A physical information long short-term memory network site seismic response prediction method based on kinematic derivative constraint and data folding

Abstract

The application provides a physical information long short-term memory network site seismic response prediction method based on kinematic derivative constraint and data folding, comprising the following steps: collecting bedrock and surface ground motion data and preprocessing; constructing displacement, velocity and acceleration supervision labels by surface acceleration integration; constructing a long short-term memory network containing a data folding and unfolding module; constructing a physical constraint loss by using the kinematic derivative relationship between displacement and velocity and between velocity and acceleration, and training the network in combination with an adaptive weight strategy; and outputting surface displacement, velocity and acceleration time history by using the trained network. The method can apply physical consistency constraints to the site seismic response prediction process without explicitly giving soil layer constitutive parameters, can reduce the long sequence training burden through sequence folding processing, and is suitable for site seismic response prediction.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of earthquake engineering, geotechnical engineering and artificial intelligence. Specifically, it relates to a physical information long short-term memory network modeling method for site seismic response time history prediction, and more particularly to a site seismic response prediction method that uses kinematic derivative constraints to improve physical consistency and data folding to improve long-term training efficiency. Background Technology

[0002] Site seismic response prediction is a crucial step in seismic amplification effect analysis, structural seismic demand assessment, and regional seismic hazard analysis. Existing site seismic response analysis methods mainly fall into two categories: equivalent linear analysis and nonlinear time history analysis. Equivalent linear analysis offers high computational efficiency but has limitations in characterizing the nonlinear behavior of soil under strong earthquakes. Nonlinear time history analysis can describe soil stiffness degradation, damping evolution, and path-dependent effects, but it typically requires detailed constitutive models, parameter inversion processes, and significant computational costs, making it difficult to simultaneously meet the need for rapid prediction.

[0003] Existing technologies also employ neural networks to establish a mapping relationship between seismic motion and site response. Long Short-Term Memory (LSTM) networks can process long-sequence data and can be used for earthquake response time-history prediction tasks. However, purely data-driven models, when lacking physical constraints, are prone to producing predictions that match the training samples but do not satisfy basic dynamic relationships. This problem is particularly pronounced when the sample size of large earthquakes is limited and the measured records are noisy.

[0004] Existing physical information neural networks typically enhance the physical consistency of the model by introducing residuals from the governing equations. However, for site seismic response problems, directly embedding the complete site motion equations into the loss function often requires complete and usable mass matrices, damping matrices, restoring forces, or soil constitutive parameters. For measured vertical array records, such parameters are difficult to obtain directly; for numerical simulation data, these parameters are often encapsulated within the solver, which is not conducive to building a unified supervision framework.

[0005] Furthermore, site seismic response records are typically long in duration. Directly training recurrent neural networks on the original, high-sampling-rate long sequences increases the time step unfolding length, memory consumption, and training time, thus limiting the application of the method in practical engineering. Measured records also commonly suffer from environmental noise, instrument noise, baseline drift, and differences in wave propagation paths, which also affect the applicability of the model under actual recording conditions.

[0006] Therefore, there is a need for a site seismic response prediction method that balances physical consistency, long-sequence training efficiency, and applicability to measured records without relying on explicit soil constitutive parameters. Summary of the Invention

[0007] The technical problem to be solved by this invention is: to address the problems of insufficient physical consistency, low efficiency of long-term training, weak adaptability to measured records, and strong dependence on explicit constitutive parameters in existing site seismic response prediction methods, a site seismic response prediction method based on physical information long short-term memory network of kinematic derivative constraints and data folding is proposed.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] A method for predicting site seismic response using a physical information long short-term memory network based on kinematic derivative constraints and data folding includes the following steps:

[0010] Step S1: Construct the input and output sample set. Obtain the bedrock input ground motion time history data and the corresponding surface response time history of the target site; the sample set comes from measured vertical array records and / or from the results of nonlinear site response numerical simulation based on a layered site model.

[0011] Step S2: Perform data preprocessing and label construction. Preprocess the bedrock input ground motion time history data and the surface response time history data in the training sample set. Use the preprocessed bedrock input ground motion time history data as the input ground motion sequence and the preprocessed surface response time history data as the target response sequence. For the surface acceleration time history in the surface response time history data, construct surface displacement time history and surface velocity time history to form three types of supervision labels: displacement, velocity, and acceleration. Step S3: Construct a physical information long short-term memory network. The network includes an input layer, a long short-term memory layer, a fully connected layer, and an output layer. The input layer receives the tensor after folding the bedrock input ground motion, and the output layer provides three types of prediction results: surface displacement, surface velocity, and surface acceleration.

[0012] Step S4: Perform data folding and data unfolding. Transform the original input tensor X into a folded tensor X through rearrangement operations. f The dimension of the original input tensor is The dimension of the folded tensor is Where X is the original input tensor, X0 f It is a folded tensor, where b is the number of samples. d is the sequence length, s is the number of feature channels, and s is the folding factor. The network output is reverse-rearranged to restore the original time length, thereby shortening the effective time step length of the recurrent network without losing sampling point information.

[0013] Step S5: Construct a joint loss function. The joint loss function includes at least data loss and physical constraint loss, wherein the data loss is used to constrain the consistency between the predicted displacement, predicted velocity, and predicted acceleration and the true labels, and the physical constraint loss is used to constrain the consistency between the time derivative of the predicted displacement and the predicted velocity, and the consistency between the time derivative of the predicted velocity and the predicted acceleration.

[0014] Step S6: Calculate the derivative and train the network using the central difference method. Apply the central difference operator to the predicted displacement and predicted velocity to form kinematic derivative constraint terms, and use the joint loss function to iteratively update the network parameters to obtain the trained site seismic response prediction model.

[0015] Step S7: Perform site seismic response prediction. Input the bedrock of the target site into the seismic motion input of the trained model, and output the time histories of surface displacement, surface velocity, and surface acceleration. Further calculations of surface response spectrum, peak ground acceleration, and other engineering requirement parameters are also possible.

[0016] The joint loss function in step S5 is expressed as follows:

[0017]

[0018]

[0019]

[0020] Where L data It is data loss; L phy It is the physical constraint loss; L is the joint loss function; α u It is the weighting coefficient of the displacement data loss term; α v It is the weighting coefficient of the velocity data loss term; α a β1 is the weighting coefficient of the acceleration data loss term; β2 is the weighting coefficient of the consistency constraint term between the displacement derivative and the predicted velocity; λ is the weighting coefficient of the consistency constraint term between the velocity derivative and the predicted acceleration; λ is the total weight of the physical constraints; (with cap symbol) , and These are the predicted displacement, predicted velocity, and predicted acceleration, respectively; the uncapped symbols u, v, and a represent the actual displacement, actual velocity, and actual acceleration, respectively; MSE is the mean square error function; and CDM is the central difference operator.

[0021] Step S6 may further include the following sub-steps:

[0022] Step S6.1: An adaptive weight initialization strategy is adopted. Based on the acceleration loss, the relative magnitudes of displacement loss, velocity loss and acceleration loss are statistically analyzed in the initial stage of training, and the corresponding displacement loss weights and velocity loss weights are automatically updated accordingly to alleviate the training imbalance problem caused by the difference in the magnitudes of the three types of responses.

[0023] Step S6.2: For the measured records, perform data augmentation operations on the training sample set before iterative training of network parameters. The data augmentation operations include at least one of the following: Gaussian noise injection, amplitude scaling, time shifting, and low-frequency perturbation. The augmented samples and the original samples together constitute an expanded training set to improve the model's adaptability to noise, baseline drift, and propagation path differences.

[0024] This invention also provides the application of the above-mentioned site seismic response prediction method in earthquake engineering.

[0025] Compared with the prior art, the present invention has at least the following beneficial effects:

[0026] 1. This invention uses the kinematic derivative relationship between displacement, velocity and acceleration as a physical constraint. Under the condition that the site mass matrix, damping matrix, restoring force term or constitutive parameters of intact soil layer are not explicitly given, it can still impose physical consistency constraints on the prediction results. It is applicable to site seismic response prediction under the condition of incomplete prior parameters.

[0027] 2. This invention shortens the time unfolding length of the cyclic network by using a data folding and unfolding mechanism while maintaining the correspondence of the original sampling point information. This can reduce the computational burden in the training process of long-term seismic records and is suitable for site response prediction tasks with high sampling rates and long durations.

[0028] 3. This invention simultaneously outputs three types of response quantities: displacement, velocity, and acceleration, and constrains the consistency relationship between the three through a joint loss function, which facilitates obtaining multi-physical quantity response results that can be used for subsequent engineering analysis within the same prediction framework.

[0029] 4. This invention can be combined with noise-sensing data enhancement strategies to specifically address instrument noise, low-frequency drift, and wave propagation uncertainties in measured vertical array records, which helps maintain the applicability of the method under different recording conditions.

[0030] 5. In the numerical simulation verification of some implementations, the method of the present invention can make the proportion of samples with normalized prediction error falling within the ±2% range reach 97.98%, and reduce the average peak relative error from 2.11% to 1.60%, which is beneficial to improving the stability of extreme value response prediction.

[0031] 6. In the field test records of some implementation methods, the method of the present invention can achieve a response spectrum correlation coefficient of 0.951 and reduce the single-round training time from 13.81 seconds to 0.66 seconds when the folding factor is 5, thereby balancing engineering applicability and computational efficiency. Attached Figure Description

[0032] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0033] Figure 1 This is a flowchart of the overall process of the present invention, showing the processing relationship between sample construction, sequence folding, neural network prediction, physical constraint training, and response output.

[0034] Figure 2 This is a schematic diagram of the neural network structure in an embodiment of the present invention, showing the connection relationship between the input layer, three long short-term memory layers, two fully connected layers, and the output layer;

[0035] Figure 3 This is a schematic diagram of sequence folding and sequence unfolding in an embodiment of the present invention, showing the original time series after folding. Convert to And the rearranged relationships are restored to their original time lengths after being expanded;

[0036] Figure 4 This is a schematic diagram of the construction of the joint loss function in an embodiment of the present invention, showing the data loss, kinematic constraint loss and their weighting relationship;

[0037] Figure 5 This is a schematic diagram of the construction of the site dataset in an embodiment of the present invention, showing the correspondence between the layered site profile, the input ground motion, and the target response;

[0038] Figure 6 This is a schematic diagram comparing typical prediction results in an embodiment of the present invention, showing the comparison relationship between the input ground motion, the target response, and the predicted response;

[0039] Figure 7 This is a distribution map of earthquake parameters in the training and test sets, showing the statistical distribution of focal depth, epicentral distance, peak ground acceleration, and magnitude.

[0040] Figure 8 This is a comparison diagram of typical bedrock inputs and surface responses, showing the correspondence between three types of time-history responses: acceleration, velocity, and displacement.

[0041] Figure 9 The training and validation loss history diagrams for three models on a numerical simulation dataset;

[0042] Figure 10The normalized prediction error probability density distribution of the three models on the numerical simulation dataset is shown.

[0043] Figure 11 A comparison chart of the best prediction samples of the three models on a numerical simulation dataset;

[0044] Figure 12 A comparison chart of the worst prediction samples of the three models on a numerical simulation dataset;

[0045] Figure 13 The model performance evaluation graph on the measured data dataset shows the normalized error distribution and the correlation coefficient distribution.

[0046] Figure 14 A comparison chart of the best and worst samples of the enhanced physical information model on the measured record dataset;

[0047] Figure 15 Box plot of peak relative error for all numerical test samples. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings, tables, and specific embodiments. These embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. For those skilled in the art, equivalent substitutions, simplifications, or extensions made without departing from the concept of the present invention should all fall within the scope of protection of the present invention.

[0049] Example 1: Overall Method Flow and Sample Screening

[0050] This embodiment illustrates a site seismic response prediction method based on kinematic derivative constraints and data folding using a physical information long short-term memory network. The overall process is as follows: Figure 1 As shown, it mainly includes five stages: data construction, label generation, network modeling, physical constraint training, and response prediction. The steps include:

[0051] S1: Obtain the bedrock input ground motion time history data and the corresponding surface response time history of the target site to form a training sample set;

[0052] S2: Preprocess the bedrock input ground motion time history data and the surface response time history data in the training sample set, and use the preprocessed bedrock input ground motion time history data as the input ground motion sequence and the preprocessed surface response time history data as the target response sequence; construct surface displacement time history and surface velocity time history for the surface acceleration time history in the surface response time history data to form three types of supervision labels: displacement, velocity and acceleration.

[0053] S3: Construct a neural network model, which includes an input layer, at least one recurrent neural network layer, at least one fully connected layer, and an output layer;

[0054] S4: Perform data folding processing on the input ground motion sequence and set the sequence unfolding processing corresponding to the data folding processing; input the folded input sequence into the neural network model to obtain the response prediction sequence at the target location, and restore the original time length of the response prediction sequence through the sequence unfolding processing;

[0055] S5: Construct a data loss based on the predicted response sequence and the target response sequence, and construct a physical constraint loss based on the kinematic derivative relationship between multiple response physical quantities;

[0056] S6: Train the neural network model based on the data loss and physical constraint loss to obtain the trained site seismic response prediction model;

[0057] S7: Input the ground motion sequence of the site to be predicted into the trained site seismic response prediction model, and output the seismic response prediction result of the site to be predicted.

[0058] In step S7, the earthquake response prediction results include at least the acceleration response time history, as well as the displacement response time history and velocity response time history synchronously output by the same neural network model.

[0059] In step S4, the data folding process involves rearranging adjacent sampling points in the original time series to the feature dimension to shorten the time dimension and expand the single-step input feature dimension. The data folding process also includes a sequence unfolding process for restoring the original time length, comprising: converting the original input tensor X into a folded tensor X through a rearrangement operation. f The dimension of the original input tensor is The dimension of the folded tensor is Where X is the original input tensor, X0 f It is a folded tensor, where b is the number of samples. d is the sequence length, s is the number of feature channels, and s is the folding factor. The network output is reverse-rearranged to restore the original time length, thereby shortening the effective time step length of the recurrent network without losing sampling point information.

[0060] In step S3, the neural network model includes an input layer, at least one recurrent neural network layer, at least one fully connected layer, and an output layer. The recurrent neural network layer is one or more stacked structures of long short-term memory layers.

[0061] In step S5, the physical constraint loss includes at least the consistency constraint loss between displacement and velocity, and the consistency constraint loss between velocity and acceleration. This consistency constraint loss is obtained by performing numerical differentiation on the predicted sequence. The numerical differentiation employs one of the following methods: central difference, forward difference, backward difference, or automatic differentiation.

[0062] In step S5, the data loss and physical constraint loss are weighted according to an adaptive weighting strategy. This adaptive weighting strategy determines the corresponding weights based on the relative magnitudes of each loss component during the initial training phase, thereby constructing a joint loss function. The joint loss function is expressed as follows:

[0063]

[0064]

[0065]

[0066] Among them, L data It is data loss; L phy It is the physical constraint loss; L is the joint loss function; α u It is the weighting coefficient of the displacement data loss term; α v It is the weighting coefficient of the velocity data loss term; α a β1 is the weighting coefficient of the acceleration data loss term; β2 is the weighting coefficient of the consistency constraint term between the displacement derivative and the predicted velocity; λ is the weighting coefficient of the consistency constraint term between the velocity derivative and the predicted acceleration; λ is the total weight of the physical constraints; (with cap symbol) , and These are the predicted displacement, predicted velocity, and predicted acceleration, respectively; the uncapped symbols u, v, and a represent the actual displacement, actual velocity, and actual acceleration, respectively; MSE is the mean square error function; and CDM is the central difference operator.

[0067] Before model training, data augmentation is performed on the training sample set, including one or more of Gaussian noise injection, amplitude scaling, time shifting, and low-frequency perturbation.

[0068] The following section will further elaborate on the application scenarios of this embodiment.

[0069] The time histories of bedrock input ground motion and surface response are obtained. In this embodiment, the data sources include two types: one is the measured records from the Japanese KiK-net vertical array station IBRH13, and the other is the numerical simulation data generated by nonlinear time history analysis using a layered site model. The measured records are used to verify the model's adaptability to the actual records, while the numerical simulation data is used to supplement the nonlinear input-output mapping relationship.

[0070] In one embodiment, the measured records were selected from seismic records of IBRH13 station from January 2000 to December 2020, totaling 1000 two-component ground motion samples. The sampling frequency was 100 Hz, the peak ground acceleration ranged from 1 gal to 100 gal, the focal depth ranged from 0 km to 150 km, the magnitude ranged from 2 to 8, and the epicentral distance ranged from 0 km to 200 km. To maintain consistency between input and output dimensions, this embodiment only retains the east-west components of the bedrock and surface records. The parameter distributions of the training and test sets are as follows: Figure 7 As shown.

[0071] The original input and output time histories are preprocessed. First, mean subtraction and baseline correction are performed on the original time histories, followed by filtering from 0.5 Hz to 20 Hz using a fourth-order Butterworth bandpass filter to reduce the effects of instrument noise and low-frequency drift. Preferably, the mean value of the pre-vibration segment from 0 to 20 seconds is used as the baseline subtraction reference. For numerical simulation data, a 60-second time window, corresponding to 6000 sampling points, can be extracted; for measured records, a 120-second time window, corresponding to 12000 sampling points, can be extracted to retain subsequent arrival time trains and long-period components.

[0072] Multi-response supervision labels are constructed based on the surface acceleration time history. Surface velocity and displacement time histories corresponding to surface acceleration are obtained through numerical integration, thus forming a ternary supervision label of displacement, velocity, and acceleration. Compared to supervising only acceleration output, this design can introduce more physical constraint information during the training phase.

[0073] In one implementation, all samples are divided into a training set, a validation set, and a test set in an 8:1:1 ratio to perform hyperparameter selection and generalization capability verification during the training phase.

[0074] Example 2: Construction of Network Structure, Folding Mechanism and Physical Constraints

[0075] like Figures 2 to 4 As shown, the network in this embodiment consists of an input layer, three long short-term memory (LSM) layers, two fully connected layers, and an output layer. The LSM layers are used to extract long-term dependencies in the seismic motion sequence, and the fully connected layers are used to complete feature mapping and output reconstruction. Preferably, each LSM unit can be set to 128 hidden nodes when training with numerical simulation data; and each LSM unit can be set to 64 hidden nodes when training with measured records.

[0076] In this embodiment, when the network is trained with physical constraints enabled, it simultaneously outputs three types of response quantities: predicted displacement, predicted velocity, and predicted acceleration. Since displacement, velocity, and acceleration satisfy a universal kinematic derivative relationship, the consistency of the prediction results can be improved through the following two types of constraints without explicitly specifying the mass matrix, damping matrix, or restoring force expression:

[0077] 1. The derivative of the predicted displacement after central difference should be consistent with the predicted velocity;

[0078] 2. The derivative of the predicted velocity after central difference should be consistent with the predicted acceleration.

[0079] The corresponding data loss and physical constraint loss are shown in the aforementioned formulas. The Central Difference Operator (CDM) performs a second-order precision derivative approximation on discrete time histories sampled at equal time intervals, and has the advantages of simple implementation, numerical stability, and embedding into an automatic differentiation framework.

[0080] Let the original input tensor be X, and its dimension be . Where (X) is the original input tensor, and (b) is the number of samples. (d) is the sequence length, and (d) is the number of input feature channels. In this embodiment, (d) is 1, indicating that the bedrock input acceleration is a single-channel input; the folding factor is denoted as F, where (F) is the folding factor, preferably 5; the folded tensor is denoted as X. f Its dimensions are , where (X) f ) is the folded input tensor. This folding operation does not delete any sampling points, but rearranges adjacent time sampling points to the feature dimension, enabling the network to learn complete sequence information in a shorter time step; the network output is restored to the original time length after inverse rearrangement.

[0081] To avoid the difference in magnitude between displacement, velocity, and acceleration leading to a single loss term dominating the training process, this embodiment only calculates the relative magnitude of the three types of data losses in the initial training phase, and updates the corresponding displacement loss weights and velocity loss weights by reciprocal of the acceleration loss. Preferably, the weight initialization is performed in the first 25% of the total training rounds to improve the stability of multi-objective joint optimization.

[0082] Example 3: Real-world recording of noise perception enhancement training

[0083] This embodiment addresses the noise and drift issues in the measured records by introducing a noise-aware data augmentation strategy during the model training phase. The data augmentation strategy includes one or more of the following:

[0084] 1. Gaussian noise injection, which is to add random noise with zero mean to the input acceleration time history, and the standard deviation of the noise increases with the enhancement rounds;

[0085] 2. Amplitude scaling, which means randomly scaling the input time history within a preset small range;

[0086] 3. Time shift, which involves shifting the input time history forward or backward according to the sampling points;

[0087] 4. Low-frequency disturbances, i.e., superimposed smoothed low-frequency noise to simulate baseline uncertainty.

[0088] In one embodiment, the enhancement operations are performed in the following order: time shift, Gaussian noise injection, low-frequency perturbation, and amplitude scaling. The time shift is controlled within ±0.02 seconds, the amplitude scaling within ±5%, and the low-frequency perturbation amplitude within 0.01. The smoothing window length can be 5 sampling points. The enhancement factor K is preferably 5, meaning each original record is expanded into 5 enhanced samples. The enhanced samples and the original samples together form an expanded training set, which helps improve the model's adaptability to low signal-to-noise ratio seismic records.

[0089] Example 4: Numerical Simulation Data Construction

[0090] like Figure 5 and Figure 8 As shown, this embodiment uses the DEEPSOIL nonlinear site response analysis tool to construct a numerical simulation sample set. Figure 5 The relationship between the construction of the numerical simulation dataset is shown, that is, based on the input of bedrock ground motion from the layered site profile, the corresponding surface target response is obtained through nonlinear site response analysis, thus forming input-output sample pairs; Figure 8 Furthermore, the time history correspondence between typical bedrock inputs and surface displacement, velocity, and acceleration responses is presented. The site profile is constructed as a seven-layered site model based on publicly available geological data from the IBRH13 station, with each layer possessing corresponding layer thickness, density, shear wave velocity, and MKZ constitutive parameters. The nonlinear behavior of the soil is characterized using MKZ constitutive relations to generate time histories of surface displacement, velocity, and acceleration corresponding to bedrock input ground motions.

[0091] In one embodiment, the parameters of the seven-layer site model can be set according to Table 1. Table 1 lists the layer thickness, density, shear wave velocity, and MKZ constitutive parameters of the seven-layer site, which can be used as the basis for setting parameters to reproduce the numerical simulation sample set of Example 4.

[0092] Table 1. Parameters of IBRH13 Station Site Model

[0093]

[0094] For each input bedrock acceleration record, nonlinear site response analysis is performed to obtain the corresponding surface response results, which are then divided into training, validation, and test sets in an 8:1:1 ratio. This numerical simulation sample set can be used to verify the physical constraint effect and peak prediction capability of the method of this invention.

[0095] Example 5: Numerical simulation data verification results

[0096] In this embodiment, a baseline Long Short-Term Memory (LSTM) network, a Physical Information Long Short-Term Memory (PIS) network with only kinematic derivative constraints, and a PIS network with both kinematic derivative constraints and data folding are compared and denoted as LSTM, PhyLSTM, and PhyLSTMs, respectively. Preferably, the number of training epochs is 6000, and the learning rate is set to... Batch size is 100. Where (MAE) is the mean absolute error, (RMSE) is the root mean square error, and (R) is the correlation coefficient.

[0097] Figure 6 This illustrates a typical expression of the method of the present invention for result comparison, namely, using bedrock input seismic motion as input, and comparing the correspondence between the surface target response and the model predicted response; in this embodiment, Figure 11 and Figure 12 The specific results of this type of comparison method are given for the best and worst prediction samples, respectively.

[0098] Figure 9 The training and validation loss trajectories of the three models on the numerical simulation dataset are shown. The baseline model stabilizes after approximately 1000 epochs, with the validation loss exceeding the training loss; however, by introducing kinematic derivative constraints and data folding, the model exhibits a faster convergence trend within the first 100 epochs. Under the same hardware environment, the single-epoch training times for LSTM, PhyLSTM, and PhyLSTMs are approximately 9.7 seconds, 11.2 seconds, and 3.6 seconds, respectively.

[0099] Figure 10 The normalized error probability density distributions of the three models are shown on the numerical simulation dataset. Within the normalized error range, the sample proportions of LSTM, PhyLSTM, and PhyLSTMs were 96.32%, 97.10%, and 97.98%, respectively.

[0100] Figure 11 and Figure 12 The best and worst predicted samples of the three models on the numerical simulation dataset are shown respectively; the overall performance of each model is shown in Tables 2 and 3.

[0101] Table 2 Comparison of prediction performance of different models on numerical simulation datasets

[0102]

[0103] Table 3 Peak prediction error of representative samples from the three models

[0104]

[0105] Tables 2 and 3 show that, under numerical simulation data conditions, after introducing kinematic derivative constraints, the MAE and RMSE of the test set decreased by 12.63% and 13.07%, respectively; after further introducing data folding, the MAE and RMSE decreased by 13.25% and 10.08%, respectively. The average peak relative error of the entire test set decreased from 2.11% to 1.60%.

[0106] Example 6: Verification Results of Actual Measurement Records

[0107] In this embodiment, LSTMs models without data augmentation and physical constraints, LSTMs-E models with only data augmentation, PhyLSTMs models with only kinematic derivative constraints, and PhyLSTMs-E models with both data augmentation and kinematic derivative constraints are constructed for the measured recorded data. Preferably, the training epochs are 10,000, the batch size is 150, and the number of hidden nodes is 64. Here, (CI95%) is the percentage of samples whose normalized error falls within a preset confidence interval, (MAE) is the mean absolute error, (RMSE) is the root mean square error, and (R) is the correlation coefficient.

[0108] Figure 13 This shows the normalized error distribution and correlation coefficient distribution on the measured data dataset. Figure 14 The table shows the best and worst sample comparison results of the PhyLSTMs-E model on the actual test dataset. The overall performance of different model configurations is shown in Table 4.

[0109] Table 4. Performance comparison of different model configurations on the measured ground motion dataset.

[0110]

[0111] Table 4 shows that data augmentation and kinematic derivative constraints can both improve the prediction performance of the measured records. The PhyLSTMs-E model with the combination of the two achieves better results: CI 95% is 88.84%, mean peak relative error is 25.02%, correlation coefficient is 66.16%, MAE is reduced by 19.2% and RMSE is reduced by 15.4% compared with the baseline model.

[0112] In one implementation, Figure 14Representative samples show that the time-domain correlation coefficient and response spectrum correlation coefficient of the better samples are 0.894 and 0.993, respectively, while the corresponding indices of the worse samples are 0.823 and 0.986, respectively. Statistical analysis of all 100 test samples shows that the average response spectrum correlation coefficient reaches 0.951, indicating that the output results of the method of this invention can be used for subsequent response spectrum evaluation and engineering analysis.

[0113] Example 7: Sensitivity Analysis of Data Augmentation Factor and Folding Granularity

[0114] To further illustrate the parameter selection range of the method of the present invention, this embodiment conducts sensitivity analysis on the data augmentation factor K and folding granularity F on the actual measured dataset. The relevant results are shown in Tables 5 and 6, respectively. The training time for each round below corresponds to the same computing hardware environment and is only used as an exemplary efficiency indicator of the method of the present invention. Wherein, (K) is the data augmentation factor and (F) is the folding granularity.

[0115] Table 5. Effect of data augmentation factor K when the folding factor F=5

[0116]

[0117] Table 6. Effect of folding particle size F when K=1

[0118]

[0119] As shown in Table 5, the overall accuracy of the model gradually improves as K increases from 1 to 5. When K=5, the correlation coefficient reaches 66.16%, and the RMSE is [value missing]. When K=3, the training time per round is controlled to 2.05 seconds while maintaining approximately RMSE, which can be regarded as a preferred implementation method for data augmentation.

[0120] As shown in Table 6, the folding operation can significantly shorten the training time; when F=5, the training time per round is reduced from 13.81 seconds when F=1 to 0.66 seconds, an improvement of approximately 21 times, while CI95% and RMSE remain within acceptable ranges. Performance begins to decline significantly when F increases to 20, therefore the preferred folding granularity is 3 to 8, more preferably 5.

[0121] Example 8: Peak Error Statistics for the Entire Test Set

[0122] Figure 15Box plots of the peak relative errors (PREs) for all numerical simulation test samples are shown. Statistical results show that the median PREs for LSTM, PhyLSTM, and PhyLSTMs are 1.28%, 0.95%, and 0.93%, respectively, while the maximum PREs are 30.06%, 9.38%, and 10.23%, respectively. These results can serve as supplementary examples to support the technical solution of this invention in suppressing extreme peak errors.

[0123] As can be seen from the above implementation results, the site seismic response prediction method based on kinematic derivative constraints and data folding physical information long short-term memory network proposed in this invention can be implemented under different implementation conditions, and can take into account the consistency of response prediction, peak control capability and training efficiency.

Claims

1. A method for predicting site seismic response using a physical information long short-term memory network based on kinematic derivative constraints and data folding, characterized in that, Includes the following steps: S1: Obtain the bedrock input ground motion time history data and the corresponding surface response time history data of the target site to form a training sample set; S2: Preprocess the bedrock input ground motion time history data and the surface response time history data in the training sample set, and use the preprocessed bedrock input ground motion time history data as the input ground motion sequence and the preprocessed surface response time history data as the target response sequence; construct surface displacement time history and surface velocity time history for the surface acceleration time history in the surface response time history data to form three types of supervision labels: displacement, velocity and acceleration. S3: Construct a neural network model, which includes an input layer, at least one recurrent neural network layer, at least one fully connected layer, and an output layer; S4: Perform data folding processing on the input ground motion sequence, and set the sequence unfolding processing corresponding to the data folding processing; The folded input sequence is input into the neural network model to obtain the response prediction sequence at the target location. The original time length of the response prediction sequence is then restored through the sequence unpacking process. The data folding process involves rearranging adjacent sampling points in the original time sequence to the feature dimension to shorten the time dimension and expand the single-step input feature dimension. The data folding process also includes a sequence unpacking process for restoring the original time length, comprising: converting the original input tensor X into a folded tensor X through a rearrangement operation. f The dimension of the original input tensor is The dimension of the folded tensor is Where X is the original input tensor, X0 f It is a folded tensor, where b is the number of samples. is the sequence length, d is the number of feature channels, and s is the folding factor; the network output is reverse-rearranged to restore the original time length, thereby shortening the effective time step length of the recurrent network without losing sampling point information; S5: Construct a data loss based on the predicted response sequence and the target response sequence, and construct a physical constraint loss based on the kinematic derivative relationship between multiple response physical quantities; S6: Train the neural network model based on the data loss and physical constraint loss to obtain the trained site seismic response prediction model; S7: Input the ground motion sequence of the site to be predicted into the trained site seismic response prediction model, and output the seismic response prediction result of the site to be predicted.

2. The site seismic response prediction method according to claim 1, characterized in that, In step S7, the earthquake response prediction results include at least the acceleration response time history, as well as the displacement response time history and velocity response time history synchronously output by the same neural network model.

3. The site seismic response prediction method according to claim 1, characterized in that, In step S3, the neural network model includes an input layer, at least one recurrent neural network layer, at least one fully connected layer, and an output layer. The recurrent neural network layer is one or more stacked structures of long short-term memory layers.

4. The site seismic response prediction method according to claim 1, characterized in that, In step S5, the physical constraint loss includes at least the consistency constraint loss between displacement and velocity and the consistency constraint loss between velocity and acceleration, and the consistency constraint loss is obtained by performing numerical differentiation on the predicted sequence.

5. The site seismic response prediction method according to claim 4, characterized in that, The numerical differentiation employs one of the following methods: central difference method, forward difference method, backward difference method, or automatic differentiation method.

6. The site seismic response prediction method according to claim 1, characterized in that, In step S5, the data loss and physical constraint loss are weighted according to an adaptive weighting strategy. This adaptive weighting strategy determines the corresponding weights based on the relative magnitudes of each loss component during the initial training phase, thereby constructing a joint loss function. The joint loss function is expressed as follows: Among them, L data It is data loss; L phy It is the physical constraint loss; L is the joint loss function; α u It is the weighting coefficient of the displacement data loss term; α v It is the weighting coefficient of the velocity data loss term; α a β1 is the weighting coefficient of the acceleration data loss term; β2 is the weighting coefficient of the consistency constraint term between the displacement derivative and the predicted velocity; λ is the weighting coefficient of the consistency constraint term between the velocity derivative and the predicted acceleration; λ is the total weight of the physical constraints; (with cap symbol) , and These are the predicted displacement, predicted velocity, and predicted acceleration, respectively; the uncapped symbols u, v, and a represent the actual displacement, actual velocity, and actual acceleration, respectively; MSE is the mean square error function; and CDM is the central difference operator.

7. The site seismic response prediction method according to claim 1, characterized in that, Before model training, data augmentation is performed on the training sample set, including one or more of Gaussian noise injection, amplitude scaling, time shifting, and low-frequency perturbation.

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