Comparative Study of Artificial Neural Network and Response Surface Methodology for Modelling and Optimization the Adsorption Capacity of Fluoride onto Apatitic Tricalcium Phosphate

M Mourabet,M.Bennani Ziatni,A Taitai,A El Rhilassi

doi:10.13189/ujam.2014.020202

Abstract

In this study, Response Surface Methodology (RSM) and Artificial Neural Network (ANN) were employed to develop an approach for the evaluation of fluoride adsorption process. A batch adsorption process was performed using apatitic tricalcium phosphate an adsorbent, to remove fluoride ions from aqueous solutions. The effects of process variables which are pH, adsorbent mass, initial concentration, and temperature, on the adsorption capacity ( ��ℯ (mg/g)) of fluoride were investigated through three-levels, four-factors Box-Behnken (BBD) designs. Same design was also utilized to obtain a training set for ANN. The results of two methodologies were compared for their predictive capabilities in terms of the coefficient of

Highlights

Response Surface methodology (RSM), introduced by Box and Willson [1], is a collection of mathematical and statistical technique useful for analyzing problems in which several independent variables influence a dependent variable or response and the goal is to optimize the response[2]
A second-order model is commonly used in response surface methodology: YY = ββ0 + ∑kiik=1 ββii xxii + ∑kiik=1 ββiiiixxi2i + ∑ikik=−11 ∑kjjk=ii+1 ββiiiixxiixxjj + E (1)
The apatitic tricalcium phosphate (Ca9 (HPO4) (PO4)5(OH)) powders were prepared by an aqueous double decomposition of the salts of calcium and of phosphate [24,25]

Summary

Introduction

Response Surface methodology (RSM), introduced by Box and Willson [1], is a collection of mathematical and statistical technique useful for analyzing problems in which several independent variables influence a dependent variable or response and the goal is to optimize the response[2]. The design procedure of response surface methodology is as follows [3]: 1. Designing of a series of experiments for adequate and reliable measurement of the response of interest. 2. Developing a mathematical model of the second order response surface with the best fittings. 3. Finding the optimal set of experimental variables that produce a maximum or minimum value of response. A second-order (quadratic) model is commonly used in response surface methodology: YY = ββ0 + ∑kiik=1 ββii xxii + ∑kiik=1 ββiiiixxi2i + ∑ikik=−11 ∑kjjk=ii+1 ββiiiixxiixxjj + E (1)

Methods

Results

Conclusion