## 3 Artificial Neural Network (ANN) Model for Structural Characterization
### Mathematical Approach for Artificial Neural Network (ANN) Model  
The proposed methodology uses Supervised Learning in the ANN models, in which the ANN models are provided labeled input data and the desired output outcomes and results. The ANN models with learning techniques are instructed, using supervised learning techniques, on what to look for and what to deliver as an output. The ANN models are completely trained until they can achieve the expected performance to detect all the patterns and ANN neurons' relationships with the weights and outputs. The trained ANN models produce the desired outputs, thereby leading to great results within the best optimized and efficient ways. Mathematically, as shown in Equation (1), the ANN function \((Y)\) is known as a composition of other functions \(f(Q_{j})\), which can be further decomposed into other functions. The ANN model, as shown in Equation (1), Equation (2) and Equation (3), respectively, \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Inputs** & **ANN Model** & **Outputs** \\ \hline \(\bullet\) & Raw material & \\ \(\bullet\) & Resin material & \\ \(\bullet\) & AM techniques & \\ \(\bullet\) & Speed of AM machines in & \\ \(\bullet\) & coupon fabrication & \\ \(\bullet\) & Temperature of the dispated and & \\ \(\bullet\) & multifunctional carbon fiber composites & \\  by AM machines & & \\ \(\bullet\) & Manufacturing processes & \\ \(\bullet\) & Coupon composition & \\ \(\bullet\) & AM locus orientations for & \\  coupon fabrication & & \\ \(\bullet\) & No. of test coupons & \\ \(\bullet\) & Statistically sound test data & \\ \(\bullet\) & Test matrix & \\ \(\bullet\) & Test plan & \\ \(\bullet\) & Software version of the machines used & \\ \(\bullet\) & Software assurance of the software used & \\  in AM machine & & \\ \(\bullet\) & Calibration of AM machines & \\ \(\bullet\) & Calibration of testing machines & \\ \(\bullet\) & Environmental: & \\ (1) & Cold Temperature Dry (CTD) & \\ (2) & Room Temperature Dry (RTD) & \\ (3) & Elevated Temperature Wet (ETW) & \\ (4) & Elevated Temperature Dry (ETD) & \\ (5) & Dry & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Relationship amongst inputs, ANN and outputs of proposed methodology. can be trained by using three learning types: supervised learning, unsupervised learning and reinforcement learning. The process of training a system to perform a desired function is called supervised learning [38]. Unsupervised machine learning is defined as ML algorithms that are used for analyzing and clustering in order to find patterns in unlabeled data, e.g., in the clustering of samples [39]. Reinforcement learning involves learning what to do and how to map situations to actions for maximizing a numerical reward signal, in which an intelligent agent (algorithm) interacts with the environment [40]. The training/learning of the ANN model can be achieved by using various algorithms and adjusting its corresponding weights to obtain the desired outputs. The mathematical ANN model/architecture, as shown in Equation (1), is defined by the number of neurons and the interconnection of those neurons with weights and biases. The ANN model, as shown in Figure 7 and Equation (1), is defined on a set of input-output pairs and is trained to produce the desired output. The structure of each ANN model is represented as \((i,j,\text{k})\), where \(i\) represents the number of nodes in the input layers, \(j\) is the number of nodes in the hidden layers, and k is the number of nodes in the output layers [41]. As shown in Figure 7, synapses connect the neurons with the input-hidden layer, hidden layer-hidden layer and hidden layer-output with links. Those links, tied to each synapse, are called weight factors.