Chaotic Time Series Prediction of Multi‐Dimensional Nonlinear System Based on Bidirectional LSTM Model

Abstract

The current work proposes a hybrid data‐driven model—Convolutional bidirectional long–short term memory (CNN‐BLSTM) for predicting chaotic behavior of three‐coupled Duffing oscillator nonlinear system, in which the CNN is for efficiently extracting the more robust and informative representations of chaotic sequences while the BLSTM is for holding the long‐term dependencies combining the past and future contexts. Different from traditional analytical and numerical approaches, the proposed prediction model features the benefit of focusing on the measured data solely without extensive professional domain knowledge. Additionally, three more recurrent neural network (RNN) models, including simple RNNs, stack LSTMs, and BLSTM, are built and comparisons of generalization performances to the CNN‐BLSTM are conducted. From the findings so far, the CNN‐BLSTM is able to learn the pattern of chaotic time sequence data with less training time and apply the acquired knowledge to the unseen dataset with lower errors. Moreover, the current work decently demonstrates that the proposed model outperforms other three models in terms of stability at different noise levels from two evaluation criteria. The CNN‐BLSTM provides useful guidance for the consideration of predicting multi‐dimensional nonlinear chaotic behavior.

Detection of Weak Pulse Signal in Chaotic Noise - Based on Att-CNN-LSTM model

“…As the neural network models have strong nonlinear processing capabilities, better results have been obtained by neural networks. Literature [15][16][17] verified that LSTM has good robustness in predicting chaotic time series and achieved high prediction accuracy. Literature [18] proposed a chaotic time series prediction method based on the brain emotion learning model (BEL) and adaptive genetic algorithm (AGA) to address the slow convergence of traditional neural network methods.…”

Based on the Improved PSO-TPA-LSTM Model Chaotic Time Series Prediction

“…This combination of two or more methods has achieved good results for chaotic data. In addition, in the literature [13][14][15][16][17][18][19][20], various methods using two prediction models have been proposed, including SVM-ARIMA-3LFFNN [13], WT-PSR [14], DAFA-BiLSTM [15], MFRFNN [16], CNN-BiLSTM [17], Att-CNN-LSTM [18], GRU-DTIGNET [19], and NCKCG-PRQ [20] hybrid models. These models have been validated on chaotic time series, such as Mackey-Glass, Rossler, and Lorenz systems, achieving satisfactory results.…”