Ensemble Bidirectional Long Short-Term Memory Network Identification for Nonlinear Autoregressive Exogenous Model: Application to Dual Double-Acting Piston Pump

System identification is essential for modeling and control of nonlinear dynamic systems. In practice, traditional linear or unidirectional recurrent models often fail to capture the oscillatory, speed-dependent behaviors of highly nonlinear processes such as dual double-acting piston pumps (DDAPPs). Recent advances in deep learning highlight the potential of recurrent neural networks; however, most studies rely on unidirectional LSTMs and neglect the benefits of bidirectional processing and ensemble learning. To address these gaps, this paper proposes an ensemble bidirectional long short–term memory (EnBiLSTM) framework for identifying a nonlinear autoregressive model with exogenous input (NARX) of the DDAPP. Specifically, the proposed method employs bidirectional temporal encoding to exploit both past and future sequence information, while ensemble averaging enhances generalization and robustness. Furthermore, a hybrid multi-objective optimization strategy integrating Pareto front analysis and TOPSIS is employed to determine the optimal system order, balancing prediction accuracy and model complexity. Regarding the scenario experiments, the proposed EnBiLSTM reduces prediction error, yielding RMSE reductions of approximately 80%, 66%, and 96% compared to GRU, SVM, and ARIMA, and achieves an RMSE of 11.9, an MAE of 8.4, and an R² of 0.92. Apart from that, the EnBiLSTM model is also characterized by low inference latency of approximately 16.5 ms and moderate resource utilization, justifying its deployability in real-time. As a result, it impressed EnBiLSTM as an appropriate and robust solution for nonlinear system identification with significant gains in predictive accuracy and practicability.