## 3 Methodology
### The Proposed ConvResBiGRU-SE Model
#### 3.3.3 SE-Residual Block  
Fundamental deep learning architectures, such as LeNet, AlexNet, and VGGNet, typically consist of convolutional layers followed by fully connected layers for classification or regression tasks. These models do not incorporate residual or skip connections. Instead, each layer feeds its output directly into the next, forming what are known as sequential networks. As the layers in a sequential network grow, concerns with vanishing or exploding gradients could arise. ResNet incorporates residual blocks that facilitate skip connections among convolutional layers. This enhances gradient propagation and facilitates the training of significantly deeper CNNs with no facing gradient vanishing issues. A residual layer could be depicted in the following format:  
\[\text{ELU}(x) = \begin{cases}x&\text{x}\geq 0\\ \alpha*(e^{x}-1)&\text{x}<0\end{cases}  \tag{12}\] \[R(x) = \text{ELU}(x\,+\,f(x)) \tag{13}\]  
In this setting, \(f(x)\) denotes the layer's result, whereas \(x\) signifies the input value. The function \(\text{ELU}(x)\) represents the exponential linear unit function, while \(R(x)\) represents the result of the residual block. The residual component \(f(x)\) in this block is defined by two consecutive sequences of three processes: convolution with a 3 \(\times\) 1 filter, batch normalization, and ELU activation. The feature map from \(f(x)\) is combined with the input \(x\). These concatenated features are subjected to the ELU activation function. This study introduces the SEResidual block, which systematically retrieves hybrid features by integrating spatiotemporal and channel-wise data [32]. This residual block comprises Conv1D, BN, ELU, SE modules, and a shortcut connection with BiGRU, as depicted in Figure 4. The SE modules augment the model's representational capacity by emphasizing channel attention. Figure 6 illustrates the configuration of a SE module. The convolution process provides multiple feature maps. Specific maps may include superfluous information. The SE component executes feature recalibration to accentuate the salient features and diminish the less pertinent ones. This module functions in two primary steps: squeeze and excitation. During the squeeze stage, all data on the channels is gathered. The dimensions of the feature map \(U\) for a single channel are \(C\times H\times W\), where \(H\times W\) denotes the feature map's dimensions. Feature maps for each channel are condensed into \(1\times 1\) feature maps utilizing a channel descriptor function, such as global average pooling (GAP) [33]. A scalar value denoting the channel's global information is generated within this period. The squeeze process is delineated in Equation (14), where \((u_{c}(i,j))\) signifies a feature map for channel \(c\) after the passage of \(X\) through the convolution layer. \(F_{squeeze}\) denotes the channel characterization function, and GAP was employed in this research. \[Z_{c} =F_{squeeze}(U_{c}) \tag{14}\] \[=\frac{1}{H\times W}\sum_{i=0}^{H}\sum_{j=0}^{W}U_{c}(i,j) \tag{15}\]  
Subsequently, during the excitation phase, channel-wise dependencies are modeled using the descriptors obtained from the preceding squeeze phase. This is achieved via fully-connected (FC) layers and non-linear functions. Equation (16) delineates the excitation phase, wherein \(z\) denotes the value derived from the squeeze phase, \(W_{i}\) signifies the \(i\)th fully connected layers, \(\sigma\) denotes the sigmoid function, and \(F_{excile}\) indicates the excitation function. The sigmoid function guarantees that the result of the excitation phase is confined within the interval of 0 to 1, which can subsequently serve as a calibration weight. The newly derived weight \(s\) from the excitation phase is multiplied by the current feature map \(U\). Figure 6 illustrates the functionality of the SE module employed in the present investigation, showcasing the configuration of the squeeze and excitation phases within the SE block.