The Knowledge-Based Modeling of Ferroelectric Hysteresis Area: An Application to Forming (1-x)PZT-(x)PZN Hysteresis Database

Abstract

In this work, Artificial Neural Network was used to model the hysteresis behavior of lead zirconate titanate-lead zinc niobate (Pb(Zr_1/2Ti_1/2)O₃−Pb(Zn_1/3Nb_2/3)O₃ or (1-x)PZT-(x)PZN mixed ferroelectric systems. The hysteresis loops were measured with varying electric filed parameters and the composition x of the mixed ferroelectrics. A knowledge-based technique, i.e. the Artificial Neural Network (ANN), was employed in modeling the hysteresis to construct the database of how field parameters and the mixed composition affect dynamic hysteresis behavior. The input data to the ANN were composition x, field amplitude E₀ and field frequency f, where the output data was the hysteresis area. The inputs-outputs were divided into training, validating and testing datasets for the ANN. Multilayer perceptron with back propagation training algorithm was applied in this work. Exhaustive search was used to obtain the best network algorithm that gives minimum error in the training process. With the best network, unseen input datasets were fed into the network to predict hysteresis area. From the results, the predicted and the actual data match very well over an extensive range of field parameters, where the scattering plot between the predicted and the actual area has R-squared greater than 0.99. This therefore indicates ANN capabilities in modeling dynamic-hysteresis phenomena across (1-x)PZT-(x)PZN systems even they have different ratios of structural phases at microscopic level.

Keywords:

• Artificial neural network
• multilayer perceptron
• hysteresis area
• PZT-PZN.