This paper describes a novel approach to modeling hysteresis using a Hysteretic Recurrent Neural Network (HRNN). The HRNN utilizes weighted recurrent neurons, each composed of conjoined sigmoid activation functions to capture the directional dependencies typical of hysteretic smart materials (piezoelectrics, ferromagnetic, shape memory alloys, etc.) Network weights are included on the output layer to facilitate training and provide statistical model information such as phase fraction probabilities. This paper demonstrates HRNN-based modeling of two- and three-phase transformations in hysteretic materials (shape memory alloys) with experimental validation. A two-phase network is constructed to model the displacement characteristics of a shape memory alloy (SMA) wire under constant stress. To capture the more general thermo-mechanical behavior of SMAs, a three-phase HRNN model (which accounts for detwinned Martensite, twinned Martensite, and Austensite phases) is developed and experimentally validated. The HRNN modeling approach described in this paper readily lends itself to other hysteretic materials and may be used for developing real-time control algorithms.

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