# The Cut-Off Frequency of High-Pass Filtering of Strong-Motion Records Based on Transfer Learning
## 1 Introduction
[25] used the point at which the linear trend of the recorded FAS decays more slowly than the theoretical spectrum [26] to define the high-pass cut-off frequency. An SNR equal to 3 was taken as the lower limit of the low-pass cut-off frequency. A better method is to filter by using a high-pass cut-off frequency from small to large and to determine the rationality and accuracy of the selected high-pass cut-off frequency by visually inspecting the effect of integral displacement after filtering. Unfortunately, low-frequency noise sometimes cannot be effectively and accurately filtered using the method above of determining the filter passband of strong-motion records. At present, a better way to ensure a high-pass cut-off frequency is to determine the rationality and accuracy of the selected cut-off frequency by visually inspecting the effect of the integral displacement after filtering, which is the traditional method [27]. If the mean value at the end of the filtered displacement time series is close to zero and the fitted straight line at the end of the range remains horizontal, the time series curve is considered qualified. A new filtered passband must be selected for filtering if it is not considered qualified. However, the efficiency of the traditional method is extremely low, and it is not suitable for processing massive strong-motion records. It is necessary to visually inspect the integral displacement after filtering to determine whether the results are acceptable. According to [PERSON] [28] and [PERSON] [29], the low-pass cut-off frequency has little effect on the baseline offset of displacement time series for strong-motion records. The low-pass cut-off frequency in this paper is taken as 35 Hz (where the sampling frequency is 100 Hz) or 20 Hz (where the sampling frequency is 50 Hz). Generally, in the traditional method, people must subjectively inspect the acceptability of the filtering result by classifying the integral displacement time series curve into qualified or unqualified. However, there is no uniform classification standard in traditional artificial identification for the integral displacement time series qualification. Computer vision has been applied to image classification with uniform criteria and a faster speed. Convolutional neural networks (CNNs) that can automatically extract higher-dimensional features of data can significantly improve the accuracy of computer vision tasks [30; 31]. However, deep neural networks (DNNs) [32] are slower to converge due to their large number of parameters. Transfer learning [33] enables the model to converge quickly by fine-tuning the pre-trained weights of the model. In this way, pre-trained network models can be better adapted to new data sets to achieve higher performance and reduce training time. In this paper, to address the shortcomings of the traditional method, deep CNNs were used to replace visual inspection to achieve the automatic judgment of the reasonableness of a filtered displacement time series in processing massive strong-motion records. The pre-trained neural network models VGG19 [34], ResNet50 [35], InceptionV3 [36], and InceptionResNetV2 [37] were adopted for transfer learning to classify the filtered displacement time series as qualified or unqualified. The classification performance of the models that only train the fully connected layer was compared with the models in which all layers are trained. Moreover, the model with higher classification performance was applied to the traversal search of the high-pass cut-off frequency. Finally, the high-pass cut-off frequencies determined using traditional methods were used as accurate values, and four metrics widely used in past investigations (i.e., the coefficient of determination, root mean square error, mean absolute error, and mean absolute percentage error) were used to evaluate the results obtained using each model. The effect of adding a probability constraint to the predictive classification for the final results was also compared and analyzed.