Optimized NRBO-VMD-AM-BiLSTM Hybrid Architecture for Enhanced Dissolved Gas Concentration Prediction in Transformer Oil Soft Sensors.

Soft sensors have emerged as indispensable tools for predicting dissolved gas concentrations in transformer oil-critical indicators for fault diagnosis that defy direct measurement. Addressing the persistent challenge of prediction inaccuracy in existing methods, this study introduces a novel hybrid architecture integrating time-series decomposition, deep learning prediction, and signal reconstruction. Our approach initiates with variational mode decomposition (VMD) to disassemble original gas concentration sequences into stationary intrinsic mode functions (IMFs). Crucially, VMD's pivotal parameters (modal quantity and quadratic penalty term) governing bandwidth allocation and mode orthogonality are optimized via a Newton-Raphson-based optimization (NRBO) algorithm, minimizing envelope entropy to ensure sparsity preservation through information-theoretic energy concentration metrics. Subsequently, a bidirectional long short-term memory network with attention mechanism (AM-BiLSTM) independently forecasts each IMF. Final concentration trends are reconstructed through superposition and inverse normalization. The experimental results demonstrate the superior performance of the proposed model, achieving a root mean square error (RMSE) of 0.51 µL/L and a mean absolute percentage error (MAPE) of 1.27% in predicting hydrogen (H