# Assessment of Earthquake Destructive Power to Structures Based on Machine Learning Methods
## 4 Backpropagation Neural Network
### Feature Extractions  
Ground motion records contain a large number of acceleration time-history data, which is well beyond the size of input suitable for the BPNN. Therefore, it is necessary to use appropriate methods to extract the features of ground motion data. The extracted features should contain enough information to reflect the destructive power of ground motion to structures. The size of the extracted feature should also be suitable for the implementation of the BPNN. In the literature, the acceleration response spectrum of ground motion is usually used to characterize the destructive power of ground motion to structures [23]. The calculation of the response spectrum requires a large number of time-history analyses for SDOF systems with different natural vibration periods, which is computationally intensive. In a real post-earthquake scenario, many ground motion sequences will be recorded, and the calculation of the response spectra of many ground motion records is time-consuming. Compared with response spectrum analysis, the fast Fourier transform (FFT) algorithm is efficient and can extract the frequency-domain features of complex signals, which is widely used in various fields [37; 38; 39; 40; 41; 42]. Figure 3: Acceleration response spectra of partial ground motions. The feature extraction of two ground motions named HECTOR-0515A360 (hereinafter referred to as HECTOR) and IMPVALL-A-E06140 (hereinafter referred to as IMPVALL) (Figure 4a) [33] are discussed. Both ground motion records are normalized to 1 m/s\({}^{2}\) for comparison. HECTOR's vibration is strong in the whole 40 s range, while IMPVALL's vibration mainly concentrates in the range of 3-7 s. By comparing the response spectra of the two ground motions (Figure 4b), it is found that the spectral acceleration of IMPVALL in the range of 0.3-1 s is greater than that of HECTOR. Considering that the natural vibration periods of multi-story buildings are usually within 0.3-1 s [43], the IMPVALL ground motion exhibits greater destructive power to these structures than the HECTOR ground motion. Nevertheless, the FFT spectrum (Figure 4c) indicates that the amplitude of IMPVALL is less than that of HECTOR in almost the entire frequency range. The difference between the response spectrum and FFT spectrum is that the seismic energy of the IMPVALL ground motion is released in a relatively short time. Therefore, the IMPVALL ground motion is very destructive to structures, even if its relatively low FFT spectrum compared to that of the HECTOR ground motion. Previous studies have shown that the short-time Fourier transform (STFT) has a good performance in time-frequency domain analysis [44]. Therefore, this study proposes a ground motion feature extraction method based on the STFT algorithm. In consideration of the duration difference of ground motion records, all ground motions are truncated to the duration of 20 s. The specific process includes the following four steps:  
1. Ground motion data truncation. Find the time point of the peak acceleration in a ground motion record, and truncate a 20 s signal with 10 s in both forward and backward. When the signals are less than 10 s in the front or back of the peak acceleration time point, the 20 s signal range should be shifted backward or forward to ensure that the peak acceleration is close to the center of the truncated signal. 2. STFT analysis. Considering that the selection of window size will affect the resolution of the STFT spectrum, the rectangular window length of 5 s and step length of 5 s are selected for the STFT analysis. Therefore, four frequency spectra of the 20 s truncated signal will be obtained. 3. Feature extraction. In this study, the natural vibration period of the adopted SDOF system is 0.5 s (Table 2). Considering that the period of the structure will be prolonged after entering the plastic state, the frequency range of interest is selected as 0.3-2.3 Hz.