Intelligent sewage discharge control in a wastewater treatment plant during rainfall periods

Figures & data

Figure 1. The methodology flow chart.

Figure 2. Pareto charts for (a) all variables (b) the best-subset regression based on R² (c) the best-subset regression based on Mallows’ C_P (d) progressive stepwise regression.

Table 1. Results of the selection of Hellwig method predictors.

The best combinations of predictors				HQ	The worst combinations of predictors			HQ
P	P-1	InF-1		0.5068	InW-1	tmin	tmean	0.0039
P	InF-1			0.4996	InW-1			0.0034
tmax	P	P-1	InF-1	0.4928	InW-1	tmean		0.0033
tmean	P	P-1	InF-1	0.4868	tmax			0.0022
InW-1	P	P-1	InF-1	0.4865	tmax	tmin		0.0020
InW-1	P	InF-1		0.4810	tmin			0.0016
tmax	P	InF-1		0.4795	tmax	tmin	tmean	0.0014
tmean	P	InF-1		0.4789	tmax	tmean		0.0012
tmin	P	P-1	InF-1	0.4767	tmin	tmean		0.0009
InW	P	P-1	InF-1	0.4757	tmean			0.0001

Figure 3. Proposals of considered predictor sets for building regression models.

Table 2. Quality of influent flow regression models based on selected predictor sets.

Variable selection techniques	Training				Testing				The best methods
	RMSE	R^2	MSE	MAE	RMSE	R^2	MSE	MAE
GRM – all effects	2018.20	0.55	4,073,100.00	1203.90					Ensemble Bagged Trees
GRM – progressive stepwise regression	1976.40	0.57	3,906,000.00	1126.10	3133.00	0.34	9,815,700.00	1804.40	Linear regression Interactions Linear
GRM – the best-subset regression Mallows’ Cp	1966.00	0.57	3,865,300.00	1122.50	3140.70	0.34	9,864,200.00	1833.50	Linear regression Interactions Linear
GRM – the best-subset regression corrected R^2	1987.40	0.56	3,949,800.00	1153.70	2795.90	0.48	7,817,200.00	1582.40	Ensemble Bagged Trees
Own type I	2538.90	0.29	6,446,100.00	1682.40	3277.10	0.28	10,740,000.00	2059.90	SVM Coarse Gauusian SVM
Own type II	2751.60	0.16	7,571,100.00	1850.50	3486.00	0.19	12,152,000.00	2006.90	Narrow Neural Network
Own type III	2495.00	0.31	6,224,900.00	1608.80	3454.50	0.20	11,933,000.00	2320.80	SVM Coarse Gauusian SVM
Regression Learner	2041.00	0.54	4,165,800.00	1122.60	2607.10	0.55	6,796,900.00	1492.30	SVM Quadratic SVM
GRM – the best-subset regression corrected R^2 (optimizable)	2009.60	0.55	4,038,400.00	1150.60	2734.50	0.50	7,477,300.00	1573.70	Optimizable Ensemble
Hellwig method I	2114.00	0.51	4,468,800.00	1237.30	2827.60	0.47	7,995,000.00	1237.30	Ensemble Bagged Trees
Hellwig method II	1957.70	0.58	3,832,500.00	1141.00	2772.80	0.49	7,688,600.00	1547.30	Ensemble Bagged Trees
Hellwig method III	1964.60	0.57	3,859,700.00	1139.20	2830.20	0.47	8,010,100.00	1565.40	Ensemble Bagged Trees
Hellwig method IV	2001.00	0.56	4,004,100.00	1172.80	2832.70	0.46	8,024,000.00	1569.40	Ensemble Bagged Trees
Hellwig method – Regression Learner	2147.20	0.49	461,060.00	1166.70	2688.20	0.52	7,226,200.00	1166.70	SVM Quadratic SVM

Figure 4. True and predicted influent flow to WTTP in each month for Quadratic SVM.

Figure 5. Decision Tree for WTTP.

Figure 6. TPR and FNR for training, test and validation sets.

Data availability statement

On analyses in this manuscript, please contact: [email protected]