Recursive bilinear subspace identification-Bayesian network enables probabilistic fault diagnosis in wastewater treatment: Modelling, diagnosis and system platform

Reliable wastewater fault diagnosis must distinguish disturbances with similar effluent responses while accounting for process dynamics. This paper developed a recursive bilinear subspace identification-Bayesian network (RBLSI-BN) framework that incorporates dissolved oxygen (DO 3 ) and nitrate (NO 3 ) prediction residuals into process-informed probabilistic diagnosis. The network represents influent, internal-process, and effluent dependencies. Fault-conditioned Gaussian likelihoods integrate shared measurements with dynamic residuals. Using plant-derived observations and BSM1-derived simulations, we compared bilinear prediction with single-input and input-matched recursive linear subspace identification (RLSI). Diagnostic comparisons used measurement-only BN and linear-residual RLSI-BN controls. In the original observation sequence, RBLSI achieved a DO 3 RMSE of 0.4188 mg/L, 23.70% lower than single-input RLSI and 19.57% lower than input-matched RLSI. It also reduced NO 3 MAE by 11.90% relative to the input-matched model. Across three historical cases, RBLSI-BN improved mean evidence similarity by 42.3% over BN, and its leading mechanisms agreed with independent expert rankings. The simulations comprised no intervention, five single faults, and three mixed-fault configurations. On 216 held-out windows from 12 unseen backgrounds, RBLSI-BN achieved 83.3% classification accuracy, compared with 80.6% for BN and 76.9% for RLSI-BN. Top-2 accuracy reached 96.8%, and the multiclass Brier score was 0.282, compared with 0.298 for BN and 0.332 for RLSI-BN. Continuous monitoring detected 78.1% of abnormal events, with a 2.38% time-point false-alarm rate on no-intervention trajectories and a median delay of 1.33 h among detected events. A web-based prototype displays posterior rankings and suggested checks. The framework links adaptive prediction to interpretable diagnosis, but prospective validation across plants is needed before operational deployment.