Artificial Neural Network (ANN) Approach for Predicting Cu Concentration in Drinking Water of Chahnimeh1 Reservoir in Sistan-Balochistan, Iran

1.1. Artificial Neural Networks Modeling

The artificial neural network is a useful computational way for predicting and modeling abstruse relationships among parameters, especially when there is no explicit relation among parameters (23, 24). The structure of artificial neural network basically consists of three layers, the input layer that all the data are imported to the network and calculation of the weight of each input variables are done, the hidden layer or layers whose data are computed, and the output layer, that the artificial neural network results are obtained. Every single layer includes one or more fundamental section (s) called a node or a neuron (25). The problem is the key factor that can be determined in the number of neurons in the layers. The small number of hidden neurons is a limiting factor to learn the process carefully, even though too high number scan be very time consuming, and the network may over fit the data (26).

In this study, three-layer neural networks were constructed for computation of the reservoir metal concentration (Cu). All the computations were performed using the EXCEL 2003 and MATLAB (Version 7.12, MathWorks, Inc., Natwick, MA).

1.2. ANN Description

The network includes an input layer, hidden layers and an output layer. The inputs for the network include water temperature; pH; electric conductivity (EC); total dissolved solids (TDS). The scaled values have been passed into the input layer and after that, propagated from the input layer to the next layer which is called hidden layer, before reaching the output layer of the network (27). Each node in both hidden and output layers in the first place will act as a summing junction with the use of the following equation inputs combined and modified from the previous layer (28). The y_i is the net input to node j in hidden or output layer, the weight related to neuron i and neuron j are indicated as wij, xi is the input of neuron j, bj is the bias connected to node j (29). Sigmoidal transfer function is usuallyused for nonlinear relationship (30, 31). The general form of this function is showed below (28):

Where Z_j is the output of node j, the sigmoidal function is between 0 and 1, thus the input as well as output data should be normalized to the range between 0 and 1 (31). Hence, normalization of values within a uniform range is vital to prevent data with larger magnitude from overriding the smaller ones. In the present work, scaling of the data to the range of 0–1 was carried out as follows (32): Where is the normalized value, X, and are (R?) the actual, the maximum and the minimum value of data sets respectively.

3.1. Study Area

Sistan-Balochistan is one of the 31 provinces of Iran and is the first largest state in terms of land area (187502 km²). It is bordered by Khorasan province from the north, Afghanistan and Pakistan from the east, Oman Sea from the south and the Kerman province from the west. Chahnimeh1 reservoir is located in the Sistan-Balochistan region that has a series of natural depressions used primarily to store water for irrigation and public water supply (34).They are not only used to store water, but also have profound impact on prevent floods. During periods of high flows, water is diverted to these reservoirs via an intake and canal which has a capacity of up to 1000 m³/s (Figure 1).

Figure 1.

Map Showing the Geographical Setting of the Chahnimeh1 Reservoir

2.2. Water Quality Data Set

The data set used in this study was generated through measuring water quality of Chahnimeh1 in Sistan-Balochistan. The sampling sites are spread over a distance of about 20kmand 2 water samples were collected in spring 2011. Grabbed water samples were collected from two depth of water column (20 cm below the surface and bottom of the reservoir) (35). All the water samples collected during the study period were analyzed for temperature; pH; electric conductivity (EC); total dissolved solids (TDS); and the Cu concentrations.

2.3. Water Analysis Methods

For analysis total copper of all water samples must be acidified at the time of collection with HNO3 (5 mL L-1). Transfer a 100-mL aliquot of well-mixed sample to a beaker then add 2 mL of concentrated HNO₃ and 5 mL of concentrated HCl. The sample is covered with a ribbed watch glass or other suitable covers and heated on a steam bath, hot plate or other heating source at 90 to 95 C until the volume has been reduced to 15-20 mL, then adjust the final volume to 100 mL with reagent water and read the concentration of Cu by flame atomic absorption spectroscopy (36). Physical water quality parameter including (EC, T, TDS and pH) is determined with portable tool (HANNA instrument model: HI 98129) (37).

4.1. ANN Modeling

To enable modeling of nonlinear and complicated functions, feed-forward neural network has been used with one or more hidden layers (28). Nevertheless, it is very hard to choose the number of hidden layers (30). Most of literatures indicate that one hidden layer is good enough to validate the prediction and maybe the best to decide for all applied feed-forward network design (38). Thus, in this paper one hidden layer was used for modeling (Figure 2).

Figure 2.

Schematic Representation of the ANN Architecture Used in This Study

It is crucial to highlight the determination of the number of neurons in hidden layers. Neurons played an important role that effected on the general characteristics of network and training time (27). The complexity of relationship among parameters determined the number of neuron in the hidden layer (39). The optimum number of neurons in a hidden layer was found by trial and error.

The network has trained with various kinds of learning algorithms but knowing about their suitability and fitness is not an easy task to do. In our research, Levenberg–Marquardt back propagation (LM) algorithm applied in order to train ANN. The LM is an approximation to the Newton’s method (40).The results show that the best performance of network design included 3 different layers: input layer, hidden layer consist of 7 nodes on it as well as output layer. The evaluation indexes MSE and R calculated 0.00008 and 0.9346;0.00019 and 0.8612 for training set; 0.000014 and 0.7348; 0.0004 and 0.9372 for validation set, testing set and all data set respectively. Prediction accuracy of all data set (training, validation and testing) is high enough as shown in Table 1. Predicted values of the best model also showed in Table 1. Table 2 shows that values of MSE are very little indicating that predicted and actual values were close enough.

5.1. Sensitivity Analysis

Sensitivity analysis is a tool to determine how “sensitive” a model is to changes in the parameters of the model as well as its structure. In this part, parameter sensitivity is a center of attention. Parameters sensitivity in this research performed as a series of tests on ANN model to understand how a change in the parameter can lead to a change in evaluation indexes including both MSE and R. Sensitivity analyses of all possible composition variables were done. The optimum network with lowest MSE and highest coefficient of correlation (R) was in group of four variables. P1, electric conductivity (EC); P2, total dissolved solids (TDS); P3, temperature (T); and P4, pH are the input variables. Table 3 shows the results of Sensitivity analysis. As it can be seen in Table 3, in the group of 1 variable p3 (T) is the most effective parameter because of its best evaluation indexes (lowest MSE and highest R), according to the Table 3, the best MSE and R were obtained with combination of P2 (TDS) and P3 (T). The best group of 3 variables were obtained with interaction of best group of two variables (P2 + P3) and applied with P1 (EC). The values of MSE and R become better in the case the interaction of P1 + P2 + P3 combined with P4 to access the optimum values of MSE and R.

The experimental data and ANN modeling prediction were juxtaposed in Figure 3. According to Figure 3, excellent agreement between experimental data and ANN results was indicated.

Figure 3.

Comparing ANN Output and Experimental Data for Cu Concentration in Chahnimeh1 Water for (a) Training, (b) Testing, (c) Validation and (d) all Data Sets