## 5 Use of Artificial Neural Network  
This methodology relies on historical data, where hyperparameter values are adjusted simultaneously to identify those most influential on the network's performance, aiming to minimize specific outputs. These outputs include the mean absolute error (MAE) defined in Equation (4), computing time per epoch, and the number of trainable parameters. \[MAE=\sum_{t=1}^{T}\frac{|\hat{y}_{t}-y_{t}|}{T} \tag{4}\]  
Here, \(y_{t}\) represents the true output, \(\hat{y}_{t}\) denotes the estimated output T corresponds to the number of data points. To manage computational complexity and resource efficiency, a reduction strategy is often necessary to limit the number of experimental runs, as the complexity scales with the number of hyperparameters. Table 2 outlines the factors evaluated in this study to determine the optimal network size for minimizing prediction errors on the provided dataset. It is important to note that these factors are presented as normalized and encoded values, ranging from \(-1\) to \(1\). The sequence size (A) denotes the number of data points extracted from the temporal sequence that are utilized for network training to generate the forecast. The head size (B) corresponds to the number of neurons comprising each attention head. The number of heads (C) represents the quantity of independent attention mechanisms embedded within the Transformer block. The feedforward dimension (D) specifies the count of one-dimensional convolutional layers. The number of encoder blocks (E) indicates the total number of encoder layers that constitute the network. The MLP units (multi-layer perceptron units--F) define the number of neurons within the fully connected dense \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Hyperparameter** & \(-\mathbf{1}\) & \(\mathbf{1}\) & & **Hyperparameter** & \(-\mathbf{1}\) & \(\mathbf{1}\) \\ \hline A & Sequence size & 5 & 35 & E & No. encoder blocks & 2 & 6 \\ B & Head size & 64 & 192 & F & mlp units & 64 & 192 \\ C & Number of heads & 2 & 6 & G & Learning rate & 0.0005 & 0.0015 \\ D & F. Forward dimension & 2 & 6 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameters considered in the model. network, while the learning rate (G) determines the magnitude of the adjustment step taken during each iteration to minimize the loss function. To minimize the computational demands on the hardware, relevant hyperparameters are optimized to their ideal values, while non-essential factors are set to their minimum thresholds. The neural network is subsequently trained using historical data, concurrently with the collection of new data from the compressor. The model generates predictions in the form of a time series. Based on the model's training, the predicted data, and their operational expertise, control room technicians evaluate the potential implications of equipment operating outside acceptable ranges or experiencing unplanned shutdowns. Decisions are then made in accordance with established operational protocols. Given the considerable number of factors under consideration (7), the adoption of a fractional factorial design is considered necessary. The resolution of the design is determined by the number of experimental runs required and the acceptable degree of aliasing among the factors, including their second-order, third-order, and higher-order interactions. Consequently, a resolution IV design is selected as the minimal configuration capable of capturing the most significant main effects and second-order interactions. While this design results in aliasing between factors and second-order interactions, it is deemed the most suitable option based on the established assumptions. By employing this design, only 16 experimental trials are required, as opposed to the 128 trials needed for a full factorial design, and two replications are included. Figure 5 illustrates the process followed. The data have been divided into three subsets: training (70%), validation (15%), and testing (15%).