## 6 Artificial Neural Network Model Development  
Artificial Neural Networks (ANNs) are fundamentally grounded in the architecture of biological neural systems and have gained significant traction across diverse disciplines [29]. The intricate associations between inputs and outputs can be effectively modeled through nonlinear statistical techniques known as ANNs. A standard ANN features three unique layers: the input layer, one or more intermediate hidden layers, and the output layer. To facilitate the processes of learning and prediction, each neuron employs activation functions and weighted connections to systematically analyze inputs [30]. The input layer processes normalized raw data within the range of [\(-\)1, 1] to enhance training stability and convergence. Normalization facilitates the equitable treatment of inputs, mitigating the impact of magnitude discrepancies on model efficacy [31]. Each input variable is linked to hidden layer neurons via weighted connections and biases. These  
Figure 5: Multiple linear regression measured vs. prediction fatigue cracking. Figure 6: Pearson’s coefficient between the dependent variable and each independent variable. weights and biases constitute parameters acquired by the network throughout the training phase. The outputs from the hidden layer are transmitted to the output layer for further processing with weights and biases. The final output is derived from these weighted inputs. The output layer may employ distinct activation functions based on the task, including linear activation for regression and sigmoid or softmax for classification. The framework of an ANN model is shown in Figure 7.  
This study's MATLAB 2024a implementation employed an ANN model of one hidden layer with two neurons to predict the fatigue cracking area of asphalt pavements. The ANN architecture illustrated in (Figure 8) is employed for forecasting fatigue cracking in asphalt pavement, incorporating a comprehensive range of parameters across structural, climatic, and traffic-related factors. After confirming the correlation of the input variables with the output variables, the 311 datapoints were used in the formulation of the prediction model for fatigue cracking in an asphalt pavement. The main objective of this study is to develop a prediction model that is simplified but still has a reasonably high R\({}^{2}\) value so that the predicted output represents the required output with high accuracy. The 311 datapoints were normalized first and fed into the input layer. The hidden layer performs computations using weighted inputs and transfer functions. The complexity of the model often depends on the number of hidden layers and the number of neurons in each layer. In our case, there was one hidden layer and two neurons. Of the 311 datapoints, 70% (217) datapoints were selected as training set, whereas the other 15% (47) were used for testing and the remaining 15% (47) were used for validation of the model. The Levenberg-Marquardt (LM) training algorithm is used for the formulation of the ANN model. The LM optimization method combines elements from both the Gauss-Newton algorithm and the method of gradient descent. It is particularly effective for solving least-squares problems, which are common in nonlinear curve fitting and data fitting applications. It is noteworthy that Artificial Neural Networks (ANNs) and other Machine Learning algorithms are frequently regarded as \"black box\" methodologies due to their lack of transparency in demonstrating the influence of individual input variables on outcomes. In contrast to conventional models that offer  
Figure 7: Structure of an ANN with normalized inputs weights, bias, and an activation function producing the output. explicit equations and defined relationships, ANNs discern patterns from data in a manner that often eludes straightforward interpretation.