# The prediction of SO_{2} removal using statistical methods and artificial neural network

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## Abstract

Artificial neural network and a statistical model have been applied in a laboratory scale trickle bed reactor (TBR) to investigate the SO_{2} removal efficiency of activated carbon. The performance of artificial neural network (ANN) model has been compared with the statistical model based on central composite experimental design. Two independent variables, which affect the amount of SO_{2} removal by the liquid phase in the TBR, were selected; namely liquid flow rate and gas flow rate. Amount of SO_{2} removal was chosen as the dependent variable (target data). A second order statistical model has been considered to show the dependence of the amount of SO_{2} removal on the operating parameters. A back-propagation ANN has been used to develop a model relating to the amount of SO_{2} removal. A series of experiments have been conducted on the basis of the statistics-based design of experimental method**.** It is observed that a neural network architecture having one input layer with two neurons, one hidden layer with three neurons, one output layer with one neuron and an epoch size of 20 gives better prediction. The predictions are more accurate than those obtained from regression models.

## Keywords

Artificial neural network Experimental design Trickle bed reactor SO_{2}removal

## List of symbols

*b*_{i}Statistical model coefficients

*U*_{i}Real value of the parameters

*U*_{iav}Average values of the parameters

*U*_{i}^{*}Average value of the independent variables at centre points

- Δ
*U*_{i} Incremental value of the parameters

*U*_{1}Liquid flow rate

*U*_{2}Gas flow rate

*X*_{1}Coded value of the liquid flow rate

*X*_{2}Coded value of the gas flow rate

- ISE
Error square integral

- Y
_{i} *i*th experimental value of the amount of SO_{2}removal- TBR
Trickle bed reactor

- Prob >
*F* Probability of seeing the observed

*F*value if the null hypothesis is true. Small probability values call for rejection of null hypothesis. The probability equals the proportion of the area under the curve of the F distribution that lie beyond the observed*F*value. The*F*distribution itself is determined by the degrees of freedom associated with the variances being compared*R*squaredA measure of the amount of deviation around the mean explained by the model

- Mean squared
Sum of squares divided by

*DF*- Model
*F*value A test for comparing model variance with residual variance. If the variances are close to the same the radio will be close to one and it is less likely that any of the factors have a significant effect on the response calculated by model mean square divided by residual mean square

*DF*Degrees of freedom

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