresis such as electromagnets, a method is often used that is based on the research results of Preisach [7] and Mayergoyz [6]. Local maxima and minima are saved and elementary hysteresis operators are weighted with an area function. This area function is the central element of this method because it determines the characteristics of the hysteresis of the piezo elements or electromagnets. It is often carried out with a defined measurement on the system. This article presents a new approach to determining the area function using a machine learning approach. Based on an initial weighting, the parameters are changed in small steps and compared with the measurement using the least square method. After a large number of iteration steps, the model fits better and better with the real system and the least square criterion is minimized. The parameters found at the end have the advantage that they can also be determined with measurements that match the dynamics of the signals occurring in the applications.