A multi-model fault-tolerant control method for concurrent faults in wastewater treatment processes based on semi-supervised learning and physical constraints

Wastewater treatment processes (WWTP) is one of the most essential means to achieve water resource protection and sustainable utilization, with dissolved oxygen and nitrate serving as main factors limiting effluent quality through their direct involvement in carbon consumption, nitrification, and denitrification processes. Existing fault-tolerant control strategies primarily focus on single sensor anomalies, while practical operations frequently encounter concurrent faults across multiple measurement channels. Moreover, the scarcity of labeled operational data in industrial settings poses significant challenges for developing reliable fault-tolerant control systems. This paper presents a passive fault-tolerant control approach using an innovative semi-supervised deep learning framework to address simultaneous failures in critical dissolved oxygen and nitrate sensors. The proposed methodology features four key innovations: (1) A novel SAE-MNN architecture that integrates stacked autoencoders with multi-output neural networks for simultaneous multi-parameter prediction through hierarchical feature extraction. (2) A confidence-based pseudo-labeling semi-supervised co-training mechanism that effectively leverages limited labeled data and abundant unlabeled operational data under data scarcity conditions. (3) Physics-constrained learning that enforces biochemical principles and mass conservation laws to ensure physically plausible predictions. (4) A multi-sensor passive fault-tolerant control strategy that handles simultaneous failures across multiple critical measurement channels without hardware redundancy or controller reconfiguration. This integrated framework enables robust operation during concurrent sensor failures, where predicted values seamlessly replace multiple faulty sensor measurements while maintaining stable control performance. The effectiveness is validated using the Benchmark Simulation Model No. 1 (BSM1), demonstrating superior system performance during multi-sensor fault scenarios compared to conventional methods, thereby enhancing the reliability and resilience of wastewater treatment systems.