## 3 Proposed Methodology
### The Proposed Att-ResBiGRU Model
#### 3.3.1 Convolution Block  
CNNs excel at extracting features from tensor data, making them particularly well suited for tasks like image analysis and behavioral recognition. This investigation employs the one-dimensional CNN (1D-CNN) for effective feature extraction. For the provided data, Figure 3 visually presents the representation of the time series on the vertical axis and the multi-axis channel features gathered by various sensors on the horizontal axis. The 2D convolution is recognized for its localized nature, which can pose challenges when dealing with many sensors. This is due to the potential disruption of sensor channel integrity caused by local convolution. Conversely, the 1D convolution operates on behavioral units and processes all sensor channels concurrently. Consequently, when designing the model for spatial feature extraction, the 1D convolution is favored over the traditional 2D convolution. Utilizing the 1D convolution serves the purpose of feature extraction. The features obtained are considered spatial characteristics within an image, comprising sensor measurement samples. This perspective implies a spatial distribution connection among the samples instead of a time-series relationship. For the computation of the 1D convolution, the input data undergo convolution with each filter and are subsequently activated through a non-linear activation function. This process is computed as follows:  
\[X_{j}=f(\sum_{i=1}^{n}(W^{i}\cdot x_{j}+b^{i})) \tag{4}\]  
The output data that are activated, represented by \(X_{j}\), are determined through a multi-step process. First, the raw input data, denoted as \(x_{j}\), interact with the weightings, \(W^{i}\), associated with the \(i\)th filter. This interaction involves convolving, or mathematically combining, the two elements. Next, a bias value, \(b^{i}\), is added to the convolved result. After that, a non-linear transformation function, \(f\), is applied to the combined data. This non-linear function further alters the data. The passage indicates multiple filters, represented by the variable \(n\). This work utilizes a specialized activation function called the Smish function [40] in its convolutional layer. Compared to the commonly used Relu activation function [41], the Smish function is better suited for handling negative input values, an issue that frequently comes up when processing sensor data. The Smish activation brings additional benefits over Relu, given the characteristics of sensor feeds. The authors defined the Smish function through the following mathematical approach:  
\[smish(x)=x\cdot tanh(ln(1+sigmoid(x))) \tag{5}\]  
The pooling layer downsamples the data after activation using the same padding to maintain a consistent output size. Within the convolution blocks, adjusting the stride parameter of the pooling filters shortens the time-series data length by altering how much the filters downsample, as follows:  
\[len_{out}=\frac{len_{input}}{s} \tag{6}\]The length of the input time series is denoted as \(len_{input}\), the pooled kernel step size is represented as \(s\), and the length of the pooled time series is denoted as \(len_{out}\). Fluctuations in the neural network layer input distributions during training can cause gradient explosion or vanishing, known as the intermediate covariate shift problem [42]. To address this, [PERSON] et al. [43] proposed batch normalization (BN). BN standardizes the batch data before each layer to stabilize training. It smooths gradient descent convergence, accelerating overall training.