Influent shock forecasting in wastewater treatment plants: Coupling of shock-preserving preprocessing with a SARIMAX model

Wastewater treatment plants (WWTPs) are essential for urban water environmental protection. However, their influent frequently experiences multisource disturbances such as rainfall-induced infiltration and atypical discharges, triggering short-term quality shocks that impose considerable operational risks. These shock events can rapidly alter organic and nutrient loading, causing mismatches in dissolved oxygen, sludge recirculation, and chemical dosing controls, thereby elevating the risk of effluent noncompliance. Accurate forecasting of influent shocks is therefore critical for stable WWTP operation. Data-driven methods have shown promise in influent prediction, but their high data requirements and reliance on external driving information unavailable at most plants often constrain their deployment. Under a realistic condition, using only in-plant online monitoring data, ARIMA-family models retain unique advantages in interpretability, low computational cost, and suitability for online deployment. However, their application to shock prediction encounters two bottlenecks: conventional preprocessing uniformly removes outliers via smoothing, inadvertently clipping genuine sustained shock peaks and causing systematic underestimation during high-risk intervals; and fixed-parameter models exhibit response lag and error amplification during shock-induced structural breaks.

This study proposes a shock forecasting framework coupling three optimization strategies with a SARIMAX model, using 4901 hourly records of COD, NH₃—N, TN, and TP from a WWTP online monitoring system (80/20 chronological split). The first strategy is shock-preserving preprocessing: a duration-based discrimination logic classifies outlier segments persisting ≤2 hours as transient instrumental spikes for local repair, while those exceeding 2 hours are considered genuine shocks and entirely preserved. Outlier detection follows the Pauta criterion applied to a 24-point sliding window, and two metrics, shock retention rate and peak preservation ratio, quantify preprocessing fidelity. The second strategy extends ARIMA to SARIMAX with a 24-hour seasonal period for diurnal-cycle modeling to capture daily periodicity driven by urban water-use rhythms. The third strategy is shock-triggered refitting: upon shock detection during the prediction phase, the model automatically refits parameters on recent data to mitigate parameter mismatch caused by structural breaks. Four model configurations are systematically compared: M0 (conventional preprocessing + ARIMA), M1 (shock-preserving preprocessing + ARIMA), M2 (conventional preprocessing + SARIMAX with strategies 2 and 3), and M3 (all three strategies combined). A three-factor factorial ablation experiment decomposes single-factor, pairwise, and three-way interaction effects to quantify each mechanism’s contribution.

Shock-preserving preprocessing raised the COD shock retention rate from 34.29% to 97.14%, with NH₃—N, TN, and TP increasing from 0% to 100%; peak preservation ratios rose to 1.000 across all indicators. For shock-period prediction, M3 achieved MAE reductions of 54.8% for COD (from 57.869 to 26.151), 61.2% for NH₃—N (from 11.999 to 4.659), 51.1% for TN (from 5.330 to 2.608), and 65.2% for TP (from 0.470 to 0.164) compared with M0. Factorial analysis revealed that shock-preserving preprocessing was the dominant contributor to shock-period improvement, with the largest single-factor MAE reductions for COD (25.430), NH₃—N (5.952), and TP (0.231). A clear positive synergy was observed between preprocessing and shock-triggered refitting, particularly for COD (interaction effect 8.196) and NH₃—N (1.389), indicating that refitting better tracks structural changes when the training data preserve shock morphology. Diurnal-cycle modeling exhibited mostly negative synergy during shock periods but contributed to overall prediction mainly through combined interactions with other strategies.

The proposed method, relying solely on in-plant monitoring data, raises shock retention rates to 97%–100% and reduces shock-period MAE by 54.8%–65.2% compared with the conventional baseline. Shock-preserving preprocessing is the primary contributor to shock-period performance gains, with notable positive synergy with shock-triggered refitting, while diurnal-cycle modeling enhances overall prediction through synergistic interactions.