Ground motion spectrum acceleration prediction method, transfer learning method, device and medium

Abstract

The application provides a ground motion spectrum acceleration prediction method, a transfer learning method, equipment and a medium. A global model is obtained through first training by using basic knowledge data set, and the first training is evaluated by using regional knowledge data set. Then, a transfer model is obtained through second training by using the regional knowledge data set, and the second training is evaluated by using the regional knowledge data set. The establishment method of the transfer model retains the data characteristics of the regional database, learns the difference between the global data set and the regional data set, thereby ensuring the prediction accuracy of the model, and additionally enhancing the generalization ability of the model.

Description

Technical Field

[0001] This application relates to the field of earthquake engineering technology, and in particular to a method for predicting seismic ground motion spectrum acceleration, a transfer learning method, equipment, and medium. Background Technology

[0002] Seismic motion models predict seismic intensity by considering various factors affecting seismic motion propagation (source, propagation, and site), and are crucial for regional seismic hazard assessment and structural seismic risk assessment. Seismic motion models are mainly divided into physics-driven theoretical models and data-driven empirical models. Physical models require a comprehensive understanding of the source, path, and site effects; however, limitations in observational methods and resulting cognitive deficiencies make it difficult for physical models to ensure that ground motion conditions are consistent with empirical records without introducing any bias. Therefore, empirical models remain a good choice for simulating strong ground motions.

[0003] Data-driven empirical models mainly consist of two parts: General Ground Motion Prediction Equations (GMPE) based on traditional regression methods and Ground Motion Models (GMMs) based on machine learning methods. Traditional GMPEs typically set preset functions based on the physical laws of seismic wave propagation, then use regression to obtain relevant parameters, providing higher reliability for GMM-based risk and hazard assessments and decision-making. However, as the captured information becomes increasingly detailed and the nonlinear behaviors to be considered become more complex, GMPEs built using traditional methods may not adequately account for these factors. Furthermore, the cumbersome modeling process of traditional methods may not be suitable for the more localized requirements of GMMs, making it difficult to meet the need for continuous and timely model updates based on new observational data. Machine learning, due to its powerful predictive capabilities and ability to automatically seek patterns in complex data structures such as high-dimensional and nonlinear data without assuming any prior functional forms, is widely used in earthquake engineering. However, since machine learning is also a data-driven modeling process, it still cannot solve the dilemma of limited regional data, making it difficult to apply regional databases for modeling. While regional databases may have limited data, the information they contain is particularly relevant to the seismic wave attenuation patterns under specific local geological conditions and should be fully utilized in modeling.

[0004] In summary, although regional databases can reflect the seismic wave characteristics under specific local geological conditions, they cannot be fully utilized because current methods make it difficult to directly use regional databases to build regional models, or the regional models built from them have a small application scope and poor generalization ability. Summary of the Invention

[0005] This application proposes a method for predicting seismic ground motion spectrum acceleration, a transfer learning method, equipment, and medium, which can solve one of the problems existing in the background art.

[0006] To achieve the above objectives, this application adopts the following technical solution:

[0007] Firstly, a transfer learning method suitable for establishing seismic motion models of arbitrary scale regions is provided, including:

[0008] A training set is obtained, which includes a basic knowledge dataset and a regional knowledge dataset. The knowledge dataset includes seismic parameters and ground motion spectrum acceleration. The basic knowledge dataset is extracted from a global database, and the regional knowledge dataset is extracted from a regional database.

[0009] The global model is first trained using the aforementioned foundational knowledge dataset, and the first training is evaluated using the aforementioned regional dataset; and,

[0010] The global model obtained from the first training is trained using the regional knowledge dataset, and the second training is evaluated using the regional knowledge dataset to obtain a transfer model for predicting seismic spectral acceleration.

[0011] Based on the above technical solution, a global model is obtained through the first training using a basic knowledge dataset, and the first training is evaluated using a regional knowledge dataset. Then, a transfer model is obtained through the second training using a regional knowledge dataset, and the second training is evaluated using a regional knowledge dataset. This method of establishing a transfer model retains the data characteristics of the regional database, learns the differences between the global dataset and the regional dataset, thereby ensuring the accuracy of the model's predictions and enhancing the model's generalization ability.

[0012] In one possible design of the first aspect, the processes of the first training and the second training specifically include:

[0013] The first regression tree is constructed using seismic parameters and ground motion spectrum acceleration as the first input, and the first pseudo residual is calculated. The second regression tree is constructed using seismic parameters and the first pseudo residual as the second input, and the second pseudo residual is calculated. This process continues until the nth regression tree is constructed and the nth pseudo residual is calculated. At this point, the iteration termination condition is met, and the weighted sum of the outputs of all n regression trees is used as the final prediction result.

[0014] In one possible design of the first aspect, the regression tree uses a greedy algorithm to divide and split the input until the splitting termination condition is met.

[0015] In one possible design approach of the first aspect, the splitting objective function for each regression tree is:

[0016] ,

[0017] Among them, Obj split Indicates the gain resulting from this split; g i h represents the first derivative of the loss function for sample i. i λ represents the second derivative of the loss function for sample i. T γ represents the L2 regularization coefficient; T I represents the complexity control coefficient; I represents the set of all samples in the parent node; I L ,I R This represents the set of samples assigned to the left and right child nodes at the current split point, where T represents the specified period.

[0018] The overall objective function of the transfer model is:

[0019] ,

[0020] in, Let represent the overall objective function to be minimized. Represents all parameters of the entire model; i represents the index of a sample in the training dataset; n represents the total number of samples in the training dataset; y i This represents the true value of the i-th sample; i Let l(y) represent the model prediction value for the i-th sample; i , i ) represents the loss function; t represents the total number of tree models; f t Represents the t-th tree model; Ω(f t ) represents the complexity regularization term for the t-th tree.

[0021] In one possible design approach of the first aspect, the processing of the regression tree is achieved by constructing a new thruster that prioritizes learning the seismic parameters with higher importance.

[0022] In one possible design approach of the first aspect, the transfer learning method applicable to establishing seismic motion models for arbitrary scale regions further includes:

[0023] The original data is preprocessed to obtain the training dataset. The preprocessing includes: eliminating non-physical trends in the displacement time series, baseline correction, zero padding, and deleting non-compliant data. The deleting of non-compliant data includes: deleting error data, deleting data in the overlapping area of ​​the wide-area dataset with the regional dataset, and deleting corresponding missing data.

[0024] In one possible design approach for the first aspect, the seismological parameters include: moment magnitude, epicentral distance, focal depth, and 30-meter average shear wave velocity.

[0025] Secondly, a method for predicting seismic ground motion spectrum acceleration is provided, including:

[0026] Obtain current seismic parameters; and,

[0027] Using the current seismological parameters as input, the current seismic spectral acceleration is obtained by utilizing the transfer model for predicting seismic ground motion spectral acceleration as trained above.

[0028] Thirdly, an electronic device is provided, comprising: a processor and a memory coupled to the processor, the memory for storing a computer program; the processor for executing the computer program stored in the memory such that the electronic device performs a transfer learning method suitable for establishing a seismic motion model of an arbitrary scale region as described in any possible implementation of the first aspect, or performs a seismic motion spectrum acceleration prediction method as described in the second aspect.

[0029] Fourthly, a computer-readable storage medium is provided, including a computer program or instructions that, when executed on a computer, cause the computer to perform the transfer learning method applicable to establishing a seismic motion model for an arbitrary scale region as described in any possible implementation of the first aspect, or to perform the seismic motion spectrum acceleration prediction method as described in the second aspect.

[0030] Fifthly, a computer program product is provided, comprising: a computer program or instructions that, when executed on a computer, cause the computer to perform the transfer learning method applicable to establishing a seismic motion model for an arbitrary scale region as described in any possible implementation of the first aspect, or to perform the seismic motion spectrum acceleration prediction method as described in the second aspect. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a schematic diagram of the overall method flow of an embodiment of this application;

[0033] Figure 2 This is a diagram showing the interrelationships between seismic parameters used in the embodiments of this application;

[0034] Figure 3 This is a schematic diagram of the model building process in the embodiments of this application;

[0035] Figure 4 This is a schematic diagram illustrating the gradient boosting algorithm in the embodiments of this application;

[0036] Figure 5 This is a schematic diagram illustrating the principle of the decision tree algorithm in the embodiments of this application;

[0037] Figure 6 (a)- Figure 6 (c) are visualization diagrams of the training process of the seismic acceleration prediction model in the embodiments of this application with periods of 0.2 / 1.0 / 3.0 seconds;

[0038] Figure 7 This is a comparison chart showing the transfer learning benefits of embodiments of this application when there is only a small amount of data in the target region. Figure 7 (a) reflects the learning gains achieved by Example M3 relative to Examples M1 and M2. Figure 7 (b)- Figure 7 (d) Reflects the learning gains of Example M4 relative to Examples M1 and M2 during training processes with periods of 0.2 / 1.0 / 3.0 seconds, respectively;

[0039] Figure 8 This is a comparison chart of the transfer learning benefits in the case of no data in the target area but a small amount of data in the adjacent area with a sufficient data range, according to embodiments of this application. Figure 8 (a) reflects the learning gains achieved by Example M3 relative to Examples M1 and M2. Figure 8 (b) Reflects the learning gains achieved by Example M4 relative to Examples M1 and M2;

[0040] Figure 9 This is a comparison chart of the transfer learning benefits in the case of no data in the target area but a small amount of data in the adjacent area, but with insufficient data range, according to embodiments of this application. Figure 9 (a) reflects the learning gains achieved by Example M3 relative to Examples M1 and M2. Figure 9 (b) Reflects the learning gains achieved by Example M4 relative to Examples M1 and M2;

[0041] Figure 10 This is a comparison diagram of the residuals (M and Zhyp) between events M1 and M3 in embodiments of this application, wherein... Figure 10 (a)- Figure 10 (c) Comparison of the residuals of M1 and M3 with respect to the seismic motion parameter M for periods of 0.2 / 1.0 / 3.0 seconds respectively; Figure 10 (d)- Figure 10 (f) Comparison of residuals of M1 and M3 for the seismic motion parameter Zhyp with periods of 0.2 / 1.0 / 3.0 seconds respectively;

[0042] Figure 11 This paper presents a comparison of the distribution of intra-event residuals of models M1 and M3 under different response spectrum periods in the embodiments of this application, along with the distribution in two dimensions: source distance (Repi) and site shear wave velocity (Vs30). Figure 11 (a)– Figure 11 (c) The distribution of intra-event residuals with respect to Repi for periods T = 0.2s, 1.0s, and 3.0s, respectively; Figure 11 (d)– Figure 11 (f) shows the distribution of the intra-event residuals with respect to Vs30 under the corresponding period;

[0043] Figure 12 This is a comparison chart of the seismic ground motion spectrum acceleration (period from 0.01 seconds to 10 seconds) predicted by the migration model in this application embodiment and the actual seismic ground motion spectrum acceleration. Figure 12 (a)- Figure 12 (i) are comparison results of the observed response spectrum and the predicted response spectrum acceleration at different observation stations 51JZW / 51JZY / 51HYQ / 51HSL / 51BCB / 51MNA / 51MNJ / 51XDM / 51MZQ. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0045] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0046] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0047] like Figure 1 As shown, this application provides a transfer learning method suitable for establishing seismic motion models of arbitrary scale regions, specifically including steps S1-S4.

[0048] S1. Obtain the basic knowledge database and the region learning database to determine the model input features. Specifically, this includes:

[0049] 1. Select a global database and choose a training library from it to learn the basic knowledge of the model.

[0050] In this embodiment, seismic wave data is selected from the basic database W2 as the training set for model learning. W2 (NGA-West2) is a strong earthquake database that records ground motions and is an important product of a large research project at the Pacific Earthquake Engineering Research Center (PEER). This database contains global ground motion data recorded by shallow crustal earthquakes in active tectonic zones since 2000, as well as a set of small to moderate earthquakes in California from 1998 to 2011.

[0051] 2. Select a regional database and choose a training library from it for the model to learn regional knowledge.

[0052] In this embodiment, ground motion data is selected from the regional database CN as the dataset for the model to learn regional knowledge. CN is a ground motion database for Sichuan and Yunnan regions extracted from the National Strong Earthquake Observation Network System of China (NSMONS). NSMONS was put into use in 2008, and almost all of its stations are digital velocimeters, providing high-quality strong earthquake data.

[0053] 3. Select the input features for model training, i.e., the learning objectives of the model.

[0054] In this embodiment, since the main focus is on how to establish a regional ground motion model with higher accuracy and stronger generalization ability with limited data, the emphasis is on the methodology. Therefore, only four seismic parameters—moment magnitude Mw, epicentral distance Repi, focal depth Zhyp, and 30-meter mean shear wave velocity Vs30—are used as model input features. The specific relationships between the selected seismic parameters are as follows: Figure 2 As shown.

[0055] S2. Preprocess the dataset obtained in step S1. Specifically, this includes:

[0056] 1. Process the acquired data into a data type acceptable for model training.

[0057] In this embodiment, preprocessing is performed using the database's built-in program. The records in the CN dataset are consistent with the NGA-West2 data processing procedure. By observing the raw wave and Fourier amplitude spectrum of each record in the dataset, the corner frequencies of the acausal band-pass Butterworth filter are selected according to the -3dB criterion of the NGA-West2 data program. When the filter fails to eliminate non-physical trends in the displacement time series, baseline correction is applied to the recorded data. Simultaneously, zero pads are added to the ends of the data before filtering and then removed after filtering. If non-physical trends still exist in the displacement time series, a new corner frequency is selected and the above process is repeated.

[0058] The IM used in the CN database in this article is "PSARotd50", which is consistent with the W2 database.

[0059] 2. Filter and delete unsuitable data in the dataset selected in step S1.

[0060] In this embodiment, for the basic knowledge dataset W2 and the regional learning database CN, the built-in data processing program in the database is used to eliminate non-physical trends in the displacement time series. If the dataset obtained in step S1 contains data with an epicentral distance error greater than 10 km from the theoretical calculation, such data should be removed. If the basic knowledge dataset W2 contains earthquake records of the region where the regional learning database CN is located, such data should also be deleted. If the data is also in CN, it should be removed from W2 to ensure that the superior performance of M3 in the test after further learning CN data comes from its generalization ability, rather than from "having seen and remembered such data in W2". Data records with missing seismic parameter information and peak ground acceleration (PSA) of the seismic response spectrum should be removed.

[0061] S3. Based on the dataset processed in step S2, train the model to obtain the global model M1 and the regional model M2. Specifically, this includes:

[0062] 1. Determine the initial learning algorithm, loss function type, and weak learner type for the model.

[0063] In this embodiment, the gradient boosting learning algorithm is selected as the initial algorithm for model learning. The loss function is "mean squared error," and the key task of the gradient boosting algorithm is to add new boosters to maximize the reduction of residuals. A regression tree is chosen as the weak learner type, and the task is refined to how to partition the data based on the seismic characteristics of the dataset. The specific process is as follows: Figure 4 As shown.

[0064] When using a greedy algorithm to partition the dataset, the objective function for splitting is shown in Equation (1). The program iterates through all numerical intervals of all seismic features at each split point of each Booster and calculates the objective function value for splitting at that numerical interval. Then, it selects the numerical interval of the feature with the largest objective function for splitting, thus maximizing the splitting benefit.

[0065] (1)

[0066] Among them, Obj split Indicates the gain resulting from this split; g i h represents the first derivative (gradient) of the loss function for sample i. i λ represents the second derivative of the loss function for sample i. T γ represents the L2 regularization coefficient; T I represents the complexity control coefficient; I represents the set of all samples in the parent node (the current node to be split); I L ,I R This represents the set of samples that are assigned to the left and right child nodes at the current split point, and T represents the specified period.

[0067] The splitting stops when the maximum return is less than 0. Then the residual is calculated and the next Booster is built until adding a new Booster no longer makes the objective function of the gradient boosting structure decrease, as shown in Equation (2).

[0068] (2)

[0069] in, Let represent the overall objective function to be minimized. The set of all parameters representing the entire tree (i.e., the entire model); i represents the index of a sample in the training dataset; n represents the total number of samples in the training dataset; y i This represents the true value of the i-th sample; i Let l(y) represent the model prediction value for the i-th sample; i , i ) represents the loss function; t represents the total number of tree models; f tRepresents the t-th tree model; Ω(f t ) represents the complexity regularization term for the t-th tree.

[0070] 2. Determine the order of learning objectives for the model based on the importance of seismic features in the seismic model.

[0071] In this embodiment, the seismological parameters Mw and Repi are the most important and should be learned first as the most basic underlying knowledge. As the model learns less and less from Mw and Repi, it gradually begins to learn more refined upper-level knowledge, with the learning focus shifting to the less important features Zhyp and Vs30.

[0072] Because the model is built using a phased cumulative expansion method, it can easily learn the local nonlinearity of regional features. In addition, since the entire model is composed of Boosters connected in series, when the model learns later features such as Zhyp and Vs30, it also naturally learns their nonlinear coupling with earlier features such as Mw / Repi. Therefore, this type of model structure is inherently suitable for the transfer learning task of ground motion models, because the propagation law of Mw / Repi learned by the earlier Boosters is ergodic, while the source and site characteristics learned by the later Boosters are non-ergodic. From the perspective of mathematical modeling, the form of this method is analogous to the correction process of the classical wave equation: the basic model corresponds to the propagation law of seismic waves in an ideal medium, as shown in formula (3), while the subsequent weak learner trained by regional data is equivalent to introducing boundary correction terms and non-homogeneous disturbances that reflect local fault structures and site conditions. The final model, as shown in formula (4), achieves the unity of global generalization ability and regional accuracy, reflecting the hybrid modeling idea of ​​"physics first, data later".

[0073] (3)

[0074] This is the non-homogeneous wave equation, describing the propagation of seismic waves in a three-dimensional medium. Wherein: It is the displacement field (seismic response), a function of space and time; x, y, and z are displacements in different directions, t is time; a is the wave velocity, which depends on the elastic properties of the medium (such as shear modulus and density). It is the Laplace operator, which represents the curvature of space; The source term represents the external force excitation caused by the rupture of the earthquake fault, such as the focal mechanism function. Physical meaning: This equation describes the propagation behavior of seismic waves in an ideal homogeneous medium, neglecting complex geological structures, attenuation mechanisms, and nonlinear effects.

[0075] (4)

[0076] in This is the final model output, namely the seismic ground motion spectrum acceleration; x is the feature vector, including magnitude / distance / site parameters, etc. It is a base model (mother model) trained based on a global database. It is a regional correction term; For the target region dataset The successively trained weak learner is used to capture the regional geological and fault effects. This structure is functionally similar to introducing a data-driven local correction term into the basic physical model, achieving a balance between model bias and variance. It is the shrinkage coefficient or learning rate weight; It is the accumulation of K iterations.

[0077] 3. The knowledge learning database is used for training and evaluation. A regional database test set is used to obtain the global model M1.

[0078] In this embodiment, a global model M1, learned from a dataset in a knowledge learning database, is used to model conventional methods. Its role is to provide ergodic assumptions, serving as the foundation for models M3 and M4. The mathematical process involves constructing a global mean function. During evaluation, overall indicators including root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) are calculated. Error analysis is performed by grouping by magnitude, distance, and site conditions, and residual distribution and prediction-measured scatter plots are plotted to identify systematic biases. Simultaneously, the model is compared with other baseline models to verify its physical rationality and relative performance. Furthermore, by analyzing the model's performance on far-field / near-field and soft soil / rock site subsets, it is determined whether the model captures universal attenuation laws and site effects, thereby comprehensively evaluating the model's reliability and applicability boundaries.

[0079] If each evaluation passes, the corresponding model is obtained; if it fails, the process returns to the previous step, and so on.

[0080] 4. The training set of the regional learning database is used for learning, and the regional database test set is used for training and evaluation to obtain the regional model M2.

[0081] In this embodiment, the regional model M2, obtained by learning from the dataset in the regional database, models the conventional method. The mathematical process essentially involves directly constructing a regional mean function. Its purpose is to serve as a comparison model (i.e., as a baseline) to explore the benefits of the transfer learning method (i.e., how much accuracy is improved compared to the baseline) and the scope of application of the data volume (i.e., establishing the relationship between the amount of data in the regional database and the amount of accuracy improvement).

[0082] S4. Based on the global model M1 obtained in step S3, a transfer model M3 is obtained by relearning the regional database, and a reconstructed model M4 is obtained by changing the leaf weights. Specifically, this includes:

[0083] 1. Using the global model M1 obtained in step S3 as the initial Booster, learn from the regional database training set and use the regional database test set for training and evaluation to obtain the transfer model M3.

[0084] In this embodiment, model M1 is used as the initial Booster to train on the regional dataset. After training and evaluation using the regional database, the transfer model M3 is obtained. Model M3 views function approximation from the perspective of numerical optimization of the function space, models the knowledge transfer method, learns the differences between regional and global ground motions, and the mathematical process is reflected in the function evolving in the direction of gradient descent.

[0085] 2. Based on the global model M1 obtained in step S3, directly modify the leaf weights to obtain the reconstructed model M4.

[0086] In this embodiment, model M1 is modified based on the updated leaf weights of the regional database (both leaf weights and split points cannot be changed; if both are changed, the result will be no different from model M2) to obtain the reconstructed model M4. Model M4 views function approximation from the perspective of numerical optimization of the parameter space, models another knowledge transfer method, and compares its advantages and disadvantages with the transfer model M3. The mathematical process is reflected in the updating of parameters in the function in the direction of gradient descent.

[0087] like Figure 3 , Figure 4 and Figure 5 The diagram shows the specific modeling process in this embodiment. Among them, Figure 3 The process of building four models is shown: M1 is the global model trained on the W2 dataset; M2 is the regional model trained on the CN dataset; M3 is the transfer learning model based on M1 and applied to the CN dataset; and M4 is the reconstructed model based on M1 and updated with the weights of the leaf nodes. Figure 4The principle of the model algorithm is illustrated, which involves iteratively constructing N trees (n=1 to N). For the first tree, the seismological parameters X and the seismic ground motion spectral acceleration Y with a specified period T (e.g., T=1 second) are input. The initial prediction value is set as the mean of all true values. Then, the pseudo residual (negative gradient) is calculated, and a tree is fitted to predict the pseudo residual. The optimal value of the leaf node output is calculated. In each subsequent iteration n, a tree is fitted to predict the pseudo residual of the existing model structure, and the fitted new tree is continuously incorporated into the model structure. The final prediction result is the weighted sum of the outputs of all trees, where 'a' represents the weight. The specific partitioning tendency is shown in step S3. The mean squared error (MSE) is used as a metric function to quantify the prediction accuracy of the model. This function measures the distance between the value and the true value, and its mathematical expression is shown in formula (5). Figure 5 This diagram illustrates the principle of a decision tree. The root node represents the entire dataset (i.e., the seismic parameters and ground motion spectral acceleration of the entire training set). By recursively bisecting the data feature space, the dataset is divided into multiple homogeneous sub-regions (leaf nodes), and each region is assigned a prediction value (obtained by maximizing the splitting benefit). The algorithm selects the optimal features and split points, continuously dividing the data space to gradually construct a decision tree. Ultimately, the regression tree makes predictions along the path from the root node to the leaf nodes, achieving a nonlinear mapping from input features (seismic parameters) to the output space (ground motion spectral acceleration). The reconstructed model M4 is obtained by modifying the weight proportions of the leaf nodes in the decision tree based on M1.

[0088] (5)

[0089] Where MSE represents the mean squared error; i represents the index of a sample in the training dataset; n represents the total number of samples in the training dataset; y i This represents the true value of the i-th sample; i represents the model prediction value of the i-th sample;

[0090] like Figure 6 The diagram shown illustrates the model training process in this embodiment. As mentioned earlier, the model training process is the process of the model evolving in the direction of maximum gradient descent. Figure 6This diagram illustrates the performance of "PSARotD50" on the training and test sets as "M1 / M2 / M3" progresses through various iterations at T=[0.2, 1.0, 3.0]. The MSE at Iteration = 0 is the MSE after the model has built the first Booster. As shown in the diagram, due to the presence of the initial Booster, the metric function of model M3 is significantly lower than that of M1 and M2 at the same time, indicating that the knowledge carried by the initial Boosters in M3 has a positive effect on the model's further learning. Furthermore, the minimum point of the M3 curve is smaller than that of M2, and the Iteration corresponding to the minimum point of M3 is also smaller than that of M2. This means that the presence of the initial Boosters enhances the model's generalization ability and allows the model to reach the optimal solution faster. This also implies that for transfer learning tasks, controlling the model to stop iterating immediately upon reaching the optimal solution is crucial.

[0091] When there is only a small amount of data in the target region, the benefits of using transfer learning are, for example... Figure 7 As shown in Figure a, it can be seen that the returns of M1 and M3 are linearly related to the logarithm of the data volume, indicating that the more data there is, the more significant the effect of transfer learning. The returns of M2 and M3 are related to the data volume in a power function (with a negative exponent), indicating that the less data there is, the more significant the effect of transfer learning. In addition, the returns of M3 are always positive, so there is no need to worry about negative returns. As shown in Figure b, compared to M1, the returns of M4 also increase with the increase of the period, consistent with the pattern in Figure a. However, unlike M3, the returns of M4 hardly increase when the data volume is greater than 200. Compared to M2, when the data volume exceeds the threshold (which decreases with the increase of the period), negative returns will occur, so it cannot be used as recklessly as M3. The decay rate in the legend is the output of the weighted leaves, and the mathematical expression is shown in formula (5). When the data volume is small, the decay rate should be set large, and when the data volume is large, the opposite is true. The reason is that when the data volume is small, the weights of the old leaves are more authoritative. As the amount of data increases, the authority of the learned leaf weights also increases. Therefore, it is advisable to reduce the decay rate to increase the proportion of new leaf weights. Overall, the transfer method used in M4 does not yield as much benefit as the transfer method used in M3; therefore, the transfer method used in M3 is recommended.

[0092] (6)

[0093] Where leaf_output represents the final output value of a leaf node after update; old_leaf_output represents the output value of the leaf node before; new_leaf_output represents the output value newly calculated based on the current data batch or the current tree structure; and decay_rate represents the decay rate.

[0094] Depend on Figure 7 The analysis shows that the performance of the M2 model increases rapidly with the amount of data, so it will be compared with the M3 model in the following analysis. Figure 8 This comparison shows the training process of models M3 and M2 when there is no data in the target region but a small amount of data in the neighboring region with a sufficient data range. It is evident that in this scenario, transfer learning significantly improves model performance, reducing MSE by approximately 43% at T=3s. Figure 9 This section compares the training processes of models M3 and M2 when there is no data in the target region but a small amount of data in neighboring regions, though the data range is insufficient. The third scenario builds upon the second scenario, emphasizing that the magnitude range of the test set exceeds the training set. In the first two scenarios, the superiority of transfer learning lies in the improvement in accuracy and efficiency within the parameter range. However, in scenario three, the superiority of transfer learning lies in the improvement beyond the parameter range, or the enhanced extrapolation ability. This allows the developed model to have higher accuracy than the regional model while extending the applicability of the regional model to the parameter range of the W2 database. In conclusion, the test results under different scenarios demonstrate the stability of the transfer model, and the transfer learning method of M3 is recommended.

[0095] Inter-event residuals reflect the median difference between events, primarily related to the epicenter, while intra-event residuals reflect the dispersion of random errors within an event, primarily related to the path and site. The aforementioned MSE is a macroscopic indicator; intra-event and inter-event residuals can provide a more detailed, microscopic explanation of the MSE results, revealing how the migration model specifically reduces MSE. Inter-event residuals are shown in... Figure 10 As can be seen, the transfer model corrects the inter-event residuals in two ways: 1. It pulls the mean of the inter-event residuals back to zero, making them exhibit a normal distribution with a mean of 0; 2. It reduces the dispersion of the residuals, i.e., the variability of the inter-event residuals. Intra-event residuals are shown below. Figure 11 As can be seen, the transfer model has no significant impact on the mean and dispersion of the residuals within the event.

[0096] Figure 12 The observed response spectra (actual values) and predicted response spectra in the test set of the target area were visualized and validated. Nine different historical earthquake scenarios were randomly selected from the test set, and these scenarios were input into the developed migration model for seismic ground motion spectral acceleration prediction. Subsequently, the predicted response spectra and the response spectra calculated from the actual observed seismic waves were plotted together. These nine different historical earthquake scenarios included three events with magnitudes of 7.0, 6.1, and 6.8. Furthermore, these nine historical earthquake scenarios included both relatively recent earthquakes (less than 50 km) and relatively distant earthquakes (greater than 200 km), showing a relatively even and reasonable distance distribution. Figure 12The MSE of the predicted response spectrum for all earthquake scenarios and the response spectrum calculated from the actual observed seismic waves are both less than 0.1, which is excellent in ground motion prediction models, especially in small-area ground motion prediction models. Such a high-precision small-area ground motion prediction model can better realize the downstream scenario-based wave selection task based on regionally related ground motion characteristics. At the same time, the transfer learning model M3 can also serve to quickly build a real-time learning model after the earthquake to learn from the data collected in real time by the seismic observation stations.

[0097] The transfer learning method provided in this embodiment is a powerful and flexible approach to enhance the performance of regional models, which can be flexibly transferred to regions of any scale. The transfer model has strong generalization ability; compared to directly developed regional models, its advantages become more pronounced under more demanding sampling scenarios. In addition to the advantages of high accuracy and strong generalization ability, the transfer model can also extend the applicability of the regional model to the coverage of the database used by the parent model; that is, for regional models, this method enhances extrapolation capabilities. On the regional data test set, the transfer model primarily corrects the inter-event residuals of the global model, specifically correcting two aspects: bringing the residual mean back to zero and reducing error dispersion.

[0098] The above embodiments clearly illustrate the method for predicting ground motion spectrum acceleration and the method for establishing a model according to the embodiments of this application.

[0099] This application also provides an electronic device, including: a processor, and a memory coupled to the processor, the memory being used to store a computer program; the processor being used to execute the computer program stored in the memory, so that the electronic device performs the method as described in any of the above embodiments.

[0100] Electronic devices can be computing devices such as desktop computers, laptops, handheld computers, and cloud servers. These electronic devices may include, but are not limited to, processors and memory.

[0101] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the electronic device, connecting various parts of the device via various interfaces and lines.

[0102] The memory can be used to store the computer program, and the processor implements various functions of the electronic device by running or executing the computer program stored in the memory and calling the data stored in the memory.

[0103] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system, applications required for at least one function, etc.; the data storage area may store data created based on the use of the mobile phone, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0104] This application also provides a storage medium, which is a computer-readable storage medium. The computer program is stored in the computer-readable storage medium, and when executed by a processor, the computer program can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0105] This application also provides a computer program product, including: a computer program or instructions that, when the computer program or instructions are run on a computer, cause the computer to perform any of the above possible implementation methods.

[0106] The above description is the preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A transfer learning method suitable for establishing a ground motion model of an arbitrary scale region, characterized in that, The method comprises the following steps: obtaining a training set, wherein the training set comprises a basic knowledge dataset and a regional knowledge dataset, the knowledge dataset comprises seismological parameters and ground motion spectrum acceleration, the basic knowledge dataset is extracted from a global database, and the regional knowledge dataset is extracted from a regional database; performing first training on a global model by using the basic knowledge dataset, and performing evaluation on the first training by using the regional dataset; and performing second training on the global model obtained through the first training by using the regional knowledge dataset, and performing evaluation on the second training by using the regional knowledge dataset, to obtain a transfer model for predicting ground motion spectrum acceleration. The first training and the second training specifically comprise the following steps: taking the seismological parameters and the ground motion spectrum acceleration as first input to construct a first regression tree, calculating a first pseudo residual, taking the seismological parameters and the first pseudo residual as second input to construct a second regression tree, calculating a second pseudo residual, and iteratively constructing an nth regression tree to calculate an nth pseudo residual, until an iteration termination condition is met, and a weighted sum of output results of all the n regression trees is taken as a final prediction result. The regression tree adopts a greedy algorithm to divide and split the input until a split termination condition is met. A split target function of each regression tree is as follows: ， wherein, Obj split represents the gain brought by the current split; g i represents the first-order derivative of the loss function of sample i; h i represents the second-order derivative of the loss function of sample i; λ T represents the L2 regularization coefficient; γ T represents the complexity control coefficient; I represents the sample set in the parent node; I L ,I R represents the sample set divided into the left child node and the right child node under the current split point, and T represents a specified period, A total target function of the transfer model is as follows: ， wherein, represents the overall objective function to be minimized, represents all parameters of the entire model; i represents the index of the sample in the training data set; n represents the total number of samples of the training data set; y i represents the true value of the i-th sample; i represents the model prediction value of the i-th sample; l(y i , i ) represents the loss function; t represents the index of the tree model, and k represents the total number of tree models; f t represents the t-th tree model; Ω(f t ) represents the complexity regularization term of the t-th tree. 2.The transfer learning method for establishing an arbitrary scale regional ground motion model according to claim 1, wherein, A new propeller is constructed to realize processing of the regression tree, and the propeller preferentially learns the seismological parameters with higher importance. 3.The transfer learning method for establishing an arbitrary scale regional ground motion model according to claim 1, wherein, The transfer learning method suitable for establishing a regional ground motion model of any scale further comprises the following steps: performing preprocessing on original data to obtain the training set, wherein the preprocessing comprises eliminating non-physical trends in displacement time series, baseline correction, zero padding, and non-compliant data deletion, and the non-compliant data deletion comprises error data deletion, partial data deletion in the basic knowledge dataset that coincides with the regional knowledge dataset, and corresponding deletion of missing data. 4.The transfer learning method for establishing an arbitrary scale regional ground motion model according to claim 1, wherein, The seismological parameters comprise moment magnitude, epicentral distance, focal depth, and 30-meter average shear wave velocity.

5. A method of predicting spectral accelerations of ground motions, characterized by, The method comprises the following steps: obtaining current seismological parameters; and taking the current seismological parameters as input, and using the transfer model for predicting ground motion spectrum acceleration that is trained by any one of claims 1-4 to obtain current ground motion spectrum acceleration. The electronic device comprises a processor and a memory coupled to the processor, 6. An electronic device, comprising: the memory is configured to store a computer program; and the processor is configured to execute the computer program stored in the memory, so that the electronic device performs the transfer learning method suitable for establishing a regional ground motion model of any scale according to any one of claims 1-4, or performs the ground motion spectrum acceleration prediction method according to claim 5. The electronic device comprises a processor and a memory coupled to the processor, the memory is configured to store a computer program; and the processor is configured to execute the computer program stored in the memory, so that the electronic device performs the transfer learning method suitable for establishing a regional ground motion model of any scale according to any one of claims 1-4, or performs the ground motion spectrum acceleration prediction method according to claim 5.

7. A computer-readable storage medium, characterized in that, The computer readable storage medium comprises computer programs or instructions, which, when running on a computer, make the computer execute the migration learning method suitable for establishing an arbitrary scale regional ground motion model as claimed in any one of claims 1-4, or execute the ground motion spectrum acceleration prediction method as claimed in claim 5.

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