Temporal convolution neural network model for simulation of site seismic effect

The simulation of site seismic effects is a critical and challenging research area in earthquake engineering, providing a scientific basis for seismic safety evaluations of engineering sites, seismic fortification of buildings, and code revisions. Four primary research paradigms are typically employed: the empirical research paradigm, which relies on earthquake damage data; the theoretical research paradigm, which uses model experiments and mathematical tools to describe experimental phenomena; the computational research paradigm, which employs numerical methods to solve complex physical problems; and the data-driven paradigm, which utilizes machine learning tools to identify patterns in large datasets. Despite these approaches, challenges such as sparse data samples, weak generalization of results, and insufficient understanding of underlying laws persist. In this study, we introduce a fifth research paradigm, artificial intelligence for science, represented by physics-embedded deep learning. We investigate site seismic effects using strong motion records from the Japanese KiK-net array on-site/borehole stations.

In this study, we primarily employ temporal convolution neural network （TCN） as the deep learning framework. Compared with traditional recurrent neural networks （RNNs, LSTMs, GRUs）, TCN offers stronger parallelism and more flexible receptive fields. TCN uses a one-dimensional fully convolutional network architecture, with dilated causal convolutions to exponentially increase the receptive field, thus avoiding the loss of historical information when processing long sequences. Additionally, TCN uses residual blocks to prevent gradient vanishing issues. We detail how to impose physical constraints on the loss function of deep learning neural networks and develop a physics-embedded temporal convolution neural network （Phy-TCN） model. To validate the effectiveness of the Phy-TCN model, we generated a simple sparse sample dataset. Specifically, we used 30 sets of random white noise sequences with length 1000 as excitations for a single degree of freedom system to generate the sparse sample dataset, with 15 sets each for training and testing. Under sparse data conditions, we compared the performance of the Phy-TCN with a purely data-driven TCN and explored the limitations of the TCN. The results show that embedding physical information provides more information for the training process, constraining the simulation results within feasible spaces.

Then, to further demonstrate the performance of the Phy-TCN in predicting soil layer seismic responses, we generated 30 sets of numerical simulation data, randomly dividing 20 sets for training and 10 sets for testing. These numerical simulation data were generated using a one-dimensional time-domain nonlinear site seismic response analysis method based on constructed site soil layer information. The seismic acceleration records input into the soil layer model were selected from the strong motion network database of the National Research Institute for Earth Science and Disaster Resilience in Japan, and the constitutive model used to describe the nonlinear behavior of the soil was a hybrid hyperbolic nonlinear soil model. The results show that the Phy-TCN can effectively simulate site seismic effects under seismic excitation. Comparing the predicted results with reference records, the coefficient of determination （R²） is generally greater than 0.97.

Finally, in order to verify the application of the Phy-TCN model in practical engineering, we selected 50 seismic events with surface peak accelerations greater than or equal to 0.3 m/s² from the KiK-net database at the IBRH11 and IBRH12 stations, randomly dividing 40 events for training and 10 events for testing, and conducted site seismic effect simulations using the Phy-TCN model. To illustrate the superiority of the Phy-TCN model, we used the equivalent linearization method, commonly used in engineering, to calculate the test set and compared the results with the Phy-TCN simulations. The results show that in the simulation of noisy signals such as KiK-net observation records, based on the response spectrum values of specific periodic points of seismic events at selected sites, the average relative errors of the Phy-TCN and the equivalent linearization method compared with the measured records are 0.067 and 0.379, respectively. As the intensity of seismic motion continues to increase, the measured surface peak acceleration gradually exceeds the surface peak acceleration simulated by the equivalent linearization method, while the surface peak acceleration simulated by the Phy-TCN method remains stable within a deviation range of ±20%. The simulation capability of the Phy-TCN remains strong, with the coefficient of determination （R²） generally remaining above 0.8. Under conditions of high uncertainty in shear wave velocity and soil dynamic parameters, or in the absence of suitable soil profile information, the simulation accuracy of the Phy-TCN model is higher than that of the equivalent linearization method.