The assessment of response surface methodology (RSM) and artificial neural network (ANN) modeling in dry flue gas desulfurization at low temperatures

Abstract

The performance of a flue gas desulfurization (FGD) system is characterized by SO₂ removal efficiency ($Y_1$) and reagent conversion ($Y_2$). Achieving a near-perfect reaction environment has been of concern in dry FGD (DFGD) due to the low reactivity compared to the wet and semi-dry units. This study will appraise output responses using modeling by response surface methodology (RSM) and artificial neural networks (ANN) approaches. The impacts of input parameters like hydration time, hydration temperature, diatomite to hydrated lime (Ca(OH)₂), sulfation temperature and inlet gas concentration will be studied using a randomized central composite design (CCD). ANN fitting tool mapped the CCD metadata using the Levenberg-Marquardt (LM) algorithm activated by the hyperbolic tangent (tansig) function. The hidden cells ranged from 7 to 10 to ascertain the effect node architecture on modeling accuracy. Validation of each procedure was assessed using root mean square error (RMSE), mean square error (MSE) and R-Squared studies. The outcomes presented a more accurate 5-10-2 ANN model in the mapping of the DFGD from R² data of $Y_1$ = 0.993 and $Y_2$ = 0.9986 with a mapping deviation from the RMSE values of $Y_1$ = 0.48465; $Y_2$ = 0.44971 and MSE results of $Y_1$ = 0.23488; $Y_2.$= 0.20229.

Keywords:

• Deep learning
• empirical modeling
• emission control
• utilization

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data that support the findings of this study are available from the corresponding author, [Robert Makomere], upon reasonable request.

Sample Levenberg-Marquardt algorithm training code.

%Author: Robert Makomere

%Developed using MATLAB R2015a on Microsoft Windows 11 Pro

%Parameters

≫ x = Input;

≫ t = Target;

[x, t] = DeSOx_dataset;

%Neural Network training environment

≫ trainFcn = ‘trainlm’;

≫ hiddenLayerSize = [10];

≫ net.trainParam.epochs = [1000] ;

≫ net.trainParam.goal = [0];

≫ net.trainParam.max_fail = [6];

≫ net.trainParam.min_grad = [1e-7];

≫ net.trainParam.mu = [0.001];

≫ net.trainParam.mu_dec = [0.1];

≫ net.trainParam.mu.inc = [10];

≫ net.trainParam.mu_max = [1e10];

≫ net.trainParam.show = [25];

≫ net.trainParam.showCommandLine = ‘false’;

≫ net.trainParam.showWindow = ‘true’;

≫ net.trainParam.time = ‘inf’;

%Dataset division with dividerand

≫ net.divideParam.trainRatio = 70/100;

≫ net.divideParam.valRatio = 15/100;

≫ net.divideParam.testRatio = 15/100;

%Network training

net = feedforwardnet(10, ‘trainlm’);

[net,tr] = train(net, x, t);

%To view network architecture

≫ view(net)

Additional information

Funding

This study was supported by the Eskom Power Plant Engineering Institute (EPPEI).