## 3 Structural Damage Detection Method Using Proposed FFT-DCNN Architecture  
This study proposes an FFT-DCNN method where FFT converts one-dimensional vibration signal into frequency information that reflects the structural damage, and the dimension of frequency information is \(M\times 1\). Considering that DCNN is powerful for extracting spatial features of input data, the frequency information \(M\times 1\) is converted to \({F}{F}{F}{M}=\sqrt{M}\times\sqrt{M}\) the matrix via dimension transformation, which can reflect the spatial information. Then, \({F}{F}{M}\) are fed into the DCNN model to distinguish different structural damage condition. Figure 3 shows the specific process of structural damage detection. Firstly, a sliding window is utilized to split the raw acceleration signals to obtain more samples, which is the term of data augmentation means [31]. Then, to make the data dimension transformation more convenient, the sliding window is set to 324 points, considering that the sampling frequency is 322.58 Hz. In addition, a sliding window with a fixed size is utilized to split the raw acceleration signals. Thus, the length of every segment is the same. Frequency information with 324 points can be acquired by utilizing the FFT method, and every segment includes frequency information of acceleration data.  
The obtained datasets are randomly divided into training datasets, validation datasets, and testing datasets with a ratio of 6:2:2. Then, the frequency feature matrix \({F}{F}{M}\) is then fed into the DCNN model. The loss function and optimizer are used to continuously iterate and update model parameters via training datasets. To reduce the overfitting training process, the model finishes the renewal of model parameters and training process when the training model obtains a preferred result of structural damage detection on verification datasets.  
During the training process of FFT-DCNN model, the vibration data are fed into FFT to analyze the frequency information. Then, the \({F}{F}{F}{M}\) matrix is fed into convolutional layers extracting spatial features and max-pooling layers reducing trained parameters in the DCNN model. To avoid overfitting problems and improve the ability of features extraction, dropout is added into a fully connected network [32]. After the four convolutional layers and two max-pooling layers extracting features from vibration signals, the features are fed into two fully connected networks with 300, 200 neurons to predict structural damage conditions.  
In addition, the optimizer, Adam, is used to update the DCNN model parameters in every iteration. The dropout value is set to 0.5, and the batch size is set to 512. The initial learning rate is 0.001. In this study, the cross-entropy loss function is utilized to assess the training results, which is shown as:  
Figure 3: Flowchart of the proposed FFT-DCNN for structural damage detection.  
\[CrossEntropy=-\sum_{K=1}^{N}\left(P_{K}\times\log Q_{\text{k}}\right) \tag{9}\]  
where \(Q_{\text{k}}\) is the predicted value and \(P_{K}\) represents the real value. Finally, after finishing the training, the testing dataset is fed into the DCNN model to identify the degree of structural damage. If the accuracy metric is high, it represents that the FFT-DCNN has excellent performance, and the proposed methods can be applied to actual structural damage detection.