## 2 Designed 1D CNN-BiLSTM-AdaBoost Model
### Detailed Model Description
#### 2.2.4 AdaBoost Network Architecture  
The AdaBoost algorithm employs a 1D CNN-BiLSTM as a weak classifier. The fundamental principle of the algorithm is illustrated in Figure 5.  
The algorithm consists of three main steps:  
(1) Initialization of Data Weight Distribution  
The initial weight distribution of the training samples is defined as follows:  
\[D_{i}=(w_{1},w_{2},\ldots w_{N})=\left(\frac{1}{N},\ldots\ldots\cdot\frac{1}{N}\right) \tag{6}\]  
where \(D_{i}\) represents the initial weight distribution; \(w_{i}\) denotes the weight of the \(i\) sample; and \(N\) represents the total number of samples.  
(2) Iterative Selection of Weak Classifiers  
The AdaBoost algorithm iteratively selects weak classifiers over multiple rounds, where t = 1, 2..., T represents the iteration step.  
1 Selection of the weak classifier. The weak classifier h with the lowest error rate in the current round is selected as the t-th base classifier H\({}_{t}\). The classification error e\({}_{t}\) on the weight distribution D\({}_{t}\) is computed as follows:  
\[e_{t}=P(H_{t}(x_{i}\
eq y_{i}))=\sum_{i=1}^{N}w_{t}I(H_{t}(x_{i})\
eq y_{i}) \tag{7}\]  
Figure 4: Basic principle of BiLSTM.  
where \(I(H_{t}(x_{i})\
eq y_{i})\) is an indicator function that takes a value of 1 when \(H_{t}(x_{i})\) makes an incorrect prediction and 0 otherwise and i denotes the index of the sample \(N\).  
2 Computation of the classifier's weight. The coefficient \(H_{t}(x)\) of the weak classifier in this iteration is calculated, representing its weight in the final ensemble classifier.  
\[a_{t}=\frac{1}{2}\ln\left(\frac{1-e_{t}}{e_{t}}\right) \tag{8}\]  
3 Weight adjustment for the next iteration. The weight distribution of the training dataset is updated to guide the subsequent iteration. The weight adjustment formula is as follows:  
\[D_{t+1}=\frac{D_{t}(i)\exp(-a_{t}y_{i}H_{t}(x_{i}))}{z_{t}} \tag{9}\]  
where \(D_{t}(i)\) is the weight of the \(i\)-th sample in the \(t\)-th iteration; \(y_{i}\) represents the ground truth label; \(H_{t}(x_{i})\) represents the prediction result of the \(t\)-th weak classifier; and \(Z_{t}\) is the normalization constant \(Z_{t}=2\sqrt{e_{t}(1-e_{t})}\).  
3 Formation of the final strong classifier  
The algorithm of AdaBoost-1 DCNN-BiLSTM is presented in Algorithm 1. After multiple iterations, the weak classifiers \(\mathrm{H_{t}(x)}\) and their corresponding weights are combined to form a strong classifier using the sign function:  
\[f(x)=\sum_{t-1}^{T}a_{t}H_{t}(x) \tag{10}\]  
The final classifier is obtained through the application of the sign function sign, as follows:  
\[H_{\text{final}}=\text{sign}(f(x))=\text{sign}\left(\sum_{t-1}^{T}a_{t}H_{t} (x)\right) \tag{11}\]  
Figure 5: Principle of AdaBoost.  
```
Input: Training dataset \(\{(x_{i},y_{i})\}_{i=1}^{N}\), weak classifier 1 DCNN-BiLSTM, number of iterations \(T\) Output: Final strong classifier \(f(x)\)  1. Initialize the weight distribution  Assign an initial weight to each training sample \(x_{i}(i=1,2,\dots,N)\) according to Equation (6).  2. Iterative training of weak classifiers  For t = 1, 2, \(\dots\), T, perform the following steps: 1 Train the weak classifier and compute the error rate * Train the weak classifier \(D_{t}\) using 1 DCNN-BiLSTM based on the current weight distribution \(h_{t}\); * Compute the classification error rate on \(D_{t}\) using Equation (9). 2 Compute the weight of the weak classifier  Determine the weight coefficient of \(h_{t}\) in the final ensemble model using Equation (10). 3 Update the weight distribution of training samples  Update the weight of each sample according to Equation (11) to guide the next iteration. 3. Construct the strong classifier 1 Combine all weak classifiers and their corresponding weights using Equation (12); 2 Obtain the final strong classifier \(f(x)\) through Equation (13).
```  
**Algorithm 1** AdaBoost-1 DCNN-BiLSTM