Partially uncertain industrial process monitoring based on hybrid-scale wavelet signal fusion using crossed transformer

Abstract In the monitoring of complex industrial processes, uncertainty arising from factors such as sensor degradation and environmental noise often leads to deviations in measurement data from true values, presenting significant challenges for fault detection. Typically, only a subset of variables is affected by uncertainty in real industrial systems. However, current methods generally assume that all variables exhibit uncertainty and apply uniform monitoring based solely on raw sampling data, neglecting the distinct characteristics of certain and uncertain data across different frequency scales. To address this issue, the paper proposes a hybrid-scale wavelet (HW) and crossed transformer (CT)-based adaptive multi-frequency signal fusion method for effective process monitoring of signals with partial uncertainty. The HW transformation is designed to handle the varying characteristics of certain and uncertain data across different frequency scales. The CT, which integrates both self-attention and mutual-attention mechanisms, is proposed to highlight the reliable features of uncertain signals by capturing the internal structures within each frequency band and learning feature interactions across different bands simultaneously. Finally, an adaptive weighted fusion strategy based on gated signals combines the enhanced multi-frequency signals, resulting in more accurate and reliable monitoring outcomes. Experiments conducted on the Tennessee Eastman process and wastewater treatment plant process demonstrate the superior performance of the proposed method in partially uncertain industrial processes monitoring.