2.1. Introduction to the STL and Surrounding Buildings

The STL building at SEU occupies an area exceeding 7000 square meters and was completed and put into use in 2021. The building includes 4 stories above ground, and the shake table system is installed on the first story. The three-dimensional shake table system has 14 actuators. The maximum load for the 8 horizontal actuators is 1084 kN, while the 6 vertical actuators have a maximum load of 993 kN. The detailed performance index of the shake table system is presented in Table 1.

Figure 3 shows the aerial view and top-down view of the STL and surrounding buildings at SEU’s Jiulonghu Campus, including the civil engineering (CE) building and the electronic information (EI) building. The laboratory building is a reinforced concrete frame structure, and the other two surrounding tall buildings are reinforced concrete frame-shear wall structures.

2.2. Structural Health Monitoring and Vibration Comfort Evaluation

2.2.1. Structural Health Monitoring System (SHMS)

To investigate the impact of shake table–induced vibration on the surrounding structures, a SHMS is established by installing accelerators at different locations of the laboratory and the two surrounding buildings; thus, the vibration comfort of every measuring point can be calculated when shake table tests are conducted. Figure 4 depicts the layout of the nine measuring points at the three buildings: the STL building has its measuring points on the foundation, 2nd story, and 4th story; the CE building on the 1st story, 8th story, and 16th story; and the EI building on the 1st story, 8th story, and 15th story, respectively. At each measuring point, three unidirectional magnetoelectric accelerometers are installed to capture the real-time vibration response in the vertical direction as well as in the two horizontal directions, as shown in Figure 5. Each accelerometer has a sensitivity of 0.3 V/m·s⁻², a max range of 20 m/s², and a frequency range of 0.25–200 Hz.

2.3. On-Site Vibration Monitoring and Comfort Evaluation

Before the STL was put into service for seismic ground motion experiments of real-sized structures, a series of tests were conducted to investigate the influence of shake table–induced vibration on the surrounding buildings. The tests included frequency sweep wave test, sine wave test, and seismic time-history wave test. In this section, the results of representative tests are briefly introduced, focusing on the vibration responses at measuring points of the three surrounding buildings and the dynamic characteristics of these vibrations, as detailed results of all tests have been provided in the previous study [11].

2.3.1. Sweep Frequency Wave Test

Figure 6 plots the acceleration curves and their corresponding spectra for the three-directional responses under sweep frequency wave excitation measured at the monitoring point on the fourth story of the STL building. Each directional response had a peak acceleration of 0.15 g during the sweep frequency wave, with the shake table bearing a load of 60 tons. The frequency range for each wave extended from 0 to 20 Hz. In the X-direction spectrum, a prominent resonance peak appeared at approximately 4.5 Hz. In the Y-direction spectrum, resonance peaks were noticeable at around 4 and 9 Hz. In the Z-direction spectrum, the resonance peak was in the 16–18.5 Hz range.

2.3.3. Ground Motion Test

The three-directional Wenchuan seismic wave, with a peak acceleration value of 8.2 m/s², was employed to conduct the ground motion test. The responses at each measuring point in both the CE building and the EI building are detailed in Table 4. The corresponding WAL results are plotted in Figure 7. In the CE building, the highest vibrational response was observed at the Z-direction sensor on the 16th story. In the EI building, all response values were below 0.5 gal, with the maximum response occurring at the Y-direction sensor on the first story. According to the bar chart in Figure 7, the Z-direction WAL at each measuring point in the two surrounding buildings was the highest among the three directions, with the Y-direction’s value exceeding that of the X-direction. The highest L_a in the CE building was observed at the Z-direction sensor on the 16th story, registering a value of 74.46 dB, which is below the 83 dB threshold. In the EI building, the highest L_a was noted at the Z-direction sensor on the 14th story, with a value of 64.23 dB, also below the threshold of 71 dB.

Table 4. Acceleration response of each measuring point under Wenchuan ground motion wave.

Measuring point	X (gal)	Y (gal)	Z (gal)
1st story of civil engineering building	2.853	3.005	4.532
8th story of civil engineering building	0.713	3.407	4.023
16th story of civil engineering building	1.314	3.595	4.735
1st story of electronic information building	0.359	0.45	0.413
7th story of electronic information building	0.332	0.335	0.328
14th story of electronic information building	0.384	0.377	0.339

2.4. Numerical Simulation of the SSS System

To investigate the vibrational characteristics and impact of the shake table test on the building occupants, a FEM of the SSS system—including the STL, foundation, and surrounding buildings—is established using ABAQUS, as shown in Figure 8. The concrete beams and columns in the three buildings are modeled using B32 elements, a type of Timoshenko beam element. The foundations are modeled with C3D8R elements, a type of solid element. The slabs between stories and the concrete walls are modeled using S4 elements, a type of shell element. C3D8R elements are also used to simulate the soil layers of the ground, and the infinite soil is simulated by defining a viscoelastic boundary [11]. According to the modal analysis results of the FEM, the first three natural periods of the two surrounding buildings are as follows: for the CE building, the periods are 1.603, 1.058, and 0.851 s; for the EI building, the periods are 1.685, 1.483, and 1.230 s. The story weights of these buildings are detailed in Tables 5 and 6.

Figure 9 compares the simulated and actual curves of the three-directional responses at the measuring point located on the second story of the STL building under ST58 ground motion. The close alignment between the two curves validated the numerical model to be generally accurate in representing the vibrational characteristics of the system.

3.1. Step 1: Preparation of Ground Motion Dataset for DL Network Training

3.1.1. Selection of Ground Motion Records

During the seismic performance experiment, ground motions with diverse dynamic characteristics may be employed for the shake table tests. To collect sufficient ground motion records for training the DL network, several open-access ground motion databases can be utilized. These include the PEER NGA-East [12], NGA-West [13], and NGA-Sub [14] databases from the United States, the ESM database [15] from the European Union, and the K-NET database [16] from Japan. In this paper, 1745 ground motion records with a magnitude greater than 4.0 were selected from the NGA-Sub database, a newly developed resource by UCLA, specializing in ground motions from global subduction zone regions. Figure 11 illustrates the distribution of V_s30 (the mean velocity of the site’s shear wave in the uppermost 30 m of soil) for the selected ground motion records.

3.1.2. Preprocessing of the Ground Motion Signals

To adapt ground motion records of various formats to the designed 1D-CNN model, this section introduces the signal preprocessing workflow for each selected record and also explains the rationale behind each procedure.

First, the acceleration signals in three directions of each ground motion record, namely, two horizontal directions (a_x and a_y) and a vertical direction (a_z), are normalized as follows:

$$ ()

$$ ()

$$ ()

where a_x,norm(t), a_y,norm(t), and a_z,norm(t) represent the normalized acceleration signals and a_x(t), a_y(t), and a_z(t) are the raw signals of the three-directional ground motion. Each channel of the acceleration signal is divided by its corresponding maximum absolute value max(|a(t)|) and then multiplied by a scaling factor [17]. The scaling factors of the three directions are 1, 0.85, and 0.65, respectively.

After the normalization procedure, the acceleration signals of each ground motion record will be resampled because the selected ground motions are recorded by different seismographs and their sampling frequencies varied. The polyphase resampling method is employed to adjust the sampling frequency of each signal to 50 Hz. This method has been proven to effectively avoid frequency aliasing and mirroring during sampling rate conversion in signal processing [18]. It also ensures data consistency when processing different ground motion records and preserves the integrity of acceleration signals for time-history analysis, in accordance with the requirements for seismic performance analysis of civil structures.

Last but not least, the duration of each ground motion should be standardized before input into the DL network. According to the Chinese specification for seismic test of buildings (JGJ/T 101-2015), the duration of the ground motion should be a minimum of 20 s and between 5 and 10 times the fundamental period of the structure being tested. Hence, after modification, we have set 60 s as the standardized duration for each signal. In detail, the standardization work is conducted as follows. (1) For signals shorter than 60 s, the original record is kept intact and extended to 60 s with padding of zeros. (2) For signals longer than 60 s, a 60-second segment centered around the X-direction signal’s PGA, comprising 30 s before and after the PGA, is preserved. In cases where the PGA occurs within the first or last 30 s of the signal, the initial or final 60-second segment is preserved. (3) For the Y- and Z-direction signals, the same time axis labels as the X-direction are applied for standardization. Figure 12 shows an example of the standardization of a three-directional ground motion record.

The three procedures described in this section will ensure that ground motion records with varying PGA values, sampling frequencies, and durations are normalized, resampled, and standardized to the same format after preprocessing. Without these procedures, the data from different records input into the 1D-CNN model will have varying physical meanings, making them incomprehensible to the network.

3.2. Step 2: Estimating Vibration Comfort With DTHA on the SSS System

In order to assess the impact of different ground motions operated by the shake table on the vibration comfort of the surrounding buildings, DTHA is conducted on the numerical model of the SSS system [19]. The triaxial acceleration responses of the nine measuring points on the surrounding buildings (as shown in Figure 4) excited by the selected ground motions are obtained, and the WAL values of vibrations at every point are computed by expressions (1) and (2).

Figure 13 illustrates the percentages of vibrations that are above and below the WAL limit, as defined by the vibration comfort criteria for the surrounding buildings, induced by ground motions with varying PGA values. Evidently, the proportion of ground motions that exceed the WAL threshold increases from 15.64% to 64.13% with the growth of the PGA values. It should also be noted that even the ground motions with lowest PGA value (0.4 g) might induce vibrations exceeding the threshold. The main reason is that the vibration comfort of the surrounding buildings not only is determined by the peak values of the excitation signals but also significantly relates to the dynamic characteristics of the time-series signals.

3.3. Step 3: DL Network Training and Testing

The 1D-CNN is utilized as the DL network to establish the surrogate model for vibration comfort estimation. The network is trained and tested using preprocessed ground motion records and computed WALs. To synchronously extract and analyze the intrinsic features of the three-directional acceleration signals, the 1D-CNN model is structured with multichannel one-dimensional convolutional kernel layers and fully connected deep neural network layers. During the training and testing procedures of the designed model, 1745 selected ground motion records with different recorded sequence numbers (RSNs) are divided into two groups: 80% for training (including 10% of the total for hyperparameter tuning) and 20% for testing.

Testing of the optimized DL network is conducted through two phases. First, the model will analyze the three-directional acceleration signals from the testing dataset and output the predicted WAL values for nine measuring points, and the nonlinear feature extraction/regression performance of the model will be examined. Second, an actual shake table experimental test will be performed, and the estimated vibration comfort level of different measuring points will be compared with the on-site monitoring data.

3.4. Step 4: Vibration Comfort Estimation of Surrounding Buildings

To effectively evaluate the performance of various seismic structure systems, the ground motions used on the shake table are always varied. To estimate the potential adverse effects of the shake table test, preprocessing program is employed to process the prepared ground motion data and to generate three channels of scaled accelerations. These signals are then input into the optimized 1D-CNN model, which can anticipate the vibration comfort at nine different locations in the three surrounding buildings by means of the WAL values. By comparing the output WALs with the predetermined thresholds at corresponding points, the vibration comfort state of these locations can be estimated. Finally, it will be straightforward to offer suggestions on the feasibility of using scaled ground motion records on the shake table. In addition, after the shake table test is conducted, the measured real vibration data, as well as the computed WAL values acquired from the SHMS, will be used to further update the 1D-CNN model.

4.1. Architecture of the 1D-CNN Model

Figure 14 illustrates the architecture of the 1D-CNN model for vibration comfort estimation. The model includes four subnetworks: a fully convolutional neural network (FCNN), two parallel deep neural networks (PDNN), and a fusion neural network (FusionNN). Their configurations are depicted in Tables 7, 8, 9, and 10.

First, the triaxial signals of the original ground motion are preprocessed and input to the FCNN that includes two convolutional layers and a max pooling layer. These layers can upsample the input time-series data with the 1D convolutional kernels. Then, the processed features are flattened and input to the PDNN1, a multilayer neural network that includes three linear layers. It can compress the 32,000-long tensor to 512-long tensor. Meanwhile, the PDNN2 is utilized to process the PGA coefficient of the input original ground motion and downsample it into 512-long tensor. The two PDNNs operate in parallel. Next, the two tensors are concatenated together to form a new 1024-long tensor. Finally, the FusionNN can combine the features from both PDNNs and output a 27-long tensor, representing the WALs for 27 accelerometers at the STL building, the CE building, and the EI building.

4.2. Network Programming and Training

The 1D-CNN model for vibration comfort estimation is implemented using the CUDA version of the PyTorch DL library [20]. The FCNN is structured with two Conv1d operators and a MaxPool1d layers, packaging by the sequential container. The two PDNNs and the FusionNN are structured with numbers of linear operators and dropout layers. The LeakyReLU with a 0.2 negative slope value is employed as the activation function to introduce nonlinearity into the model [21]. The mean square error (MSE) is used as the loss function to compare the predicted WAL values and the ground truth [22]. The optimizer is AdaMAX [23] and the learning rate is 0.00005. The model is trained at least 2000 epochs until the MSE value is < 0.50. To boost the DL network training, a computer equipped with an Intel Core i9–12900 5.10 GHz CPU and Nvidia RTX GPU with 8704 CUDA cores was used.

The training dataset, comprising 9772 pairs of normalized ground motion signals and PGAs, is employed to optimize the network parameters of the model, while the testing dataset, containing 2443 such pairs, is used to validate the model’s performance. The loss curves for both the training and testing datasets are depicted in Figure 15. During the training process, hyperparameter tuning and optimization were performed using a 10% subset of the total dataset, while the remaining 70% of the dataset was used for training.

4.3. Network Test Based on Real Ground Motions

After optimizing the 1D-CNN model, the proposed DL method is applied to analyze the testing dataset that includes 2443 pairs of real ground motions and PGAs. To verify the performance of the model, a statistical analysis and a vibration comfort estimation test were conducted.

4.3.2. Test for Vibration Comfort Estimation

To estimate the vibration comfort of nine different measuring points, the maximum WAL values from each of the three directions are analyzed for every measuring point. Figure 16 illustrates scatter plots of the maximum WAL values for predictions and ground truths at each measurement point. Figure 16(a) compares the WAL values for the training dataset, while Figure 16(b) displays those for the testing dataset.

According to Figure 16, the predicted WAL values in both the training and testing datasets show a linear correlation with the corresponding true WAL values. The R-squared (R²) coefficients [25] for both the prediction and the ground truth are ≥ 0.975, indicating an outstanding fit of the optimized 1D-CNN model to vibration comfort quantification. Also, the R² values of the testing dataset closely align with those of the training dataset, suggesting that there is no overfitting of the surrogate model. In addition, for the EI building, a few input samples’ predictions in the testing dataset were overestimated by the 1D-CNN model. Since both the predicted and actual values of these samples are < 50 dB and below the threshold for the EI building (71 dB), this will not impact the structural vibration comfort work of the model. Figure 17 depicts the predicted and actual WAL values of different PGA levels for the 349 samples in the testing dataset. With the growth of the PGA level, most of the predicted and actual WAL values increase, and their values remain close. It is also found that the percentages of predicted WAL values exceeding the threshold (15.76%, 40.69%, and 55.59%) closely approximate those of the ground truth values (15.47%, 40.11%, and 56.16%).

5.1. Description of the Shake Table Test

The shake table test is to investigate the seismic performance of a self-centering concrete bridge high pier [26] under three-directional ground motion. Figure 18(a) shows the arrangement of the test structure model on the shake table. The height of the model is 10.9 m, and the mass of the model is 69 ton. The Taft earthquake record is selected to simulate the ground motion, and the three-directional acceleration waves of it are plotted in Figure 18(b). The PGA values of the waves in three directions are 0.940, 0.799, and 0.611 g, respectively. The target wave curves and the curves measured from the shake table during the test are also compared in Figure 18(b), showing good concordance.

Before the shake table test, the three-directional ground motion was input to the 1D-CNN model to estimate the vibration comfort of the surrounding buildings. The estimated maximum WAL values for the STL building, CE building, and EI building were 80.80, 62.38, and 58.62 dB, respectively. The estimated WAL values for each building did not exceed the corresponding thresholds, and thus the influence of the shake table during operation was acceptable in this case.

5.2. Comparison of the Estimated and Real Vibration Comfort

During the shake table test, the vibration responses of the surrounding buildings of the shake table were obtained from the SHMS. The Taft ground motion test was conducted on 27th October 2023, from 13:30 to 13:31 UTC + 8. Figure 19 shows the monitored accelerations in three directions at the 8th story of the EI building, as well as their Fourier spectra. The real vibration comfort of the surrounding buildings was calculated using the method introduced in Section 2.2.2. Figure 20 compares the real and estimated WAL values for the nine measuring points at the three buildings. The maximum relative errors of the estimated and real values for the STL building, CE building, and EI building were 3.37%, 4.96%, and 6.06%, respectively. As a result, the proposed method can accurately estimate the vibration comfort before conducting the shake table test, thus validating its practical value.