An Attention-BiLSTM network identification method for time-delay feedback nonlinear system

This paper addresses the identification problem of feedback nonlinear system with time delay (FNTD). A data-driven identification method for the FNTD system based on bidirectional long short-term memory (BiLSTM) networks is proposed. First, considering the long input and output data sequence and the existence of bidirectional features, the BiLSTM network is chosen for identification. In addition, in order to mine the complex nonlinear mapping relationship between input and output, the attention mechanism is introduced into the BiLSTM algorithm to highlight the influence of key factors. The Gaussian kernel function selects the optimal complexity model to enhance the extrapolation performance, and further improves the identification accuracy. Then, the attention-BiLSTM algorithm is proposed. In the simulation, a numerical example and two application examples are implemented. The results show that the attention-BiLSTM method can effectively identify the FNTD system, and is superior to LSTM and BiLSTM in terms of identification accuracy and speed. The proposed attention-BiLSTM method has the highest identification accuracy, and the RMSE is \(5.57\%\) $5.57\%$ and \(1.05\%\) $1.05\%$ lower than the LSTM and BiLSTM models, respectively. The \(R^2\) $R^2$ value reaches 0.9997, which is \(16.17\%\) $16.17\%$ and \(0.77\%\) $0.77\%$ higher than LSTM and BiLSTM, respectively.