The use of output-dependent data scaling with arti ﬁ cial neural networks and multilinear regression for modeling of cipro ﬂ oxacin removal from aqueous solution

In this study, an experimental system entailing cipro ﬂ oxacin hydrochloride (CIP) removal from aqueous solution is modeled by using arti ﬁ cial neural networks (ANNs). For modeling of CIP removal from aqueous solution using bentonite and activated carbon, we utilized the combination of output-dependent data scaling (ODDS) with ANN, and the combination of ODDS with multivariable linear regression model (MVLR). The ANN model normalized via ODDS performs better in comparison with the ANN model scaled via standard normalization. Four distinct hybrid models, ANN with standard normalization, ANN with ODDS, MVLR with standard normalization, and MVLR with ODDS, were also applied. We observed that ANN and MVLR estimations ’ consistency, accuracy ratios and model performances increase as a result of pre-processing with ODDS.

The most common method used for CIP removal in activated sludge processes is adsorption. The removal efficiency in this process is 52.8-90.8% (Li & Zhang 

Materials
We received CIP with a purity level higher than 99% from SANOVEL Pharmaceutical Industry in Turkey. Turkey. It has a particle size of less than 0.6 mm. The activated carbon used in the set-up has a particle size of 0.5-1 mm.

Experimental procedure
The adsorption of CIP on bentonite and activated carbon was measured using batch equilibrium experiments at room temperature (23 W C). For each experiment with initial concentration of CIP, a different amount of adsorbent was mixed with 50 mL CIP solution, at a different pH level.
The mixture was then shaken for different agitation periods, at different rates.
After mixing, the supernatants were separated through filters with a mesh size of 0.45 μm. The equilibrium concentrations of CIP in the filtered residual solutions were determined using a UV spectrometer (Hach-Lange DR 5000). The wavelength used to analyze the concentration of CIP was 275 nm. The calibration curve was established with 10 standards between 1 and 45 mg/L with the R 2 higher than 99%.
The adsorption capacities were calculated with reference to a mass balance of CIP in the solutions and were represented in units of milligrams of CIP per gram of adsorbent. The adsorption capacities at equilibrium were calculated according to Equation (1): where q e and C e are the CIP amount adsorbed (mg/g) and the residual concentration (mg/L) at equilibrium, respectively; C 0 is the initial concentration of CIP (mg/L); V and m are the volume of CIP solution (L) and the mass of adsorbent used (g), respectively.

Experiment dataset and statistical analysis
Data obtained with respect to the variables of CIP adsorption on bentonite and activated carbon measured in the experiment are presented in Tables 1 and 2, respectively.
In this study, agitation rate (rpm), contact time (min), adsorbent dose (g/L), pH, initial concentration (mg/L) are fed into ANN as inputs; q e is the output of ANN.

ODDS and normalization
Normalizing the data by pre-processing is quite important for managing calculation load and improving ANN success ratio when estimation modeling is based on ANN. The conventional way of doing this in the literature is by taking the maximum and minimum values of the dataset and normalizing them within the 0.1-0.9 interval.
The working of ODDS method depends on the relationship between the attributes constituting the dataset and the output variable of the dataset. The first step in achieving this is to reduce the calculation costs of classification and prediction algorithms by placing each parameter from the dataset in an interval calculated using the ODDS method.
Following the normalization step during which the dataset was pre-processed using ODDS, the ANN and MVLR estimation models were formed.
If 'A' is defined as an experiment dataset comprising a matrix of [m × n], Y mn will be the output variable of set A, whereas X mn will be the input variable of set A. Accordingly, Equation (2) whereX mn represents the new input-output parameters for ODDS; m and n are the dimensions of the experiment dataset 'A'; and j is the number of the input variable.

Data division and pre-processing
Data division and pre-processing for use in MVLR was carried out in three stages, applying the ANN model on the experimental data, the statistics for which were presented in Tables 1 and 2 above.
In Stage 1, the experimental data are divided into two groups, so that 75% (243 items) is used for training and 25% (81 items) comprises the test data. In Stage 2, the data divided are normalized in the interval 0.1-0.9 according to Equation (3). In Stage 3, the divided data were first scaled using the ODDS method, and then normalization was carried out according to Equation (3).
where x represents the experimental data; x min is the minimum value of the variable; x max is the maximum value of the variable; and x n is the normalized experimental dataset.
The data were divided into two groups as training and test data, using the three stage process described in Figure 1, then underwent pre-processing. These processes were carried out separately for both bentonite and activated carbon experiment data.

Evaluation of prediction performance
Even though the performance of an ANN is generally assessed by measuring its learning ability, the fact that a network has given the correct answers for all examples in the training set does not necessarily mean that its performance will be strong. Strong performance entails an expectation that when the test data that were not previously fed into by the system are finally entered, the ANN would perform at a comparable level of accuracy (Öztemel ).
In this study, the approximate performance of ANN with test data was also evaluated using a multitude of statistical analysis methods, including the determination of coefficient (R 2 ), MSE, RMSE, MAE, MAPE, MEDAE and AARE. These parameters were calculated according to Equations (4)- (12): pre ¼ 1 n X n i¼1 pre i (5) where SS e represents the residual sum of squares; SS t is the total sum of squares; mea is measured value; mea is the mean of measured value; pre is the prediction value; pre is the mean of prediction value; and n is the number of experiments.
Equation (13) is defined in order to quantify the increase in the performance values calculated using the formulas given above.   Accordingly, we used trainlm training function in this study.
Furthermore, logsig, a sigmoid transfer function is used as the transfer function. ANN modeling was performed on MATLAB 2012a, using the Neural Network Training tool.
In this study, the Statistical Analysis tool in Microsoft Excel (http://office.microsoft.com) is used to carry out MVLR analysis. CIP removal results were estimated statistically via this analysis.

Performance measures
The estimation results of data pre-processed with standard

MVLR results
We also calculated CIP removal results achieved with bentonite and activated carbon, using a statistical regression analysis. The following equations were obtained as a result of this analysis.
Estimations of the amount of adsorbed substance during CIP removal with bentonite and activated carbon, using regression equations, and expressed as q e , are summarized in Table 5.

Experiment results and discussion
We investigated, within the framework of the removal of CIP, which is a type of antibiotic, adsorption methods using different adsorbents, with standard normalization and ODDS methods used for scaling, in addition to the use of ANN and MVLR hybrid models as an estimation model.
The relationships between q e experimental and q e estimated for each adsorbent were determined using different statistical methods and are presented in Table 6.
The consistency graph of the q e values obtained through experiment and the q e values obtained through ANN and MVLR estimation models scaled with standard normalization is presented in Figure 3. The consistency graph for the amounts of substance adsorbed, predicted through ANN and MVLR models is presented in Figure 4.
A review of the performance analyses over Figures 3 and 4, and
We concluded the study with estimation equations for bentonite and activated carbon. We produced a general model to predict the adsorption rate on the basis of these estimation models. The model was then applied to achieve

CONCLUSIONS
We developed a model for CIP removal from aqueous solution using activated carbon and bentonite as adsorbents.
Adsorbed CIP amount per unit of adsorbent is expressed with further reference to process variables. ANN and MVLR estimation models were then used to estimate the accuracy of the q e value, expressing the amount adsorbed under certain operating conditions.
Four distinct hybrid models were applied in the study: ANN with standard normalization, ANN with ODDS, MVLR with standard normalization, and MVLR with ODDS. First of all, we applied pre-processing via standard normalization and ODDS methods on the data used in   We also found that ANN and MVLR estimation consistency, accuracy ratios and model performances increase as a result of the pre-processing with ODDS.
In the experiments with bentonite carried out by taking into account the R 2 values, we found that the performance of ANN with ODDS estimation model is 15% higher than that of ANN with standard normalization model whereas the performance of MVLR with ODDS estimation model is 16% higher than that of the MVLR with standard normalization model.
The analysis with activated carbon taking into consideration the R 2 values indicates that the performance of ANN with ODDS estimation model is 19% higher than that of ANN with standard normalization model, while the performance of the MVLR with ODDS estimation model is 17% higher than that of MVLR with standard normalization model.
Moreover, we found that, among estimation models scaled with ODDS, the performance increase of the ANN estimation model with activated carbon is greater than that using bentonite.