Innovative NARX recurrent neural network model for ultra-thin shape memory alloy wire

The Nonlinear Autoregressive model with Exogenous inputs (NARX) has been utilized in many dynamic systems with complicated nonlinearities. Since NARX models can employ past values of time series as inputs, it is possible to estimate the property of hysteresis to Shape Memory Alloys (SMAs). The innovation of this paper lies in the development of a creative Jordan-plus-Elman NARX recurrent neural network (Jordan–Elman network) model as well as its training procedure. In this paper, the proposed model is applied to an ultra-thin SMA wire with a diameter of 0.001 in., which can be actuated/heated by an electric current. Experimental results demonstrate that the Jordan–Elman network dramatically improves the modeling error (mean squared error) in comparison with a Jordan NARX neural network. In addition, with good generalization results, the proposed model successfully identifies and estimates the hysteretic behavior of the ultra-thin SMA wire including major loops and minor loops at various frequencies.