A Lightweight Multivariate Time Series Prediction Method for Wastewater Treatment

doi:10.12141/j.issn.1000-565X.250132

Abstract

Abstract:

In wastewater treatment processes, the efficient modeling of key water quality parameters is crucial for achieving process control optimization, anomaly detection, and decision support. However, the process data generally exhibits characteristics such as temporal dependence, multivariable coupling, and non-stationarity under varying operating conditions, posing significant challenges to accurate modeling. To address these issues, this paper proposes a Lightweight Multivariate Time Series Prediction Method for Wastewater Treatment based on the Stationary Wavelet Transform (SWT) and Collaborative Attention (CA) mechanism. This model first performed multi-scale decomposition on wastewater data and used the stationary wavelet transform to extract data features from sequences at different scales. Subsequently, a collaborative attention mechanism based on geometric attention and sparse attention was constructed to effectively capture the complex coupling relationships and temporal features among key water quality parameters. Finally, the features reconstructed via inverse wavelet transform were mapped to the final prediction results through a dual-prediction layer. The model was trained and validated on a measured dataset from a wastewater treatment plant in Dongguan, with multi-step prediction tasks and partial data visualization analyses conducted. Experimental results show that, in the 24-step multi-output prediction tasks, the proposed model achieves a reduction of 9.15% to 37.70% in multi-output root mean square deviation (RMSSD) compared to benchmark models. In other prediction tasks, its accuracy ranks second only to TimesNet, which has a significantly larger parameter scale. These results demonstrate an effective balance between lightweight design and high accuracy, thereby validating the efficacy of the proposed model for time-series prediction in wastewater treatment.

Key words: multivariate time series prediction, stationary wavelet transform, collaborative attention mechanism, lightweight, wastewater treatment

CLC Number:

TP277

TANG Lili, LIU Yiqi. A Lightweight Multivariate Time Series Prediction Method for Wastewater Treatment[J]. Journal of South China University of Technology(Natural Science Edition), 2026, 54(1): 60-69.

Figures/Tables 10

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序号	变量符号	变量含义	单位
1	COD-in	进水化学需氧量	mg/L
2	NH+4-N	铵态氮浓度	mg/L
3	TN-in	进水总氮浓度	mg/L
4	pH-in	进水pH值
5	SS-in	进水悬浮固体浓度	mg/L
6	Q-in	进水流量	m³/d
7	Efflu-TN	出水总氮浓度	mg/L
8	Efflu-SS	出水悬浮固体浓度	mg/L
9	Efflu-COD	出水化学需氧量	mg/L

模型	步长	参数量
Autoformer	12	10 515 459
	24	10 515 459
	48	10 515 459
FEDformer	12	16 544 771
	24	16 806 915
	48	16 806 915
Informer	12	11 313 667
	24	11 313 667
	48	11 313 667
TimesNet	12	1 199 621 359
	24	1 199 622 523
	48	1 199 624 851
SimpleTM	12	10 052
	24	10 448
	48	11 240
SWT-CA	12	10 388
	24	10 592
	48	11 000

模型	预测变量	PCC	MSE	MAE	RMSSD
Autoformer	TN	0.640	0.713 1	0.630 5	1.988 5
	SS	0.599	0.505 3	0.533 5
	COD	0.617	0.770 1	0.678 5
FEDformer	TN	0.781	0.420 7	0.486 3	1.318 8
	SS	0.683	0.368 9	0.466 6
	COD	0.742	0.529 2	0.560 0
Informer	TN	0.834	0.326 6	0.410 0	1.081 5
	SS	0.739	0.348 2	0.464 8
	COD	0.809	0.406 6	0.478 7
TimesNet	TN	0.839	0.324 1	0.411 4	1.009 2
	SS	0.753	0.289 5	0.395 9
	COD	0.807	0.395 5	0.479 3
SimpleTM	TN	0.837	0.325 9	0.400 8	1.033 5
	SS	0.751	0.301 4	0.402 1
	COD	0.801	0.487 1	0.487 1
SWT-CA	TN	0.835	0.329 8	0.402 7	1.026 7
	SS	0.755	0.294 8	0.400 2
	COD	0.803	0.402 1	0.483 2

模型	预测变量	PCC	MSE	MAE	RMSSD
Autoformer	TN	0.674	0.624 3	0.583 2	1.799 3
	SS	0.631	0.438 0	0.495 9
	COD	0.635	0.736 9	0.679 9
FEDformer	TN	0.724	0.509 5	0.545 7	1.517 3
	SS	0.618	0.432 2	0.503 4
	COD	0.706	0.575 4	0.599 1
Informer	TN	0.709	0.534 9	0.556 3	1.621 3
	SS	0.660	0.440 8	0.522 7
	COD	0.734	0.645 4	0.625 9
TimesNet	TN	0.790	0.417 3	0.473 1	1.248 7
	SS	0.745	0.307 1	0.403 2
	COD	0.756	0.524 1	0.556 8
SimpleTM	TN	0.651	0.662 5	0.585 9	1.821 0
	SS	0.627	0.426 6	0.494 4
	COD	0.622	0.731 6	0.668 1
SWT-CA	TN	0.819	0.383 8	0.497 6	1.134 4
	SS	0.763	0.322 5	0.402 1
	COD	0.776	0.518 0	0.537 1

模型	预测变量	PCC	MSE	MAE	RMSSD
Autoformer	TN	0.446	1.043 8	0.768 3	2.591 4
	SS	0.526	0.547 5	0.564 3
	COD	0.488	1.000 1	0.811 0
FEDformer	TN	0.541	0.833 6	0.687 8	2.223 4
	SS	0.550	0.538 8	0.564 7
	COD	0.536	0.850 9	0.748 0
Informer	TN	0.626	0.674 8	0.635 7	1.905 1
	SS	0.638	0.490 2	0.558 0
	COD	0.611	0.739 9	0.673 6
TimesNet	TN	0.695	0.575 7	0.568 2	1.661 9
	SS	0.670	0.383 4	0.458 2
	COD	0.647	0.702 7	0.654 2
SimpleTM	TN	0.623	0.693 1	0.600 4	1.838 8
	SS	0.615	0.431 4	0.498 9
	COD	0.624	0.709 2	0.672 0
SWT-CA	TN	0.644	0.671 1	0.584 9	1.733 8
	SS	0.650	0.403 5	0.476 6
	COD	0.655	0.664 2	0.646 5