## 2 Methodology
### Modeling of MFNN  
The predictive power of ANNs depends heavily on its architecture. In general, the architecture of an MFNN is defined by four elements [53]: number of layers, number of nodes in each layer, type of transfer function in each layer, and type of training function.  
Recently, many studies have been undertaken to optimize ANN architecture [53]. However, there is still no scientific method or general rule for finding the optimal architecture of an ANN [34]. Therefore, in this study, the architecture of the ANN was determined through a case study, which is the technique generally followed [34]. The four elements as applied in the case study method are as follows.  
1. The numbers of input layers and output layers are both fixed at one. Therefore, regarding the total number of layers, the number of hidden layers is the only variable. In general, as the number of hidden layers increases, the computational speed decreases proportionately, and the learning efficiency decreases because of the large amount of computer memory required. With consideration of these points, in this research, the case study was conducted with the number of hidden layers limited to two.
2. The number of nodes in the input layer and the output layer is already determined because it is equal to the number of variables that are input and output, respectively, for the problem to be studied [54]. Therefore, the number of nodes in hidden layer is the only variable. There are no general rules for setting the number of hidden nodes [53]. The number of nodes proposed by [PERSON] et al. was used [55]. In their study, they proposed \(n/2\), \(n\), \(2n\), and \(2n+1\) for the number of hidden nodes, where \(n\) is the number of input nodes. In this study, as the number of nodes in the input layer is 55, 28 (\(n/2\)), 55 (\(n\)), 110 (\(2n\)), and 111 (\(2n+1\)) was used as the number of nodes in the hidden layer.  
3. The transfer function transforms the weighted sum of the input values to the output node and determines the strength of the output value [56]. [PERSON] et al. [57] asserted that the transfer function is determined by the nature of the problem to be solved. In this study, a log-sigmoid function (logsig) was used for the hidden layer and a linear function (purelin) for the output layer, which is a commonly used transfer function [33].
4. The training function determines the method of calculating the error of the predicted output value and adjusts the weight and bias. The training function is important because it can considerably affect the learning speed and accuracy [53]. The training function is affected by many factors, such as the nature of the problem, amount of data, and the number of weights. That is, even for a given function, the accuracy and the learning time may vary depending on the nature of the problem. In this study, a relatively large quantity of data (57,600) was used for learning. Therefore, trainscg was used as the learning function, which has relatively low memory consumption and low time consumption, as well as high accuracy when there are many data [58].  
The above parameters are shown in Table 4. With two cases for the number of hidden layers and four cases for the number of nodes in the hidden layers, a total of eight cases were created for the ANN architecture (no. of input nodes-no. of first hidden nodes (-no. of second hidden nodes)-no. of output nodes): 55-28-55, 55-28-28-55, 55-55-55-55, 55-55-110-55, 55-110-110-55, 55-111-55, and 55-111-111-55. The log-sigmoid function is set in the hidden layer and the pure linear function in the output layer. The scaled conjugate gradient backpropagation algorithm was used for training. A total of eight case studies were conducted to evaluate the accuracy of the neural network architecture.