Hysteretic recurrent neural networks: a tool for modeling hysteretic materials and systems

This paper introduces a novel recurrent neural network, the hysteretic recurrent neural network (HRNN), that is ideally suited to modeling hysteretic materials and systems. This network incorporates a hysteretic neuron consisting of conjoined sigmoid activation functions. Although similar hysteretic neurons have been explored previously, the HRNN is unique in its utilization of simple recurrence to 'self-select' relevant activation functions. Furthermore, training is facilitated by placing the network weights on the output side, allowing standard backpropagation of error training algorithms to be used. We present two- and three-phase versions of the HRNN for modeling hysteretic materials with distinct phases. These models are experimentally validated using data collected from shape memory alloys and ferromagnetic materials. The results demonstrate the HRNN's ability to accurately generalize hysteretic behavior with a relatively small number of neurons. Additional benefits lie in the network's ability to identify statistical information concerning the macroscopic material by analyzing the weights of the individual neurons.