### 1. Introduction

_{2}, H

_{2}O and a low concentration of organic acids. Instead of near UV region, this process could be carried out using the close to the solar band (λ < 380 nm) [1]. The semiconductor-based catalyst used in the analysis can either be in powder form suspended in the water or it may be fixed on a solid support.

_{2}(like WO

_{3}, TiO

_{2}, ZnO, Fe

_{2}O

_{3}, CdS, ZnS, V

_{2}O

_{5}, ZrO

_{2}, SnO

_{2}, CeO

_{2}, and Sb

_{2}O

_{4}) is known to be a good photocatalyst for the degradation of several pollutants due to its high photosensitivity and large bandgap. The large bandgap of TiO

_{2}of the order of 3.2 eV makes it difficult for charge carriers to be generated by thermal excitation. This instead requires absorption of the photon with energy ≥ 3.2 eV, which corresponds to UV light of wavelength < 380 nm.

_{2}, photo-Fenton, and visible light/TiO

_{2}processes.

_{2}and optimizing the parameters like pH, catalyst loading, initial concentration of dye, area to volume ratio, UV light intensity and time. (2) Modeling and optimization of the process parameters by artificial neural network and response surface methodology (3) comparison of the results obtained by ANN, RSM, and experiments (4) Reaction kinetics and total mineralization study by total organic carbon (TOC) analyzer. (5) Identification of relative contribution of the parameters for decolorization and degradation

### 2. Materials and Methods

### 2.1. Photo Degradation of AR114

_{2}(Degussa P25) remains suspended and the concentration of the pollutant within the reactor could be assumed to be constant at any time.

_{2}particles from the dye sample, centrifugation is done at the high speed of 15,000 rpm for 10 min. While centrifugation is done it has to be ensured that the level of the sample in each centrifuge tube is same. As a result, the TiO

_{2}particles get settled at the bottom of the tube.

_{o}is the initial concentration of dye and C

_{t}is the concentration of dye at time t.

### 2.2. Modeling by Artificial Neural Network

### 2.3. Multi Response Optimization Using RSM

_{1}, p

_{2}… p

_{n}. The correlation between the output (response) and the input process parameters is designated by function ‘k’ as:

##### (2)

$$E=k({p}_{1},{p}_{2},{p}_{3},{p}_{4}\dots \hspace{0.17em}\dots \hspace{0.17em}\dots .{p}_{n})$$##### (3)

$$E={m}_{0}+\sum _{i=1}^{n}{m}_{ii}{p}_{i}+\sum _{i=1}^{n}{m}_{ii}{p}_{i}^{2}+\sum \sum _{i<j}{m}_{ii}{p}_{i}{p}_{j}+\varepsilon $$_{0}is constant, m

_{i}is the slope accounting for the linear effect of the input factor p

_{i}, m

_{ij}is the linearly mapped interaction effect between the input factors p

_{i}and p

_{j}, and m

_{ii}is the quadratic effect of input factor p

_{i}[31].

_{i}, lies between 0 and 1, signifying the closeness of a response to its ideal value [33]. Overall desirability D

_{e}is achieved by the combined effect of individual desirability functions using:

##### (4)

$${D}_{e}={({d}_{1}\times {\text{d}}_{2})}^{\frac{1}{2}}\hspace{0.17em}\text{such\hspace{0.17em}that},0\le {\text{D}}_{\text{e}}\le 1$$_{1}and d

_{2}are the individual desirability values for the first and second response, respectively.

### 3. Result and Discussion

### 3.1. Modeling and Optimization

#### 3.1.1. Artificial Neural Network Model Development

_{1}and Y

_{2}. The network is trained using a supervised learning algorithm back-propagation. The range of input and output values used in this analysis has been listed in Table 1.

_{1}and Y

_{2}. In Fig. 2 analysis of experimental and predicted values of Y

_{1}and Y

_{2}show a good approximation of output using ANN with R

^{2}values of 0.9924 and 0.9983 Y

_{1}and Y

_{2,}respectively, which establishes the ability of proposed ANN model to effectively predict the outputs.

##### (5)

$${\text{I}}_{j}=\frac{{\sum}_{l=1}^{{N}_{{h}_{1}}}\left(\left(\raisebox{1ex}{$\mid {W}_{jl}^{i{h}_{1}}\mid $}\!\left/ \!\raisebox{-1ex}{${\sum}_{k=1}^{{N}_{i}}\mid {W}_{kl}^{i{h}_{1}}\mid $}\right.\right){\sum}_{m=1}^{{N}_{{h}_{2}}}\mid {W}_{lm}^{{h}_{1}{h}_{2}}\mid \right)\hspace{0.17em}\mid {W}_{mn}^{{h}_{2}o}\mid}{{\sum}_{k=1}^{{N}_{i}}\left\{{\sum}_{l=1}^{{N}_{{h}_{1}}}\left(\left(\raisebox{1ex}{$\mid {W}_{jl}^{i{h}_{1}}\mid $}\!\left/ \!\raisebox{-1ex}{${\sum}_{k=1}^{{N}_{i}}\mid {W}_{kl}^{i{h}_{1}}\mid $}\right.\right){\sum}_{m=1}^{{N}_{{h}_{2}}}\mid {W}_{lm}^{{h}_{1}{h}_{2}}\mid \right)\hspace{0.17em}\mid {W}_{mn}^{{h}_{2}o}\mid \right\}}$$_{j}is the measure of the relative contribution of the j

^{th}input factor on the output. Here subscripts k, l, m, and n represent the input layer, first hidden layer, the second hidden layer, and output layer neurons, respectively. N

_{i}is the number of neurons in the input layer; N

_{h1}and N

_{h2}are the numbers of neurons in the first and second hidden layers, respectively. The relative importance of input parameters on outputs, Y

_{1}, and Y

_{2}as evaluated using Eq. (5) have been shown in Fig. 3. All parameters showed strong effects on the dye degradation and decolorization efficiencies, the [TiO

_{2}]

_{o}was most effective than other parameters. A/V is the second largest influence parameter for the degradation and decolorization of AR114.

#### 3.1.2. Statistical Analysis using BBD

_{2}]

_{o}, [AR114]

_{0}, [pH]

_{o}, A/V, LI, and t has been used for the optimization.

_{1}and Y

_{2}for photo-degradation of AR114 have been analyzed conferring to the design matrix as proposed by BBD.

_{2}]

_{o}, [AR114]

_{o}, LI, [TiO

_{2}]

_{o}* [pH]

_{o}, [pH]

_{o}* A/V are the highly significant parameters for degradation of AR114. On the other hand [AR114]

_{o}, LI, (LI)

^{2}, [AR114]

_{o}* [pH]

_{0}, [AR114]

_{o}* LI and [pH]

_{o}* LI are the highly significant parameters for decolorization of AR114. Findings of ANOVA are fall in line with the results from previous analysis by 37[] which reported that pH and initial dye concentration are the most significant process parameters for the photocatalytic degradation of methylene blue.

^{2}) to be the maximum for the quadratic model for the Y

_{1}(R

^{2}= 0.9311) and Y

_{2}(R

^{2}= 0.9872). For the Y

_{1}and Y

_{2}adequate precision ratios of 11.048 and 26.503, respectively, have been obtained. For a model to efficiently a problem precision ratio of greater than 4 is required. With precision ratio higher than 4 a model effectively explore the design space [36]. The findings of the analysis of variance (ANOVA) for the Y

_{1}and Y

_{2}have been tabulated in Table 2. The F-value of 13.02 and 74.37 Y

_{1}and Y

_{2,}respectively establish the significance of the used model. Removal of insignificant terms from ANOVA, reduced quadratic model is obtained which summarizes the outcomes for each response and shows the significant model terms.

^{−2}. Results also indicate that the degradation of AR114 increases with an increase in A/V of the reactor (Fig. 4(c) and (d)) i.e. from 0.20 to 0.26 cm

^{−1}.

^{−1}are found to be [TiO

_{2}]

_{o}= 1.2 g L

^{−1}, [pH]

_{o}= 3.6, A/V = 0.25 cm

^{−1}, LI = 10.22 Wm

^{−2}and T = 150 min.

#### 3.1.3. Reaction kinetics of degradation and decolorization of AR114

_{o}/C = k′t, where, C

_{o}is the initial dye concentration, C is the concentration at any given time t) has been plotted in Fig. 5(a). The reaction rates were found to be 0.253 and 0.0542 min

^{−1}for Y

_{1}and Y

_{2,}respectively.

#### 3.1.4. TOC Removal versus degradation and decolorization

#### 3.1.5. Determination of dye degradation products/intermediates in UV/TiO_{2} process

### 4. Conclusions

_{2}. Modeling and optimization results using ANN and RSM are presented for the photocatalytic treatment of AR114. Multi-response optimization by desirability function approach was used to optimize the photocatalytic process variables.

_{2}dose as the most effective input parameter in comparison to other input operating parameters followed by area to volume ratio. For the photocatalytic treatment of AR114 dye, the optimum conditions were evaluated. The predicted values for Model F using ANOVA are 74.37 and 13.02 for decolorization and degradation efficiency of AR114, respectively implying that the developed model is significant. The first order kinetics was obtained for decolorization and degradation of AR114. The first order rate constants were found to be 0.0547 min

^{−1}and 0.0253 min

^{−1}for the decolorization and degradation, respectively of AR114. The mineralization of the dye has also been confirmed by removal of TOC as well as GC-MS analysis under the optimum conditions.