Novel Dual Residual-Enhanced Deep Bidirectional LSTM Network for Soft Sensing of Rare Earth Component Content

Long short-term memory (LSTM) networks demonstrate superior time-series feature extraction capabilities and have exhibited significant advantages in the soft sensing of key indicators in complex industrial processes. However, conventional LSTM networks rely solely on the output information from forward propagation through network units, neglecting the residual information between the LSTM cell outputs and the key indicators. Moreover, unidirectional LSTM networks fail to fully exploit the inherent bidirectional temporal dependencies in industrial data. These issues lead to excessive redundancy in the features learned by the network and suboptimal prediction efficiency. This paper proposes a novel dual residual-enhanced deep bidirectional LSTM (DResBiLSTM) framework that integrates bidirectional temporal modeling and dual residual learning for the soft sensing of key variables in complex industrial processes. Firstly, residual information derived from the discrepancy between previous network outputs and key indicators is introduced into the input of the traditional LSTM cell, thereby constructing a residual bidirectional LSTM (ResBiLSTM) network. Secondly, a deep neural architecture is established using residual structures to incorporate input variable residuals, enabling effective soft sensing of key industrial indicators. This framework simultaneously extracts and utilizes latent features characterized by nonlinearity and dynamics from both process and quality variables, significantly enhancing prediction performance. Finally, through both numerical simulations and experimental validations employing real-world operational data from the LaCe/PrNd solvent extraction process, the proposed method demonstrates superior predictive accuracy and better practical effectiveness compared to existing soft sensing approaches.