## 2 Proposed Method
### Model
#### 2.1.4 Data Generation  
Consider a structure equipped with \(n\) joints (or accelerometers). A total of \(m\) experiments are carried out to construct the training data set. The first experiment (\(E=1\)) involves measuring \(n\) acceleration signals across the entire structure. In the remaining \(m-1\) experiments, each experiment has one joint damaged. For the data collected by each accelerometer, we can divide it into damaged data and undamaged data, as follows:  
\[Damaged_{i}=\left[D_{E=i+1,J=i}\right] \tag{13}\]  
\[Undamaged_{i}=\left[U_{E=1,J=i},U_{E=2,J=i}\cdots U_{E=i,J=i},U_{E=i+2,J=i} \cdots U_{E=m,J=i}\right] \tag{14}\]  
where \(D\) and \(U\) indicate the measurements acquired for the damaged and undamaged structural cases, respectively. \(\left(U|D\right)_{E=m,J=i}\) represents the data obtained by the \(i\)th accelerometer in the \(m\)th experiment. We can notice that the undamaged data set for the \(i\)th joint includes signals measured when all joints are undamaged (\(U_{E=1,J=i}\)) and signals measured when one of the other joints is damaged. The purpose of this is to eliminate the mutual influence between joints.  
The next step is to normalize the data. To be more realistic, we do not normalize the damaged and undamaged data separately, which most current studies use, but normalize the damaged and undamaged data together. The normalization process is expressed as follows:  
\[N_{i}=Normalize(Damaged_{i},Undamaged_{i}) \tag{15}\]  
\[DN_{i}=N_{id} \tag{16}\]  
\[UN_{i}=N_{iu} \tag{17}\]  
where \(N_{i}\) is the vectors after uniform standardization, and \(Normalize(\cdot)\) represents the normalization function. \(DN_{i}\) and \(UN_{i}\) represent damaged and undamaged vectors in \(N_{i}\), respectively. The next step is to partition the undamaged and damaged vectors into many frames, each with a fixed number(\(n_{s}\)) of samples. This operation's outcome for joint \(i\) can be written as:  
\[DF_{i} =\left[DF_{i,1},DF_{i,2},DF_{i,3}\cdots DF_{i,\mu_{d}}\right] \tag{18}\] \[UF_{i} =\left[UF_{i,1},UF_{i,2},UF_{i,3}\cdots UF_{i,\mu_{u}}\right] \tag{19}\]  
where \(DF_{i}\) and \(UF_{i}\) are vectors containing the damaged and undamaged frames for the joint \(i\), respectively. \(n_{d}\) and \(n_{u}\) are the total number of damaged and undamaged frames, respectively. Given the total number of samples in each acceleration signal \(n_{T}\); \(n_{d}\) and \(n_{u}\) can be computed as:  
\[n_{d}=\frac{n_{T}}{n_{s}} \tag{20}\]  
\[n_{u}=n\times\frac{n_{T}}{n_{s}} \tag{21}\]  
It is clear from Equations (20) and (21) that the number of undamaged frames will be much greater than the number of damaged frames for a given joint \(i\). Some researchers choose the same amount of damaged and undamaged frames for training to avoid the impact of imbalance on performance, which is impracticable. As a result, selecting the same number of damaged and undamaged frames is skipped. Then, send the damaged and undamaged frames to train in a jumble. Figure 6 depicts the specific flow chart. After the data has been processed, it is fed into the model for training, and a trained model is generated. After processing data from an unknown state according to the previous stages, input it into the trained model for testing. Finally, the model generates a score \(s\), representing the current data's damage score.