## 2 Proposed Seismic Damage Prediction Model for a Building Structure
### Neural Network Configurations
#### 2.3.2 Model \(M_{1}\)  
\(M_{1}\): The time-frequency feature extraction process is implemented by an adaptive feature extraction module (AFEM), and the same classification network module as the baseline network is used. However, rather than the MFCC extraction process, AFEM automatically generates time-frequency features that are best suited to the target task with a data-driven approach, and features are learned in the frequency domain. Compared to data-driven feature learning methods conducted directly from time-domain waveforms [64; 65; 66], frequency-domain learning does not need to consider the complexity of time-domain convolution and additional parameter tuning. At the same time, the Fourier transforms without any parameters would be simpler and improve calculation efficiency [67]. On the other hand, a similar method exists in the study of NLP [68; 69; 70]. However, we extend the structure and different parameter settings for seismic wave data. Specifically, as shown in Figure 5-\(M_{1}\), the preprocessed GM dataset is used to input AFEM. A sample is split into multiple segments along the time dimension after the short-time Fourier transform (STFT), and the step is similar to frame splitting, windowing, and the FFT used in extracting MFCCs. Here, the same parameters are chosen: a frame length of 0.05 s and a frameshift of 0.03 s. Next, the data flows through two normalized transformation layers (Norm-1 and Norm-2). The first normalization layer is used to transform data from the complex domain to the real domain to obtain the power spectrum (or amplitude spectrum). The first normalization layer uses the squared (or absolute) value. The second normalization layer removes the distribution differences between layers and improves the training stability and model performance. A detailed discussion of the parameter settings is given in Section 3.3.  
Then, a linear transform layer that can be learned is used to process the samples, and its weight matrix is similar to filters in MFCCs, where each row represents an n-dimensional filter. Benefiting from the idea of sharing neural network weights [71], which allows the weights to be replicated at least once over a small frequency range, the final learned frequency features will be more prosperous and more adapted to the target task.  
The data is fed to the classification module through a non-linear activation layer. A power function or a logarithmic function can be chosen for the activation layer function, which has different contributions to the AFEM. The detailed analysis is presented  
Figure 5: Neural network configurations: \(M_{0}\) model (baseline model): hand-crafted time-frequency feature and classification network module; \(M_{1}\) model: \(M_{1}\)-AFEM and classification network module; \(M_{2}\) model: \(M_{2}\)-AFEM and classification network module; \(M_{3}\) model: \(M_{3}\)-AFEM and classification network module.  
in Section 3.3.4. Moreover, DCT and short-time energy connections are also added to AFEM (Figure 5-\(M_{1}\)) for easy comparison with the baseline model (\(M_{0}\)).  
Note that although the feature learning process here is similar to MFCCs, it can be combined with other parts of the neural network to learn features through the objective function for the task at hand instead of being designed in advance. Furthermore, we believe that this module, with a slight transformation, can be combined with other FFT transform-based feature extraction methods (i.e., LFCC [72], BFCC [73], etc.) that provide multiple feature choices for different types of tasks using GM data as the input.