Fault estimation for multi‐rate descriptor systems using bi‐directional long short‐term memory neural network

Abstract Fault estimation in multi‐rate descriptor systems, which involve both differential and algebraic states, is particularly challenging due to the complexity introduced by multi‐rate measurements. This paper proposes a novel fault estimation approach that combines a differential‐algebraic equation based extended Kalman filter (DAE‐EKF) with a bi‐directional long short‐term memory (bi‐LSTM) neural network. The DAE‐EKF is used to generate multi‐rate residuals, which serve as inputs to neural networks to estimate faults. bi‐LSTM networks improve upon LSTMs by processing data in both forward and backward directions, using past and future information. This bidirectional approach enhances temporal dependency capture, making bi‐LSTMs ideal for accurate fault estimation. The efficacy of the proposed method is demonstrated using simulation studies on a two‐phase reactor‐condenser system with recycle and a reactive distillation system. The proposed approach has shown superior fault estimation capability for multi‐rate descriptor systems compared to DAE‐EKF with conventional feedforward neural networks and DAE‐EKF with LSTM.