Production system efficiency optimization through application of a hybrid artificial intelligence solution

Figures & data

Table 1. Key subject areas of the SCOPUS keyword search (N.B. one document may belong to multiple subject areas).

	production efficiency and DEA	production efficiency and ML	DEA and ML
Engineering	67	32	33
Environmental Science	109	7	8
Agricultural and Biological Sciences	88	13	2
Computer Science	31	27	39
Business, Management and Accounting	71	6	16
Social Sciences	55	4	10
Economics, Econometrics and Finance	63	-	4
Energy	51	6	10
Mathematics	31	3	21
Decision Sciences	29	3	17
Chemical Engineering	6	10	3
Total documents	331	70	88

Figure 1. Conceptual model of the production system.

Figure 2. Schematic diagram of the thermoelectric plant.

Figure 3. DEA efficiency estimation and ML training phases of the hybrid AI solution.

Figure 4. The Genetic algorithm optimisation phase of the hybrid AI solution.

Figure 5. DEA relative efficiency distributions of the two models for year 2020.

Figure 6. Correlation table of selected input, output, process control and state variables of the two models.

Figure 7. Relationship between process control and state variables as well as DEA efficiency achieved.

Table 2. ML model optimal parameters and performance.

Dependent variable	Learning rate	Pre-processing method	R2	MSE
steam pressure (bar)	0.20	Power Transformer	0.2808	6.9069
steam temperature (°C)	0.20	Quantile Transformer (Uniform)	0.3029	5.4983
furnace temperature A (°C)	0.20	Min-Max Scaler	0.6103	646.2882
furnace temperature B (°C)	0.20	Power Transformer	0.5485	449.4722
flue gas temperature A (°C)	0.20	Quantile Transformer (Normal)	0.5168	319.0069
flue gas temperature B (°C)	0.20	Power Transformer	0.8686	27.0330
flue gas NOx conc. (ppm)	0.20	Max-Abs Scaler	0.2363	473.2964
flue gas CO conc. (ppm)	0.15	Quantile Transformer (Normal)	0.2533	252467.0000
pre-ECO flue gas temperature A (°C)	0.20	Min-Max Scaler	0.6534	71.1030
pre-ECO flue gas temperature B (°C)	0.15	Power Transformer	0.6915	74.9431
flue gas flow rate (m3/h)	0.20	Quantile Transformer (Normal)	0.5446	14.9431
steam production (MJ/h)	0.20	Quantile Transformer (Normal)	0.5217	157.6350
generated electricity (MW/hr)	0.20	Quantile Transformer (Normal)	0.6616	8.1102
Predict efficiency (model 1)	0.20	Max-Abs Scaler	0.9960	0.000082
Predict efficiency (model 2)	0.20	Max-Abs Scaler	0.9981	0.000065

Figure 8. Improvement of the fitness through generations of GA.

Table 3. Optimal recommendations for an output of 168 MJ/h and 48 MW/hr (model 1 and 2).

		Recommendation for optimal efficiency Model 1 for 168 MJ/h	Recommendation for optimal efficiency Model 2 for 48 MW/hr
Input	wood infeed A (t/h)	32.4	28.30
	wood infeed B (t/h)	39.6	28.56
	oil infeed (kg/h)	0.0	0.0
Process control	burner primary air pressure (bar)	0.0	0.00084
	burner secondary pressure (bar)	0.3	0.28
	burner tertiary air pressure (bar)	0.0	0.00091
	fluid bed primary air pressure (bar)	12.2	10.73

Table 4. State variable values for the optimal solution.

State variable	Value for the optimal solution (model 1)	Value for the optimal solution (model 2)	Desired Min. value	Desired Max. value
Steam pressure (bar)	96.8	97.2	95	102
Steam temperature (°C)	532.1	534.3	532	535
Furnace temperature A (°C)	824.1	799.8	None	900
Furnace temperature B (°C)	824.4	787.9	None	900
Pre-ECO flue gas temperature A (°C)	432.2	414.2	None	None
Pre-ECO flue gas temperature B (°C)	434.4	43.7	None	None
Flue gas temperature A (°C)	15.2	181.3	120	None
Flue gas temperature B (°C)	137.9	123.7	120	None
Flue gas NOx conc. (ppm)	198.2	184.2	None	200
Flue gas CO conc. (ppm)	1083.2	348.6	None	5000
Flue gas flow rate (m3/h)	66.5	62.9	None	None

Table 5. Calculation time of the AI solution for models 1 and 2.

Model	DEA Calculation Time	ML Model Calculation Time	GA Calculation Time
Model 1	2906.49s	1965.89s	248.86s
Model 2	2681.01s	2925.68s	3285.34s

Figure 9. Efficiencies with and without the AI solution for model 1 and 2 (grey points are observations violating state variable constraints).