Modeling method and device of series neural network model for calculating seismic response of structure

Abstract

The application provides a modeling method and device of a series neural network model for calculating structural seismic response, belongs to the technical field of building structures, and particularly relates to prediction of structural seismic response. The method solves the problems of the prior art, such as long time consumption and high hardware requirement in calculating by using a traditional time history analysis method when predicting the seismic response of a building structure, and incapability of considering generalization ability, efficiency, precision, model training simplicity and physical interpretability when using an artificial intelligence prediction model. The modeling method of the series neural network model for calculating structural seismic response obtains the optimal series neural network model by simulating the calculation process of a time history analysis method. The method is mainly used for structural seismic response prediction, design of aseismic structures and rapid evaluation of structural component damage after an earthquake.

Description

Technical Field

[0001] This invention relates to the field of building structure technology, and in particular to the prediction of structural seismic response. Background Technology

[0002] Earthquakes are natural disasters caused by the movement of tectonic plates, and their direct and secondary damage seriously threaten human life and property. Building damage and collapse caused by earthquakes are the main causes of casualties and property losses. Therefore, calculating the structural response of buildings under seismic loading and further assessing their seismic performance are crucial for disaster prevention and mitigation efforts in the field of earthquake engineering.

[0003] Currently, the commonly used method for calculating the seismic response of structures is the time history analysis method based on the finite element method. This method typically uses ground acceleration records caused by earthquakes as input. After performing time history analysis on the finite element model of the structure, it can output the response time histories of all degrees of freedom at any node of the structure, such as displacement, velocity, acceleration, and internal force time histories. The main steps are as follows:

[0004] (1) Establish the finite element model of the structure;

[0005] (2) Input the ground acceleration time history of the site where the structure is located as the external excitation;

[0006] (3) Establish the structural motion equations and solve the motion equations by step-by-step integration to obtain the seismic response time history of the structure.

[0007] The nonlinear Newmark method is a commonly used step-by-step integration method. When dealing with nonlinear cases, the nonlinear Newmark method uses Newton's iteration method to solve the equations of motion. Newton's iteration method uses tangent stiffness calculation to linearize the nonlinear problem, and gradually approximates the true solution of the equations of motion through iterative calculation.

[0008] Time history analysis has gained widespread acceptance in academia and industry, but it has the following drawbacks when performing nonlinear time history analysis on complex, large structures:

[0009] (1) The time history analysis method based on the finite element model has low computational efficiency under nonlinear conditions. The time history analysis method generally uses iterative algorithms such as Newton-Raphson iteration to solve the motion equations at each time step for nonlinear problems. When the degree of structural nonlinearity increases, more iterations are required in the calculation of each time step to ensure accuracy, and convergence cannot be guaranteed in some cases.

[0010] (2) The computation time of the time history analysis method based on the finite element model is closely related to the complexity and scale of the structure. The more complex the structure or the larger its scale, the longer the computation time, resulting in extremely time-consuming seismic response prediction and high hardware requirements. When using the time history analysis method to predict the seismic response of a structure, it is necessary to calculate the system matrix of the structure. The system matrix includes the stiffness matrix, damping matrix, and mass matrix. The size of the system matrix is ​​proportional to the degrees of freedom of the structure. When the structure has n degrees of freedom, the size of the system matrix is ​​n rows and n columns. The larger the scale and complexity of the structure, the more degrees of freedom the structure has, and the larger the size of the corresponding system matrix. The longer the matrix operation time, the more time and memory are consumed in the assembly of the system matrix and the inverse calculation of each iteration step, and the higher the requirements for computer hardware.

[0011] In recent years, artificial intelligence (AI) technology has developed rapidly, opening up great application prospects in various fields due to its ability to discover complex structures in high-dimensional data. AI technology mainly refers to machine learning and deep learning. Machine learning technology includes specific algorithms such as linear regression; deep learning technology mainly refers to artificial neural networks that simulate the working principle of neurons in the human brain. The principles of machine learning and deep learning are basically similar: both provide a large amount of input data (i.e., features) and corresponding output data (i.e., labels) to an AI model for learning, in order to obtain the correspondence between input and output data. After the AI ​​model has learned, when given new data, it can predict the corresponding output data with high accuracy. Among those skilled in the art, some researchers have developed AI-based structural seismic response prediction models. Compared with traditional analysis methods, introducing machine learning or deep learning algorithms can greatly improve efficiency and reduce workload, even at the cost of some accuracy.

[0012] Existing AI-based structural seismic response prediction models are mainly divided into two categories: purely data-driven AI models and AI models that incorporate physical mechanisms. AI models that incorporate physical mechanisms can be further subdivided into two categories: AI models that impose physical constraints on the results and AI models that impose physical constraints on the process.

[0013] While AI-based structural seismic response prediction models have addressed some of the problems encountered by traditional methods, they also have some drawbacks, as follows:

[0014] (1) Existing AI-based prediction models have weak generalization ability. Generalization ability refers to the model's predictive ability when encountering unknown situations. Unknown situations refer to situations not included in the model's training set. When building conditions, site type, or earthquake damage severity change and exceed the situations included in the training set, AI-based prediction models cannot accurately predict earthquake damage results. To include as many "unknown situations" as possible, AI-based prediction models need to use more data as training and testing sets, and the training set should account for a larger proportion.

[0015] (2) Existing AI-based prediction models have fixed format requirements for the input ground motion records, such as specific sampling frequency, ground motion duration and peak acceleration.

[0016] (3) Existing AI-based prediction models have a lot of self-selected parameters (i.e. hyperparameters, inherent parameters of AI models). Although the prediction time is short and the accuracy is high, a lot of time is required to select appropriate hyperparameters when training the model. Moreover, for deep learning models represented by neural networks, there are generally no specific rules to follow when adjusting hyperparameters, and they often depend on the researcher's personal experience.

[0017] (4) Pure data-driven artificial intelligence models are similar to black box models. The internal structure of artificial intelligence models is not visible and lacks physical interpretability, which may lead to prediction results that violate human common sense under certain circumstances. The engineering community pays more attention to safety and requires that earthquake response prediction data strictly follow the constraints of physical laws. Therefore, the prediction data of pure data-driven artificial intelligence models are generally not easily accepted by the engineering community.

[0018] (5) Artificial intelligence models that impose physical constraints on the results refer to the direct introduction of variables governed by physical mechanisms into the objective function (loss function) to be optimized. Commonly used physical mechanisms include differential equations, energy conservation, symmetry, and differential or integral relationships between variables. Artificial intelligence models that impose physical constraints on the results only modify the results to make them appear to conform to physical laws, but the data calculation process is still not constrained by physical laws and still lacks physical interpretability.

[0019] (6) Artificial intelligence models that impose physical constraints on the process have calculation results and calculation processes that conform to physical laws and have strong physical interpretability. However, artificial intelligence models that impose physical constraints on the process are difficult to balance efficiency and accuracy. Moreover, excessive physical constraints can make the model difficult to train and require special processing or optimization of the data.

[0020] In summary, existing technologies have several drawbacks when predicting structural seismic response. Traditional time history analysis is time-consuming and requires high-end hardware, while artificial intelligence prediction models cannot simultaneously address issues such as generalization ability, efficiency, accuracy, ease of model training, and physical interpretability. Summary of the Invention

[0021] This invention proposes a modeling method and apparatus for a cascaded neural network model for calculating structural seismic response, which solves the following problems existing in the prior art: when predicting structural seismic response, the traditional time history analysis method is time-consuming and has high hardware requirements; the artificial intelligence prediction model cannot simultaneously take into account generalization ability, efficiency, accuracy, ease of model training, and physical interpretability.

[0022] The modeling method for calculating the seismic response of structures using a cascaded neural network, as described in this invention, has the following technical solution:

[0023] The method specifically includes:

[0024] Step 1: Establish a structural finite element model, wherein the structural finite element model contains at least one degree of freedom;

[0025] Step 2: Using time history analysis, calculate the response time history and equivalent load time history of the finite element model of the structure when any seismic acceleration time history in the pre-acquired seismic acceleration record is used as the external excitation.

[0026] Step 3: After grouping the earthquake acceleration time history, the response time history, and the equivalent load time history, perform data slicing to obtain at least 3 sets of modeling datasets, namely the pre-training set, the post-training set, and the validation set.

[0027] Step 4: Determine the architecture, training parameters, and value range of the initial cascaded neural network model, and construct at least one initial cascaded neural network model based on the architecture, training parameters, and value range of the training parameters.

[0028] Step 5: Using the pre-training set and the post-training set, train each of the initial concatenated neural network models to obtain the corresponding post-trained concatenated neural network models.

[0029] Step 6: Simulate the calculation process of time history analysis, adjust the structure of each trained cascaded neural network model, and obtain the cascaded neural network model to be verified; the cascaded neural network model to be verified is used to calculate the displacement, velocity, acceleration and internal force of each degree of freedom in the finite element model of the structure at the same sampling time based on the ground motion acceleration at any sampling time using an autoregressive mechanism.

[0030] Step 7: Using the validation set, validate each of the serial neural network models to be validated to obtain the optimal serial neural network model.

[0031] Furthermore, a preferred implementation method is provided:

[0032] The pre-acquired seismic acceleration records in step 2 are as follows:

[0033] The pre-acquired seismic acceleration records contain at least two seismic acceleration time histories with the same sampling frequency;

[0034] The seismic acceleration time history is a data sequence composed of at least one seismic acceleration arranged in chronological order of sampling time; the seismic acceleration time history includes seismic accelerations sampled at least at one sampling time.

[0035] In any given seismic acceleration time history, the seismic acceleration at the i-th sampling time is expressed as: Where i is a positive integer greater than 1.

[0036] Furthermore, a preferred implementation method is provided:

[0037] In step 2:

[0038] The response time history includes the displacement, velocity, acceleration, and internal force calculated for each degree of freedom in the structural finite element model over at least one sampling time; specifically:

[0039] In the finite element model of the structure, the displacement of any degree of freedom at the i-th sampling time is X. i Speed ​​is acceleration is And internal force is F s i Where the displacement at the 0th sampling time is X0 = 0 and the velocity is acceleration is And internal force is F s 0 =0;

[0040] The equivalent load time history includes the equivalent load calculated for each degree of freedom in the structural finite element model at at least one sampling time; specifically:

[0041] In the finite element model of the structure, the equivalent load of any degree of freedom at the i-th sampling time is R. i .

[0042] Furthermore, a preferred implementation method is provided:

[0043] Step 3 is as follows:

[0044] Step 3.1: Take any seismic acceleration time history, the corresponding response time history and equivalent load time history obtained when it is used as an external excitation, as a slice data source;

[0045] Step 3.2: Divide all slice data sources into at least two groups, one group for training data sources and the other group for validation data sources;

[0046] Step 3.3: Using data slicing method one, slice the data sources in the training data source group to obtain the pre-training set. In the pre-training set:

[0047] For any given slice data source, the modeling data feature F of any degree of freedom in the structural finite element model at the i-th sampling time is... q i , is represented as:

[0048]

[0049] Corresponding to any of the same slice data sources, the modeling data label L for any degree of freedom in the structural finite element model at the i-th sampling time. q i , is represented as:

[0050] L q i =R i ;

[0051] Step 3.4: Using data slicing method two, slice the data sources in the training data source group to obtain the post-training set. In the post-training set:

[0052] For any given slice data source, the modeling data feature F of any degree of freedom in the structural finite element model at the i-th sampling time is... h i , is represented as:

[0053]

[0054] Corresponding to any of the same slice data sources, the modeling data label L for any degree of freedom in the structural finite element model at the i-th sampling time. h i , is represented as:

[0055] Among them, R ε The pre-defined target equivalent load;

[0056] Step 3.5: Using data slicing method three, slice the data sources in the verification data source group to obtain a verification set. In the verification set:

[0057] For any given slice data source, the modeling data feature F of any degree of freedom in the structural finite element model at the i-th sampling time is... y i , is represented as:

[0058]

[0059] Corresponding to any of the same slice data sources, the modeling data label L for any degree of freedom in the structural finite element model at the i-th sampling time. y i , is represented as:

[0060]

[0061] Furthermore, a preferred implementation method is provided:

[0062] Step 4 is as follows:

[0063] Step 4.1: The initial cascaded neural network model includes a pre-neural network model and a post-neural network model, wherein the post-neural network model adopts a residual neural network;

[0064] Step 4.2: Based on the finite element model of the structure, determine the construction parameters of the pre-neural network model and the post-neural network model respectively. The construction parameters include the model type, the number of network layers of the model, the number of neurons in each network layer, and the adjustable hyperparameters of the model.

[0065] Step 4.3: The training parameters include pre-training parameters and post-training parameters; the value range of the training parameters is the value range of the pre-training parameters and the value range of the post-training parameters.

[0066] Determine the pre-training parameters of the pre-neural network model, and the range of values ​​for the pre-training parameters;

[0067] Determine the post-training parameters of the post-neural network model, and the range of values ​​for the post-training parameters;

[0068] Step 4.4: Obtain all possible combinations of values ​​for the pre-training parameters and the post-training parameters, and construct the pre-neural network model and the post-neural network model in the corresponding initial concatenated neural network model based on each combination of values ​​and the construction parameters.

[0069] Furthermore, a preferred implementation method is provided:

[0070] Step 5 is described in detail below:

[0071] Step 5.1: Train the pre-network in each of the initial cascaded neural network models using the pre-training set to obtain the trained pre-network model; the trained pre-network model is used to simulate the time history analysis method, based on the ground motion acceleration at the i-th sampling time. Calculate the equivalent load R for each degree of freedom in the finite element model of the structure at the i-th sampling time. i ;

[0072] Step 5.2: Train the post-neural network in each of the initial cascaded neural network models using the post-training set to obtain the trained post-neural network model; the trained post-neural network model is used to simulate the time history analysis method, based on the equivalent load R of each degree of freedom in the structural finite element model at the i-th sampling time. i Calculate the displacement X of each degree of freedom in the finite element model of the structure at the i-th sampling time. i ,speed acceleration and internal force F s i .

[0073] Furthermore, a preferred implementation method is provided:

[0074] Step 6 is as follows:

[0075] Step 6.1: In each of the trained concatenated neural network models, the equivalent load R of the output of the trained pre-neural network model at the i-th sampling time is... i And the displacement X of each degree of freedom in the finite element model of the structure at the (i-1)th sampling time. i-1 and internal force F s i-1 , which serves as the input to the trained post-neural network model at the i-th sampling time;

[0076] Step 6.2: In each of the trained cascaded neural network models, add a velocity and acceleration calculation module, and calculate the displacement value of any degree of freedom in the structural finite element model output by the trained post-neural network model at the i-th sampling time. As input to the velocity and acceleration calculation module;

[0077] The velocity and acceleration calculation module is used to calculate the displacement value of each degree of freedom in the structural finite element model at the i-th sampling time. and the displacement calculation value at the (i-1)th sampling time and calculated speed values Obtain the velocity calculation value of each degree of freedom in the finite element model of the structure at the i-th sampling time. Where, when i = 1, the

[0078] The velocity and acceleration calculation module is also used to calculate the velocity value of each degree of freedom in the structural finite element model at the i-th sampling time. And the calculated velocity value at the (i-1)th sampling time and acceleration calculation value Obtain the calculated acceleration value for each degree of freedom in the finite element model of the structure at the i-th sampling time. Where, when i = 1, the

[0079] Step 6.3: In each of the trained concatenated neural network models:

[0080] The input of the pre-trained neural network model is used as the input of each post-trained cascaded neural network model; the output of the post-trained neural network model and the velocity and acceleration calculation module are used as the output of each post-trained cascaded neural network model; after the structure of each post-trained cascaded neural network model is adjusted, the corresponding cascaded neural network model to be verified is obtained.

[0081] Furthermore, a preferred implementation method is provided:

[0082] Step 7 is described in detail below:

[0083] Step 7: Using the validation set, simulate the time history analysis method to validate each of the serial neural network models to be validated, so as to obtain the optimal serial neural network model; the optimal serial neural network model is used to simulate the time history analysis method, and calculate the displacement, velocity, acceleration and internal force of each degree of freedom in the structural finite element model at the same sampling time based on the ground motion acceleration at any sampling time.

[0084] Step 7.1: In the verification set, select the modeling data feature F of any degree of freedom in the structural finite element model corresponding to any slice data source at the i-th sampling time. y i , which serves as the input to each of the aforementioned concatenated neural network models to be verified;

[0085] Step 7.2: For each of the concatenated neural network models to be verified, based on the input modeling data features F... y i Calculate the internal force values Displacement calculation value Calculated speed value And acceleration calculation values

[0086] Based on the internal force calculation values ​​of each of the aforementioned serial neural network models to be verified at all sampling times. Displacement calculation value Calculated speed value And acceleration calculation values Obtain the response time history calculation result corresponding to any one of the slice data sources;

[0087] Step 7.3: Compare the response time history calculation result with the data recorded in the modeling data label in any slice data source; and calculate the evaluation index for each of the concatenated neural network models to be verified based on the comparison result. The evaluation index is used to evaluate the calculation effect of the concatenated neural network model to be verified.

[0088] Step 7.4: Based on the evaluation index, obtain the performance ranking of each of the concatenated neural network models to be verified when verifying any slice data source in the verification set, according to the calculation effect from best to worst; wherein, the better the calculation effect, the lower the performance ranking.

[0089] Step 7.5: For each of the concatenated neural network models to be verified, sum the performance rankings when verifying all slice data sources in the verification set to obtain a comprehensive performance ranking; the concatenated neural network model with the smallest comprehensive performance ranking is the optimal concatenated neural network model.

[0090] This invention also proposes a modeling device for a cascaded neural network model to calculate the seismic response of a structure, the technical solution of which is as follows:

[0091] The device specifically includes:

[0092] Module 1 is used to establish a structural finite element model, wherein the structural finite element model contains at least one degree of freedom;

[0093] Module 2 is used to calculate the response time history and equivalent load time history of the finite element model of the structure when any seismic acceleration time history in the pre-acquired seismic acceleration record is used as the external excitation, using the time history analysis method.

[0094] Module 3 is used to group the seismic acceleration time history, the response time history, and the equivalent load time history and then perform data slicing to obtain at least 3 sets of modeling datasets, namely, the pre-training set, the post-training set, and the validation set.

[0095] Module 4 is used to determine the architecture, training parameters, and value range of the initial concatenated neural network model, and to construct at least one initial concatenated neural network model based on the architecture, training parameters, and value range of the training parameters.

[0096] Module 5 is used to train each of the initial concatenated neural network models using the pre-training set and the post-training set to obtain the corresponding post-trained concatenated neural network model.

[0097] Module 6 is used to simulate the calculation process of time history analysis, adjust the structure of each trained cascaded neural network model, and obtain the cascaded neural network model to be verified. The cascaded neural network model to be verified is used to use an autoregressive mechanism to calculate the displacement, velocity, acceleration and internal force of each degree of freedom in the finite element model of the structure at the same sampling time based on the ground motion acceleration at any sampling time.

[0098] Module 7 is used to verify each of the serial neural network models to be verified using the verification set, so as to obtain the optimal serial neural network model.

[0099] The present invention also proposes an electronic device, the technical solution of which is as follows:

[0100] An electronic device includes a processor and a memory, the memory being used to store executable instructions of the processor, the processor being configured to perform the above-described modeling method for a cascaded neural network model of a structural seismic response by executing the executable instructions.

[0101] The present invention has the following beneficial effects:

[0102] 1. The modeling method for calculating the seismic response of structures using a cascaded neural network model, as described in this invention, calculates the seismic response of structures through an optimal cascaded neural network model. Leveraging the inherent advantages of neural network models in handling nonlinear problems, it avoids matrix operations and inversion processes in traditional time history analysis methods, saving significant computation time. The computation time for structural seismic response analysis using the neural network model is mainly related to the duration of the ground motion and the sampling frequency, and is largely independent of the size and complexity of the structure. It does not increase computation time as the earthquake intensity increases and the structure enters a nonlinear state, and convergence issues do not need to be considered. Compared to existing time history analysis methods, using the optimal cascaded neural network model for structural seismic response calculation has an efficiency advantage, which becomes increasingly apparent with increasing structural complexity.

[0103] 2. The modeling method of the tandem neural network model for calculating the seismic response of a structure described in this invention obtains the optimal tandem neural network model by simulating the calculation process of time history analysis. It is applicable to any structure that can be analyzed by traditional time history analysis, not limited to building structures, but also applicable to mechanical structures, such as aircraft wings or memorial towers. It has strong generalization ability compared with existing artificial intelligence prediction models.

[0104] 3. The modeling method of the tandem neural network model for calculating the seismic response of a structure as described in this invention, wherein the tandem neural network model to be verified adopts an autoregressive mechanism and calculates the structural response for only one time step at a time. Compared with existing artificial intelligence prediction models, it does not have fixed requirements on the length and duration of the input seismic acceleration time history. The model does not require complex preprocessing of the seismic acceleration time history when used, which is convenient for practical applications.

[0105] 4. The modeling method for calculating the seismic response of structures using a cascaded neural network model as described in this invention obtains the optimal cascaded neural network model by simulating the calculation process of time history analysis. Compared with purely data-driven artificial intelligence models and artificial intelligence models that impose physical constraints on the results, it has stronger physical interpretability and is easier for the engineering community to use. It can calculate a complete set of seismic response time histories at all nodes of the structural finite element model and can further directly derive other engineering requirement parameters.

[0106] 5. The modeling method of the tandem neural network model for calculating the seismic response of a structure described in this invention obtains the optimal tandem neural network model by simulating the calculation process of time history analysis. Compared with artificial intelligence models that impose physical constraints on the process, it ensures higher calculation accuracy, simplifies data processing, reduces model training difficulty, and is suitable for small sample situations (training set percentage < 6% of the total modeling dataset), which is difficult for most AI models to handle.

[0107] 6. The modeling method of the tandem neural network model for calculating the seismic response of a structure described in this invention uses the validation set to validate each of the tandem neural network models to be validated. The training parameters can be automatically selected. Compared with existing artificial intelligence prediction models, it does not require manual adjustment, does not rely on personal experience, and the model training is simple and efficient. It solves the problem that existing artificial intelligence prediction models require time-consuming and laborious parameter tuning based on human experience.

[0108] 7. The cascaded neural network model for calculating the seismic response of a structure described in this invention can predict all response quantities of all nodes (degrees of freedom) of the structure, and can verify the seismic bearing capacity and deformation of the cross section. It can not only assess the overall damage of the structure, but also know the damage state of the structural components. Other artificial intelligence models can only predict the seismic response of a certain floor or a few nodes of the structure, and can only obtain the overall damage state of the structure.

[0109] The modeling method of the cascaded neural network model for calculating the seismic response of structures described in this invention is applicable to the prediction of structural seismic response, the design of seismic-resistant structures, and the rapid assessment of post-earthquake structural component damage. Attached Figure Description

[0110] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0111] Figure 1 A flowchart of a modeling method for a cascaded neural network model for calculating the seismic response of a structure, as described in a preferred embodiment of the present invention;

[0112] Figure 2 Schematic diagrams of three different structural finite element models in a preferred embodiment of the present invention;

[0113] Figure 3 This is a schematic diagram of two constitutive relations used when establishing a structural finite element model, in a preferred embodiment of the present invention.

[0114] Figure 4 A schematic diagram of three data slicing methods used to build the modeling dataset in a preferred embodiment of the present invention;

[0115] Figure 5 In a preferred embodiment of the present invention, a neural network architecture diagram of the pre-neural network model is shown.

[0116] Figure 6 In a preferred embodiment of the present invention, a neural network architecture diagram of the post-neural network model is shown.

[0117] Figure 7 In a preferred embodiment of the present invention, a flowchart of the computation of the cascaded neural network model to be verified is provided.

[0118] Figure 8In a preferred embodiment of the present invention, a comparison diagram of the displacement time histories of the top node in the six-degree-of-freedom lumped mass shear model system architecture is shown when the ground motion acceleration time histories of different peak ground accelerations are used as external excitations.

[0119] Figure 9 In a preferred embodiment of the present invention, a comparison diagram is shown between the force-displacement relationship predicted by the optimal cascaded neural network model and the actual results. Detailed Implementation

[0120] To make the technical solutions and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0121] Implementation Method 1: Combination Figure 1 This embodiment describes a modeling method for a cascaded neural network model to calculate the seismic response of a structure. The specific implementation details are as follows:

[0122] The method specifically includes:

[0123] Step 1: Establish a structural finite element model, wherein the structural finite element model contains at least one degree of freedom;

[0124] Step 2: Using time history analysis, calculate the response time history and equivalent load time history of the finite element model of the structure when any seismic acceleration time history in the pre-acquired seismic acceleration record is used as the external excitation.

[0125] Step 3: After grouping the earthquake acceleration time history, the response time history, and the equivalent load time history, perform data slicing to obtain at least 3 sets of modeling datasets, namely the pre-training set, the post-training set, and the validation set.

[0126] Step 4: Determine the architecture, training parameters, and value range of the initial cascaded neural network model, and construct at least one initial cascaded neural network model based on the architecture, training parameters, and value range of the training parameters.

[0127] Step 5: Using the pre-training set and the post-training set, train each of the initial concatenated neural network models to obtain the corresponding post-trained concatenated neural network models.

[0128] Step 6: Simulate the calculation process of time history analysis, adjust the structure of each trained cascaded neural network model, and obtain the cascaded neural network model to be verified; the cascaded neural network model to be verified is used to calculate the displacement, velocity, acceleration and internal force of each degree of freedom in the finite element model of the structure at the same sampling time based on the ground motion acceleration at any sampling time using an autoregressive mechanism.

[0129] Step 7: Using the validation set, validate each of the serial neural network models to be validated to obtain the optimal serial neural network model.

[0130] In this embodiment, the structure can be any structure whose seismic response can be calculated using traditional time history analysis, such as a single-degree-of-freedom system, a lumped-mass shear model system, or a two-dimensional frame system. The structure can be a building structure or other structures, such as an aircraft wing or a memorial tower. The structure contains at least one degree of freedom, which refers to the part of the structure that can move independently under seismic loading.

[0131] In this embodiment, the structural finite element model can be established using the finite element analysis software OpenSees. OpenSees stands for Open System for Earthquake Engineering Simulation. OpenSees is a comprehensive and continuously evolving open finite element analysis software for simulating seismic responses in structures and geotechnical systems.

[0132] In this embodiment, the optimal cascaded neural network model can be used for elastoplastic time history analysis of structural seismic response. The elastoplastic time history analysis is also known as nonlinear time history analysis; nonlinearity refers to the fact that the relationship between internal forces and displacements in the structure is not linearly related, and this relationship is called the constitutive relation of the structure. The optimal cascaded neural network model combines the advantages of traditional time history analysis methods and artificial intelligence models. This model is suitable for calculating the response time history of a structure under arbitrary sampling frequency, peak ground acceleration, or duration of seismic acceleration time history.

[0133] In this embodiment, the autoregressive mechanism refers to using the result predicted at the previous time as input to further predict the result at the next time. This data processing method, which uses the output of the prediction model at the previous time as the input at the current time, is called the autoregressive mechanism.

[0134] In this embodiment, the serial neural network model to be verified employs an autoregressive mechanism, that is, it calculates the response data at the current moment using response data from previous moments, and its calculation of the response time history is performed at each time point. Traditional neural network models input an entire seismic acceleration time history into the neural network model to directly obtain response time histories of the same length; this traditional approach requires the length of the seismic acceleration time history input to the neural network model to be fixed each time. However, in this embodiment, the data input to the neural network model each time is only data from a single time point, so the seismic acceleration time histories do not need to have the same length. That is, with the same sampling frequency, the seismic acceleration time histories can have different durations. The serial neural network model to be verified in this embodiment can be applied to seismic acceleration time histories of various lengths.

[0135] In this embodiment, step 3 may also construct a fourth modeling dataset, namely a test set; the test set is used to test the optimal concatenated neural network model to evaluate its prediction performance.

[0136] Implementation Method Two: Combination Figure 1 This embodiment further defines the pre-acquired seismic acceleration records in step 2 of the modeling method for calculating the seismic response of structures using a cascaded neural network as described in Embodiment 1. The specific implementation details are as follows:

[0137] The pre-acquired seismic acceleration records contain at least two seismic acceleration time histories with the same sampling frequency;

[0138] The seismic acceleration time history is a data sequence composed of at least one seismic acceleration arranged in chronological order of sampling time; the seismic acceleration time history includes seismic accelerations sampled at least at one sampling time.

[0139] In any given seismic acceleration time history, the seismic acceleration at the i-th sampling time is expressed as: Where i is a positive integer greater than 1.

[0140] In this embodiment, the pre-acquired seismic acceleration record is one type of seismic ground motion record, which also includes seismic displacement records and seismic velocity records. The pre-acquired seismic acceleration record can be downloaded from the Pacific Earthquake Engineering Research Center website (peer website).

[0141] In this embodiment, the seismic acceleration at sampling time 0 is expressed as: and The 0th sampling time is any time when the finite element model of the structure is in a static state before the seismic acceleration time history is used as an external excitation.

[0142] Throughout the entire seismic acceleration time history, the seismic acceleration at different sampling times is different. The seismic acceleration with the largest value in a seismic acceleration time history is called the peak ground acceleration (PGA). PGA is a commonly used indicator to measure the intensity of a seismic motion within a seismic acceleration time history; its magnitude provides a direct measure of the intensity of the seismic motion within that time history.

[0143] In this embodiment, the time history, also known as time series data, refers to a set of data with temporal characteristics obtained by sampling (collecting and recording) a physical quantity at a specific frequency. If the sampled physical quantity is seismic acceleration, the obtained data is the seismic acceleration time history; if the sampled physical quantity is seismic displacement, the obtained data is the seismic displacement time history. In the concept of time history, the time interval between two adjacent sampling times is called a time step, and the specific frequency of data sampling is called the sampling frequency. For example, during an earthquake, a set of data on ground displacement, velocity, and acceleration is collected and recorded every 0.01 seconds. If the earthquake lasts for a total of 100 seconds, then 10,000 sampling times will be collected and recorded from the beginning to the end of the earthquake. The data sequence formed by arranging these data in chronological order of sampling time is a seismic time history. The sampling frequency of the seismic time history is 100 Hz, one time step of the seismic time history is 0.01 s, and the duration of the seismic time history is 100 seconds, which is the duration of the earthquake.

[0144] In this embodiment, each ground motion acceleration time history in the pre-acquired ground motion acceleration record has the same sampling frequency, but the duration of each ground motion acceleration time history may be different.

[0145] In a further implementation, amplitude modulation (AM) can be used to obtain more seismic acceleration time histories of different intensities based on the initial seismic acceleration records. Since there is not a large amount of recorded strong earthquake data, and artificial intelligence-based neural networks require a certain amount of data to construct, AM can effectively solve the problem of insufficient seismic acceleration record data.

[0146] Amplitude modulation is a common method for processing seismic acceleration time histories. Specifically, it involves multiplying the original seismic acceleration time histories by different amplification or reduction coefficients to achieve multiple predetermined peak values ​​for the peak ground acceleration. Under the influence of seismic acceleration time histories with different predetermined peak values ​​(i.e., as external excitation), the structure will enter different degrees of nonlinearity, such as elastic or weakly nonlinear, moderately nonlinear, and strongly nonlinear states. By amplitude modulation of the original seismic acceleration time histories, more seismic acceleration time histories of different intensities can be obtained quickly and conveniently.

[0147] In a more specific embodiment, the original ground motion acceleration records contain 364 ground motion acceleration time histories: 21 of these time histories are selected to generate a training set; 5 of these time histories are selected to generate a validation set; and the remaining 338 time histories are used to generate a test set. For the 21 ground motion acceleration time histories used to generate the training set, amplitude modulation is performed three times using three predetermined peak values ​​(PGA1, PGA2, and PGA3), resulting in 63 ground motion acceleration time histories. For the 5 ground motion acceleration time histories used to generate the validation set, amplitude modulation is performed three times using three predetermined peak values ​​(PGA4, PGA5, and PGA6), resulting in 15 ground motion acceleration time histories. For the 338 ground acceleration time histories used to generate the test set, six amplitude modulations were performed using six predetermined peak values ​​from PGA7 to PGA12, resulting in 5408 ground acceleration time histories. These six predetermined peak values, sorted from smallest to largest, are used as the external excitation. When the ground acceleration time histories obtained by amplitude modulation using the predetermined peak values ​​PGA7 and PGA8 are used as the external excitation, the structure will be in an elastic or weakly nonlinear state; when the ground acceleration time histories obtained by amplitude modulation using the predetermined peak values ​​PGA9 and PGA10 are used as the external excitation, the structure will be in a moderately nonlinear state; and when the ground acceleration time histories obtained by amplitude modulation using the predetermined peak values ​​PGA11 and PGA12 are used as the external excitation, the structure will be in a strongly nonlinear state. Thus, the test set contains ground acceleration time histories of various intensities, allowing for sufficient testing of the optimal cascaded neural network model to verify its generalization ability.

[0148] Implementation Method 3: Combination Figure 1 This embodiment further defines step 2 of the modeling method for calculating the seismic response of a structure using a cascaded neural network, as described in Embodiment 2. The specific implementation details are as follows:

[0149] Step 2 is described in detail below:

[0150] Step 2.1: Based on the finite element model of the structure, obtain the stiffness matrix and mass matrix of the finite element model of the structure;

[0151] Step 2.2: Obtain the damping matrix of the structural finite element model based on the stiffness matrix. The damping matrix adopts Rayleigh damping.

[0152] Step 2.3: Add any one of the pre-acquired seismic acceleration time histories as the external excitation for the finite element model of the structure; specifically:

[0153] The bottom of the finite element model of the structure is constrained to move according to the ground motion acceleration at each sampling time in any given ground motion acceleration time history;

[0154] Step 2.4: Construct the structural motion differential equations based on the seismic acceleration time history, stiffness matrix, mass matrix, and damping matrix;

[0155] Step 2.5: Using time history analysis, solve the differential equations of motion for the structure to obtain the response time history and equivalent load time history of the finite element model of the structure; specifically as follows:

[0156] Step 2.5.1: Using the Newmark-β method (average acceleration method), based on the ground motion acceleration at the i-th sampling time... And the internal force F of each degree of freedom in the finite element model of the structure at the (i-1)th sampling time. s i-1 ,speed and acceleration Obtain the equivalent load R for each degree of freedom in the finite element model of the structure at the i-th sampling time. i The internal force F at sampling time 0 s 0 =0, speed acceleration

[0157] Step 2.5.2: Using Newton's iteration method, based on the equivalent load R at the i-th sampling time... i And the internal force F of each degree of freedom in the finite element model of the structure at the (i-1)th sampling time. s i-1 and displacement X i-1 , obtain the internal force F of each degree of freedom in the finite element model of the structure at the i-th sampling time. s i and displacement X i The process continuously determines the tangent stiffness matrix and internal force column vector based on the constitutive relation of the structure (the values ​​of which change continuously during the iterative calculation), where X0 = 0 at the 0th sampling time;

[0158] Step 2.5.3: Calculate the velocity using the average acceleration method, based on the displacement X of each degree of freedom in the finite element model of the structure at the i-th sampling time. i and the displacement X at the (i-1)th sampling time i-1 and speed Obtain the velocity of each degree of freedom in the finite element model of the structure at the i-th sampling time. Represented as:

[0159] Where Δt is a time step, i.e., the reciprocal of the sampling frequency of any seismic acceleration time history;

[0160] Step 2.5.4: Calculate the velocity using the average acceleration method, based on the velocity of each degree of freedom in the finite element model of the structure at the i-th sampling time. and the speed at the (i-1)th sampling time and acceleration Obtain the acceleration of each degree of freedom in the finite element model of the structure at the i-th sampling time. Represented as:

[0161]

[0162] Step 2.5.6: Calculate the displacement X of each degree of freedom in the obtained structural finite element model at the i-th sampling time. i ,speed acceleration and internal force F s i This forms a single-column matrix, which represents the response data R of each degree of freedom in the finite element model of the structure at the i-th sampling time. e i The response data of each degree of freedom in the structural finite element model are arranged into a sequence according to the sampling time, which is the response time history of each degree of freedom in the structural finite element model; similarly, the equivalent load of each degree of freedom in the structural finite element model is arranged into a sequence according to the sampling time, which is the equivalent load time history of each degree of freedom in the structural finite element model.

[0163] The response time history includes the displacement, velocity, acceleration, and internal force calculated for each degree of freedom in the structural finite element model over at least one sampling time; specifically:

[0164] In the finite element model of the structure, the displacement of any degree of freedom at the i-th sampling time is X. i Speed ​​is acceleration is And internal force is F s iWhere the displacement at the 0th sampling time is X0 = 0 and the velocity is acceleration is And internal force is F s 0 =0;

[0165] The equivalent load time history includes the equivalent load calculated for each degree of freedom in the structural finite element model at at least one sampling time; specifically:

[0166] In the finite element model of the structure, the equivalent load of any degree of freedom at the i-th sampling time is R. i .

[0167] In this embodiment, the time history analysis method is a time-domain method that discretizes time into individual time points, such as 0.02s, and then updates the dynamic load and dynamic stiffness of the structure at each time point. The response at the next time point is obtained by solving the static problem at each time point, so it is also called the stepwise integration method.

[0168] In this embodiment, the stiffness matrix and mass matrix of the structural finite element model can be obtained using a self-written Python program, OpenSees' "Two Node Link" and "Nonlinear Beam Column" elements, etc.

[0169] In this embodiment, Rayleigh damping is used as the damping matrix to simplify the data processing. Currently, there is no highly accurate method to determine the damping matrix of a structure; ignoring the influence of mass on damping, obtaining Rayleigh damping from the stiffness matrix, and approximating Rayleigh damping as the structure's damping matrix is ​​a common practice in engineering. Rayleigh damping is simple and convenient, and therefore widely used in structural dynamic analysis. Rayleigh damping assumes that the damping matrix of a structure is a combination of the mass matrix and the stiffness matrix. The mode shapes of the structure are orthogonal to the mass matrix and stiffness matrix. It is easy to see that a linear combination of the mass matrix and stiffness matrix must satisfy the orthogonality condition; therefore, Rayleigh damping is an orthogonal damping.

[0170] In this embodiment, the structural motion differential equation can be expressed as: Where m is the mass matrix of the finite element model of the structure, c is the damping matrix of the finite element model of the structure, and k is the stiffness matrix of the finite element model of the structure. This is a column vector consisting of the acceleration of each degree of freedom in the finite element model of the structure at each sampling time. Let X be a column vector representing the velocity of each degree of freedom in the finite element model of the structure at each sampling time, and let p(t) represent the external load, which is related to the time history of the seismic motion as the external excitation. The This is a column vector consisting of the ground motion accelerations at each sampling time in the ground motion time history, which serves as the external excitation. Additionally, in nonlinear cases, F is often used. s Replace kX.

[0171] In this embodiment, the Newmark-β method is a numerical integration method used to solve certain differential equations.

[0172] In this embodiment, the Newton iteration method is a common approach. Its calculation process roughly involves iteratively eliminating unbalanced forces (i.e., the equivalent load at the current moment) using tangent stiffness, obtaining displacement increments, and ultimately approximating the true solution (i.e., the true displacement value of each degree of freedom of the structure at the current moment). Specifically, by setting an equivalent load limit, the equivalent load at the current moment is continuously consumed until it approaches this limit. When the equivalent load at the current moment is consumed to be equal to or less than the equivalent load limit, the displacement value obtained through iteration is considered approximately equal to the true displacement value of each degree of freedom of the structure. Sometimes, the Newton iteration method may fail to converge; that is, no matter how many iterations are performed, the equivalent load at the current moment cannot be consumed to be equal to or less than the equivalent load limit. In this case, an iteration count can be set. Once a sufficient number of iterations is reached, the displacement value obtained through iteration is considered approximately equal to the true displacement value of each degree of freedom of the structure. In a further embodiment, an improved Newton iteration method can be used instead of the original Newton iteration method. The improved Newton iteration method is more stable and less prone to solution failure, but its computational efficiency is relatively low.

[0173] In this embodiment, due to the presence of static load, F S 0 The value at sampling time 0 is not necessarily 0. The internal force value of the initial state can be exported from the finite element method software as F. S 0 Alternatively, 0 can be directly used as F. S 0 ; Treat 0 as F s 0 At this time, it is equivalent to embedding the internal forces caused by static loads into the neural network model; two types of F s 0 The way the value is chosen has little impact on the result.

[0174] Implementation Method 4: Combination Figure 1 This embodiment further defines step 3 of the modeling method for calculating the seismic response of a structure using a cascaded neural network, as described in Embodiment 3. The specific implementation details are as follows:

[0175] Step 3.1: Take any seismic acceleration time history, the corresponding response time history and equivalent load time history obtained when it is used as an external excitation, as a slice data source;

[0176] Step 3.2: Divide all slice data sources into at least two groups, one group for training data sources and the other group for validation data sources;

[0177] Step 3.3: Using data slicing method one, slice the data sources in the training data source group to obtain the pre-training set, as follows:

[0178] Step 3.3.1: Select any slice data source from the group of data sources used for training;

[0179] Step 3.3.2: In any of the slice data sources, select the seismic acceleration at the i-th sampling time. And the internal force F of any degree of freedom in the finite element model of the structure at the (i-1)th sampling time. s i-1 and speed F is the modeling data feature of any degree of freedom in the structural finite element model described in the pre-training set at the i-th sampling time. q i , is represented as:

[0180]

[0181] In any of the same slice data sources, select the equivalent load R of any degree of freedom in the structural finite element model at the i-th sampling time. i L serves as the modeling data label for any degree of freedom in the structural finite element model described in the pre-training set at the i-th sampling time. q i , is represented as:

[0182] L q i =R i ;

[0183] Step 3.3.3: In the pre-training set, the modeling data feature F of any degree of freedom in the structural finite element model at the i-th sampling time. q i and modeling data labels L q iThe data pairs formed are used as modeling data items for any degree of freedom in the structural finite element model in the pre-training set at the i-th sampling time.

[0184] Based on all slice data sources in the training data source group, obtain the modeling data items for all degrees of freedom in the structural finite element model in the pre-training set at the i-th sampling time;

[0185] The single-column matrix composed of the modeling data items of all degrees of freedom in the structural finite element model in the pre-training set at the i-th sampling time is used as the modeling data list of the structural finite element model in the pre-training set at the i-th sampling time.

[0186] The modeling data time series of the structural finite element model at all sampling times in the pre-training set, arranged in the order of sampling time, shall be the modeling data time series of the pre-training set; the data series composed of all the modeling data time series of the pre-training set in the training data source group, arranged in order, shall be the pre-training set.

[0187] Step 3.4: Using data slicing method two, slice the data sources in the training data source group to obtain the post-training set, as follows:

[0188] Step 3.4.1: Select any slice data source from the group of data sources used for training;

[0189] Step 3.4.2: In any of the slice data sources, select the equivalent load R of any degree of freedom in the structural finite element model at the i-th sampling time. i And the internal force F of any degree of freedom in the finite element model of the structure at the (i-1)th sampling time. s i-1 and displacement X i-1 F, as the modeling data feature F of any degree of freedom in the structural finite element model in the post-training set at the i-th sampling time. h i , is represented as:

[0190]

[0191] In any of the same slice data sources, select the pre-defined target equivalent load R. ε And the internal force F of any degree of freedom in the finite element model of the structure at the i-th sampling time. s i and displacement X i L serves as the modeling data label for any degree of freedom in the structural finite element model described in the post-training set at the i-th sampling time. hi , is represented as:

[0192]

[0193] Step 3.4.3: In the post-training set, the modeling data features F of any degree of freedom of the structural finite element model at the i-th sampling time are... h i and modeling data labels L h i The data pairs formed are used as modeling data items for any degree of freedom in the structural finite element model in the post-training set at the i-th sampling time.

[0194] Based on all slice data sources in the training data source group, obtain the modeling data items for all degrees of freedom in the structural finite element model in the post-training set at the i-th sampling time;

[0195] The single-column matrix consisting of the modeling data items of all degrees of freedom in the structural finite element model at the i-th sampling time in the post-training set will be used as the modeling data list of the structural finite element model at the i-th sampling time in the post-training set.

[0196] In the post-training set, the data sequence formed by arranging the modeling data list of the structural finite element model at all sampling times in the order of sampling time is used as the modeling data time history of the post-training set; in the training data source group, the data sequence formed by arranging all the modeling data time histories of the post-training set in order is the post-training set.

[0197] Step 3.5: Using data slicing method three, slice the data sources in the validation data source group to obtain the validation set, as follows:

[0198] Step 3.5.1: Select any slice data source from the data source group for verification;

[0199] Step 3.5.2: In any of the slice data sources, select the seismic acceleration at the i-th sampling time. F is the modeling data feature of any degree of freedom in the structural finite element model in the validation set at the i-th sampling time. y i , is represented as:

[0200]

[0201] In the same slice data source, select the internal force F of any degree of freedom in the structural finite element model at the i-th sampling time. s i Displacement Xi ,speed and acceleration L serves as the modeling data label for any degree of freedom in the structural finite element model described in the validation set at the i-th sampling time. y i , is represented as:

[0202]

[0203] Step 3.5.3: In the verification set, the modeling data feature F of any degree of freedom in the structural finite element model at the i-th sampling time is... q i and modeling data labels L q i The data pairs formed are used as modeling data items for any degree of freedom in the structural finite element model in the verification set at the i-th sampling time.

[0204] Based on all slice data sources in the verification data source group, obtain the modeling data items for all degrees of freedom in the structural finite element model in the verification set at the i-th sampling time;

[0205] The single-column matrix composed of the modeling data items of all degrees of freedom in the structural finite element model at the i-th sampling time in the verification set will be used as the modeling data list of the structural finite element model at the i-th sampling time in the verification set.

[0206] In the validation set, the modeling data list of the structural finite element model at all sampling times, arranged in order of sampling time, is used as the modeling data time history of the validation set; in the validation data source group, the data sequence composed of all the modeling data time histories of the validation set arranged in order is the validation set.

[0207] In this embodiment, the data slicing involves dividing the time-series data into segments and combining the inputs (features) and outputs (labels) according to the requirements of training the neural network. This allows the neural network to be trained using these data, facilitating the learning of the relationship between the inputs (features) and the outputs (labels).

[0208] Implementation Method 5: Combination Figure 1 This embodiment describes step 4 of the modeling method for calculating the seismic response of a structure using a cascaded neural network, as described in Embodiment 4. The specific implementation details are as follows:

[0209] Step 4 is as follows:

[0210] Step 4.1: The initial cascaded neural network model includes a pre-neural network model and a post-neural network model, wherein the post-neural network model adopts a residual neural network;

[0211] Step 4.2: Based on the finite element model of the structure, determine the construction parameters of the pre-neural network model and the post-neural network model respectively. The construction parameters include the model type, the number of network layers of the model, the number of neurons in each network layer, and the adjustable hyperparameters of the model.

[0212] Step 4.3: The training parameters include pre-training parameters and post-training parameters; the value range of the training parameters is the value range of the pre-training parameters and the value range of the post-training parameters; the pre-training parameters and their value range are determined based on the pre-neural network model construction parameters; the post-training parameters and their value range are determined based on the post-neural network model construction parameters.

[0213] Step 4.4: Obtain all possible combinations of values ​​for the pre-training parameters and the post-training parameters, and construct the pre-neural network model and the post-neural network model in the corresponding initial concatenated neural network model based on each combination of values ​​and the construction parameters.

[0214] In this embodiment, the model type in the construction parameters refers to the category of the pre-processor neural network model and the post-processor neural network model. The pre-processor neural network model can be any type of neural network. For example, the simplest and most classic neural network is the Multi-Layer Perception (MLP). The most typical MLP includes a three-layer structure: an input layer, a hidden layer, and an output layer. The different layers of the MLP neural network are fully connected (fully connected: any neuron in the previous layer is connected to all neurons in the next layer).

[0215] In this embodiment, the type of the post-processor neural network model is a residual neural network. The use of a residual network in the post-processor neural network model is to simulate the step-by-step iteration of an iterative algorithm through the progressive computation of the residual network, thereby enhancing the physical interpretability of the cascaded neural network model. The residual network is a convolutional neural network proposed by four scholars from Microsoft Research, which won the image classification and object recognition categories in the 2015 ImageNet Large Scale Visual Recognition Challenge (ILSVRC). Residual networks are characterized by their ease of optimization and the ability to improve accuracy by significantly increasing their depth. The residual blocks within them use skip connections, mitigating the gradient vanishing problem that arises when increasing depth in deep neural networks.

[0216] In this embodiment, the number of network layers and the number of neurons in each network layer are the main parameters of the neural network architecture. In a neural network, the larger the number of network layers and the number of neurons per layer, the stronger the learning ability of the neural network. However, the training difficulty also increases, and the training speed slows down. The optimal number of network layers and the number of neurons per layer need to be determined through actual testing.

[0217] For the pre-neighborhood neural network model, testing showed that 5 layers are sufficient. The number of neurons in each layer of the pre-neighborhood neural network model is related to the number of degrees of freedom (Nubs) in the finite element model of the structure. Generally speaking, for a 5-layer pre-neighborhood neural network model, the number of neurons in each layer should be 4×Nubs, 7×Nubs, 10×Nubs, 7×Nubs, and 4×Nubs respectively. When these conditions are met, the learning ability of the pre-neighborhood neural network model can meet the requirements.

[0218] For the post-negative neural network model, which is formed by residual connections of multiple neural network blocks (i.e., residual neural network), testing shows that 4 layers are sufficient for each neural network block (residual block). The number of neurons in each layer of each neural network block (residual block) is related to the number of degrees of freedom (Nubs) in the finite element model of the structure. Generally speaking, for each 4-layer neural network block (residual block), the number of neurons in each layer is 4×Nubs, 8×Nubs, 8×Nubs, and 4×Nubs respectively. When this is the case, the learning ability of the post-negative neural network model can meet the requirements.

[0219] Both the pre-processor neural network model and the post-processor neural network model have adjustable hyperparameters. Different values ​​of these adjustable hyperparameters result in different computational performances. Choosing appropriate adjustable hyperparameters affects the accuracy of the model's computation or prediction. The optimal adjustable hyperparameters can be verified using a validation set. The process is roughly as follows: select some adjustable hyperparameters as training parameters and determine the value range of each training parameter; then construct the corresponding neural network model based on all combinations of training parameter values; next, validate each neural network model using a validation set and evaluate its prediction accuracy using various metrics; the training parameters corresponding to the neural network model with the highest overall prediction accuracy are the optimal adjustable hyperparameters, and the corresponding neural network model is the optimal neural network model. In this process, selecting more adjustable hyperparameters as training parameters leads to more accurate predictions or computations in the resulting optimal neural network model, but the validation process becomes more time-consuming and inefficient. This embodiment includes both a pre-processor neural network model and a post-processor neural network model, both of which require validation. Selecting too many adjustable hyperparameters as training parameters will result in excessively low training and validation efficiency for the entire cascaded neural network. Testing revealed that adjustable hyperparameters other than the learning rate have a relatively small impact on the prediction or computation results, while the learning rate has a significant impact. Therefore, the adjustable hyperparameters can be set to their default values, and only the learning rate in the pre-neural network model and the post-neural network model should be used as training parameters.

[0220] In a further implementation, the learning rate Lr1 of the pre-neighborhood model is selected as the pre-training parameter, with a value range of (0.0005, 0.001, 0.0025, 0.005, 0.0075, 0.01, 0.025, 0.05); and the learning rate Lr2 of the post-neighborhood model is selected as the post-training parameter, with a value range of (0.0005, 0.001, 0.0025, 0.005, 0.0075, 0.01, 0.025, 0.05). All combinations of Lr1 and Lr2 values ​​are enumerated (a total of 8×8=64 cases), and based on each combination and other construction parameters, the pre-neighborhood model and post-neighborhood model in the corresponding initial concatenated neural network model are constructed.

[0221] Implementation Method Six: Combination Figure 1 This embodiment describes step 5 of the modeling method for calculating the seismic response of a structure using a cascaded neural network, as described in Embodiment 5. The specific implementation details are as follows:

[0222] Step 5 is described in detail below:

[0223] Step 5.1: Train the pre-network in each of the initial cascaded neural network models using the pre-training set to obtain the trained pre-network model; the trained pre-network model is used to simulate the time history analysis method, based on the ground motion acceleration at the i-th sampling time. Calculate the equivalent load R for each degree of freedom in the finite element model of the structure at the i-th sampling time. i ;

[0224] More specifically, in step 5.1, during the training step at the i-th sampling time:

[0225] Step 5.1.1: Model the data features F of the pre-training set. q i In F s i-1 as well as Perform data normalization, where when i = 1, the F s i-1 =F s 0 =0, and

[0226] Step 5.1.2: Normalize the data. F s i-1 as well as As the input to the preceding neural network model, the output of the preceding neural network model is the equivalent load calculation value of any degree of freedom in the structural finite element model at the i-th sampling time.

[0227] Step 5.1.3: Calculate the equivalent load value. The training objective of the preceding neural network model is to perform inverse data normalization, so that the equivalent load calculation value after inverse data normalization is... The modeling data label L of the pre-training set is gradually approximated. q i R in i ;

[0228] Step 5.1.4: Based on the pre-training set, and with the training objective of the pre-training neural network model as the target, train the pre-training neural network model until the number of training iterations reaches the preset number of pre-training iterations, at which point the training of the pre-training neural network model is complete.

[0229] Step 5.2: Train the post-neural network in each of the initial cascaded neural network models using the post-training set to obtain the trained post-neural network model; the trained post-neural network model is used to simulate the time history analysis method, based on the equivalent load R of each degree of freedom in the structural finite element model at the i-th sampling time. i Calculate the displacement X of each degree of freedom in the finite element model of the structure at the i-th sampling time. i ,speed acceleration and internal force F s i ;

[0230] More specifically, in step 5.2, during the training step at the i-th sampling time:

[0231] Step 5.2.1: Model the data features F of the post-training set. h i R in i F s i-1 and X i-1 Perform data normalization, where when i = 1, the F s i-1 =F s 0 =0, and X i-1 =X0=0;

[0232] Step 5.2.2: Normalize the data and then apply the resulting R... i F s i-1 and X i-1 As the input to the post-neural network model, the output of the post-neural network model is the calculated internal force value of any degree of freedom in the structural finite element model at the i-th sampling time. Displacement calculation value and residual equivalent load

[0233] Step 5.2.3: Calculate the internal force values. Displacement calculation value and residual equivalent load The data undergoes inverse normalization, and the training objective of the post-neural network model is to make the calculated internal force values ​​after inverse normalization of the data... Displacement calculation value and residual equivalent load The modeling data labels L of the preceding and following training sets are gradually approximated. h i F in s i Xi and R ε ;

[0234] Step 5.2.4: Based on the post-training set, and with the training objective of the post-neural network model as the target, train the post-neural network model until the number of training iterations reaches the preset number of post-training iterations, at which point the training of the post-neural network model is complete.

[0235] In this embodiment, data normalization is a fundamental task in data preprocessing. Different evaluation indicators often have different dimensions and units. To avoid affecting the data analysis results and eliminate the influence of dimensions between indicators, data must be standardized. Data normalization scales the data proportionally to fit it into a small, specific interval, removes unit restrictions, and transforms it into dimensionless pure numerical values. This facilitates comparison and weighting of indicators with different units or magnitudes, accelerating the convergence of neural network training. The most typical method of data normalization is to uniformly map the data to the interval [0, 1].

[0236] In this embodiment, the inverse data normalization is a technique corresponding to data normalization. When building and training a neural network, data normalization is usually required to facilitate network training. Conversely, data inverse normalization is typically needed for visualizing training results. This is because training results are physical quantities, and using normalized representations makes it difficult to understand their physical meaning. Inverse normalization, followed by calculations in other steps, makes the entire process more physically interpretable.

[0237] In this embodiment, the preceding neural network model is used to obtain the equivalent load of any degree of freedom in the structural finite element model at the current moment based on the current seismic acceleration and the velocity and internal force of any degree of freedom in the structural finite element model at previous moments. The time history analysis method (i.e., the step-by-step integration method) also has a corresponding calculation step for calculating the equivalent load at the current moment; however, in the time history analysis method, the equivalent load is calculated based on the seismic acceleration, internal force, velocity, and acceleration. The preceding neural network model does not use acceleration as a parameter because using acceleration as a parameter would significantly affect the computational efficiency of the preceding neural network model, while not using acceleration has little impact on the computational accuracy of the preceding neural network model.

[0238] In this embodiment, the post-neighborhood model is used to obtain the internal forces and displacements of any degree of freedom of the structural finite element model at the current moment based on the equivalent load at the current moment. The general method is to iteratively consume the equivalent load to make it approximate a small target value, or to iterate a sufficient number of times to obtain a high-precision approximate solution for the true values ​​of internal forces and displacements. Because it is an approximation algorithm, there is still a slight error. Therefore, the equivalent load cannot be completely converted to zero; there will still be a small residual equivalent load. However, as long as the residual equivalent load is less than the pre-set target value, or the number of iterations is sufficient, the error of the high-precision approximate solution can be considered very small and acceptable, not affecting the final result.

[0239] In a further embodiment, the preceding neural network model includes a symmetry correction step when calculating equivalent loads and displacements. This symmetry correction typically involves inputting a certain input parameter and its opposite value into the neural network model, then averaging the two outputs to obtain the corrected output value. The purpose of this symmetry correction is to average the error of a calculated value to avoid excessively large errors. For example, a formula can be used... To perform symmetry correction on the equivalent load calculation values ​​output in the preceding neural network model, where MLP... 0 This represents the front-end neural network model.

[0240] Implementation Method Seven: Combination Figure 1 This embodiment describes step 6 of the modeling method for calculating the seismic response of a structure using a cascaded neural network, as described in Embodiment 6. The specific implementation details are as follows:

[0241] Step 6 is as follows:

[0242] Step 6.1: In each of the trained concatenated neural network models, the equivalent load R of the output of the trained pre-neural network model at the i-th sampling time is... i And the displacement X of each degree of freedom in the finite element model of the structure at the (i-1)th sampling time. i-1 and internal force F s i-1 , which serves as the input to the trained post-neural network model at the i-th sampling time;

[0243] Step 6.2: In each of the trained cascaded neural network models, add a velocity and acceleration calculation module, and calculate the displacement value of any degree of freedom in the structural finite element model output by the trained post-neural network model at the i-th sampling time. As input to the velocity and acceleration calculation module;

[0244] The velocity and acceleration calculation module is used to calculate the displacement value of each degree of freedom in the structural finite element model at the i-th sampling time. and the displacement calculation value at the (i-1)th sampling time and calculated speed values Obtain the velocity calculation value of each degree of freedom in the finite element model of the structure at the i-th sampling time. Where, when i = 1, the

[0245] The velocity and acceleration calculation module is also used to calculate the velocity value of each degree of freedom in the structural finite element model at the i-th sampling time. And the calculated velocity value at the (i-1)th sampling time and acceleration calculation value Obtain the calculated acceleration value for each degree of freedom in the finite element model of the structure at the i-th sampling time. Where, when i = 1, the

[0246] Step 6.3: In each of the trained concatenated neural network models:

[0247] The input of the pre-trained neural network model is used as the input of each post-trained cascaded neural network model; the output of the post-trained neural network model and the velocity and acceleration calculation module are used as the output of each post-trained cascaded neural network model; after the structure of each post-trained cascaded neural network model is adjusted, the corresponding cascaded neural network model to be verified is obtained.

[0248] In this embodiment, the velocity and acceleration calculation module uses the following formula: And the formula: Calculate the velocity value and acceleration calculation value In this embodiment, the data processing process of the serial neural network model to be verified is similar to the calculation process of time history analysis (i.e., stepwise integration method), that is, the serial neural network model to be verified simulates the time history analysis method (i.e., stepwise integration method). The calculation steps of the time history analysis method (i.e., stepwise integration method) are as described in step 2.5 of embodiment three. The main steps are: (1) Calculate the equivalent load at the current moment using the displacement, acceleration, internal force at the current moment and the seismic acceleration at the next moment; (2) Calculate the displacement and internal force at the current moment according to the equivalent load at the current moment through an iterative algorithm; (3) Further calculate the velocity and acceleration at the current moment; (4) Repeat the above steps to calculate the structural response at each moment, and the response time history can be obtained.

[0249] In this embodiment, the data processing of the pre-neighborhood model simulates the calculation step in the stepwise integration method of "calculating the equivalent load at the current moment using the displacement, acceleration, internal force, and seismic acceleration at the next moment." However, the pre-neighborhood model does not use acceleration as a parameter to calculate the equivalent load, which, although sacrificing some accuracy (within an acceptable range), significantly improves efficiency. The data processing of the post-neighborhood model simulates the calculation step in the stepwise integration method of "calculating the displacement and internal force at the current moment based on the equivalent load at the current moment using an iterative algorithm." The data processing of the velocity and acceleration calculation module simulates the calculation step in the stepwise integration method of "further calculating the velocity and acceleration at the current moment." The serial neural network model to be verified superimposed an autoregressive mechanism, meaning that the serial neural network model to be verified calculates the data at the current moment based on the data from the previous moment, thus simulating the step in the stepwise integration method of "repeating the above steps to calculate the structural response at each moment to obtain the response time history."

[0250] Implementation Method 8: Combination Figure 1 This embodiment further defines step 7 of the modeling method for calculating the seismic response of a structure using a cascaded neural network, as described in Embodiment 7. The specific implementation details are as follows:

[0251] Step 7 is described in detail below:

[0252] Step 7: Using the validation set, simulate the time history analysis method to validate each of the serial neural network models to be validated, so as to obtain the optimal serial neural network model; the optimal serial neural network model is used to simulate the time history analysis method, and calculate the displacement, velocity, acceleration and internal force of each degree of freedom in the structural finite element model at the same sampling time based on the ground motion acceleration at any sampling time.

[0253] Step 7.1: In the verification set, select the modeling data feature F of any degree of freedom in the structural finite element model corresponding to any slice data source at the i-th sampling time. y i , which serves as the input to each of the aforementioned concatenated neural network models to be verified;

[0254] Step 7.2: For each of the concatenated neural network models to be verified, based on the input modeling data features F... y i Calculate the internal force values Displacement calculation value Calculated speed value And acceleration calculation values

[0255] Based on the internal force calculation values ​​of each of the aforementioned serial neural network models to be verified at all sampling times. Displacement calculation value Calculated speed value And acceleration calculation values Obtain the response time history calculation result corresponding to any one of the slice data sources;

[0256] Step 7.3: Compare the response time history calculation result with the data recorded in the modeling data label in any slice data source; and calculate the evaluation index for each of the concatenated neural network models to be verified based on the comparison result. The evaluation index is used to evaluate the calculation effect of the concatenated neural network model to be verified.

[0257] Step 7.4: Based on the evaluation index, obtain the performance ranking of each of the concatenated neural network models to be verified when verifying any slice data source in the verification set, according to the calculation effect from best to worst; wherein, the better the calculation effect, the lower the performance ranking.

[0258] Step 7.5: For each of the concatenated neural network models to be verified, sum the performance rankings when verifying all slice data sources in the verification set to obtain a comprehensive performance ranking; the concatenated neural network model with the smallest comprehensive performance ranking is the optimal concatenated neural network model.

[0259] In this embodiment, the modeling data feature F mentioned in step 7.2 y i That is, the ground motion acceleration at the i-th sampling time. The calculation steps in step 7.2 simulate the time history analysis method, as follows:

[0260] Step 7.2.1: Measure the ground motion acceleration at the i-th sampling time. Perform data normalization;

[0261] Based on the data normalization And the calculated velocity value of any degree of freedom in the finite element model of the structure at the (i-1)th sampling time. and internal force calculation values The equivalent load calculated at the i-th sampling time for any degree of freedom in the finite element model of the structure is obtained by using the preceding neural network model in the cascaded neural network model to be verified.

[0262] Where, when i = 1, the The

[0263] Step 7.2.2, according to And the calculated displacement value of any degree of freedom in the finite element model of the structure at the (i-1)th sampling time. The post-neural network model in the cascaded neural network model to be verified is used for calculation to obtain the internal force value of any degree of freedom in the structural finite element model at the i-th sampling time. and displacement calculation value

[0264] Where, when i = 1, the

[0265] Step 7.2.3, will And the calculated velocity value of any degree of freedom in the finite element model of the structure at the (i-1)th sampling time. Perform inverse data normalization;

[0266] Based on the data after inverse normalization as well as Formula used: Calculate the velocity value of any degree of freedom in the finite element model of the structure at the i-th sampling time. Where Δt is a time step, i.e., the reciprocal of the sampling frequency of the seismic acceleration time history. The value is the result of inverse normalization of the data;

[0267] Step 7.2.4: Calculate the acceleration value of any degree of freedom in the finite element model of the structure at the (i-1)th sampling time. Perform inverse data normalization;

[0268] Based on the data after inverse normalization as well as Formula used: Calculate the acceleration value of any degree of freedom in the finite element model of the structure at the i-th sampling time. Where, when i = 1, the

[0269] Here The value is the result of inverse normalization of the data;

[0270] Step 7.2.5, the aforementioned Perform data normalization for calculation at the (i+1)th sampling time.

[0271] Implementation Method Nine: Combination Figure 1 This embodiment further defines the modeling method for calculating the seismic response of structures using a cascaded neural network, as described in Embodiment Eight. The specific implementation details are as follows:

[0272] In step 3, a fourth modeling dataset, namely the test set, is also obtained; the test set is used to test the optimal concatenated neural network model to evaluate its prediction performance.

[0273] The process of testing the optimal cascaded neural network model using the test set is similar to the process of verifying the cascaded neural network model to be verified using the verification set.

[0274] In this embodiment, the test set is used to evaluate the computational performance of the optimal cascaded neural network model because the training set used to train the model is completely known data for the optimal cascaded neural network model; the validation set used for parameter adjustment is not directly used to train the model and is partially known data for the optimal cascaded neural network model; while the test set is completely unknown data for the optimal cascaded neural network model. Therefore, using the test set to evaluate the computational performance of the optimal cascaded neural network model yields the most objective conclusion.

[0275] In a further embodiment, a test set is used to conduct seismic response tests on the optimal tandem neural network model constructed based on three different structures to evaluate the calculation effect of the optimal tandem neural network model on the seismic response of the structure. The three different structures are a single-degree-of-freedom system, a lumped mass shear model system, and a two-dimensional frame system.

[0276] Tables 1-3 show the seismic response test results of the optimal tandem neural network model constructed based on three different structures. In the table, PSNN represents the optimal tandem neural network model, PGA represents peak ground acceleration, r represents the average correlation coefficient, RE represents the average relative error, and MAE represents the average mean absolute error. The calculation effect can be evaluated based on the average correlation coefficient r; the closer r is to 1, the better the calculation effect. As can be seen from the table, regardless of whether it is based on a single-degree-of-freedom architecture, a lumped mass shear model architecture, or a two-dimensional frame architecture, under all seismic ground acceleration time histories, the correlation coefficient r of the optimal tandem neural network model used to calculate the response time histories of the test set is above 0.9. This indicates that the optimal tandem neural network model described in this embodiment has high calculation accuracy and strong generalization ability, and can adapt to different structures or seismic ground acceleration time histories.

[0277] Table 1 shows the performance of PSNN based on a single-degree-of-freedom architecture on the test set.

[0278]

[0279]

[0280] Table 2 shows the performance of PSNN based on the lumped mass shearing model architecture on the test set.

[0281]

[0282] Table 3 shows the performance of PSNN based on the two-dimensional framework architecture on the test set.

[0283]

[0284] In a further embodiment, six different intensities of seismic ground acceleration time histories were used as external excitations for three different structures. The seismic responses of these three structures were then calculated using the optimal cascaded neural network model (PSNN), OpenSees combined with time history analysis, and a self-developed Python program combined with time history analysis, respectively. The three different structures were a single-degree-of-freedom system, a lumped-mass shear model system, and a two-dimensional frame system. The time taken to calculate the time history response using the three methods was statistically analyzed.

[0285] Table 4 shows the calculation times for the seismic responses of the three different structures using the optimal cascaded neural network model (PSNN), OpenSees combined with time history analysis, and a self-written Python program combined with time history analysis. Shorter calculation times indicate higher efficiency.

[0286] Table 4 shows the time (in seconds) for calculating the seismic response of three different structures using three different methods.

[0287]

[0288]

[0289] As shown in the table, the optimal tandem neural network model (PSNN) constructed based on single-degree-of-freedom systems or lumped-mass shear model systems takes a relatively long time to calculate the seismic response of the structure. For example, when using PGA 1 as the external excitation based on a single-degree-of-freedom system, the calculation time of the optimal tandem neural network model is 5082.2 seconds, while the calculation time using a self-written Python program combined with time history analysis is 2011.5 seconds. This is because the structures of single-degree-of-freedom systems and lumped-mass shear model systems are relatively simple and have low complexity, and the efficiency advantage of the optimal tandem neural network model has not yet been demonstrated in these cases.

[0290] However, as structural complexity increases, traditional calculation methods using OpenSees combined with time history analysis or self-written Python programs combined with time history analysis experience a corresponding increase in computation time. In contrast, the calculation method using the optimal serial neural network model (PSNN) for structural seismic response shows virtually no increase in computation time with increasing structural complexity. This means that the higher the structural complexity, the more computationally efficient the PSNN method becomes compared to traditional finite element model combined with time history analysis. As shown in the table, the PSNN model, built on a two-dimensional frame architecture, is approximately three times more efficient than the OpenSees method using time history analysis. For example, when using PGA 1 as the external excitation for a two-dimensional frame architecture, the PSNN model takes 5412.6 seconds, while the OpenSees method takes 17526.7 seconds. This is because the two-dimensional frame architecture has higher complexity, giving the PSNN a significant computational advantage. Therefore, the optimal cascaded neural network model (PSNN) is more suitable for calculating the seismic response of highly complex structures.

[0291] Implementation Method 10: Combination Figure 1 This embodiment describes a modeling apparatus for calculating a cascaded neural network model of structural seismic response. The specific implementation details are as follows:

[0292] The device specifically includes:

[0293] Module 1 is used to establish a structural finite element model, wherein the structural finite element model contains at least one degree of freedom;

[0294] Module 2 is used to calculate the response time history and equivalent load time history of the finite element model of the structure when any seismic acceleration time history in the pre-acquired seismic acceleration record is used as the external excitation, using the time history analysis method.

[0295] Module 3 is used to group the seismic acceleration time history, the response time history, and the equivalent load time history and then perform data slicing to obtain at least 3 sets of modeling datasets, namely, the pre-training set, the post-training set, and the validation set.

[0296] Module 4 is used to determine the architecture, training parameters, and value range of the initial concatenated neural network model, and to construct at least one initial concatenated neural network model based on the architecture, training parameters, and value range of the training parameters.

[0297] Module 5 is used to train each of the initial concatenated neural network models using the pre-training set and the post-training set to obtain the corresponding post-trained concatenated neural network model.

[0298] Module 6 is used to simulate the calculation process of time history analysis, adjust the structure of each trained cascaded neural network model, and obtain the cascaded neural network model to be verified. The cascaded neural network model to be verified is used to use an autoregressive mechanism to calculate the displacement, velocity, acceleration and internal force of each degree of freedom in the finite element model of the structure at the same sampling time based on the ground motion acceleration at any sampling time.

[0299] Module 7 is used to verify each of the concatenated neural network models to be verified using the verification set, so as to obtain the optimal concatenated neural network model.

[0300] In this embodiment, the modeling device for calculating the cascaded neural network model of the structural seismic response is used to implement the modeling method for calculating the cascaded neural network model of the structural seismic response described in Embodiment 1.

[0301] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, reasonable combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A modeling method for a cascaded neural network model to calculate the seismic response of a structure, characterized in that, The method specifically includes: Step 1: Establish a structural finite element model, wherein the structural finite element model contains at least one degree of freedom; Step 2: Using time history analysis, calculate the response time history and equivalent load time history of the finite element model of the structure when any seismic acceleration time history in the pre-acquired seismic acceleration record is used as the external excitation. Step 3: After grouping the earthquake acceleration time history, the response time history, and the equivalent load time history, perform data slicing to obtain at least 3 sets of modeling datasets, namely the pre-training set, the post-training set, and the validation set. Step 4: Determine the architecture, training parameters, and value range of the initial cascaded neural network model, and construct at least one initial cascaded neural network model based on the architecture, training parameters, and value range of the training parameters. Step 5: Using the pre-training set and the post-training set, train each of the initial concatenated neural network models to obtain the corresponding post-trained concatenated neural network models. Step 5 is described in detail below: Step 5.1: Train the pre-network in each of the initial cascaded neural network models using the pre-training set to obtain the trained pre-network model; the trained pre-network model is used to simulate the time history analysis method, according to the... i Seismic acceleration during sampling time Calculate the degree of freedom of each degree of freedom in the finite element model of the structure at the 1st... i Equivalent load of sampling time ; Step 5.2: Train the post-neural network in each of the initial cascaded neural network models using the post-training set to obtain the trained post-neural network model; the trained post-neural network model is used to simulate the time history analysis method, based on each degree of freedom in the structural finite element model at the 1st... i Equivalent load of sampling time Calculate the degree of freedom of each degree of freedom in the finite element model of the structure at the 1st... i Displacement of sampling time ,speed acceleration and internal strength ; Step 6: Simulate the calculation process of time history analysis, adjust the structure of each trained cascaded neural network model, and obtain the cascaded neural network model to be verified; the cascaded neural network model to be verified is used to calculate the displacement, velocity, acceleration and internal force of each degree of freedom in the finite element model of the structure at the same sampling time based on the ground motion acceleration at any sampling time using an autoregressive mechanism. Step 7: Using the validation set, validate each of the serial neural network models to be validated to obtain the optimal serial neural network model.

2. The modeling method for calculating the seismic response of a structure using a cascaded neural network model according to claim 1, characterized in that, The pre-acquired seismic acceleration records in step 2 are as follows: The pre-acquired seismic acceleration records contain at least two seismic acceleration time histories with the same sampling frequency; The seismic acceleration time history is a data sequence composed of at least one seismic acceleration arranged in chronological order of sampling time; the seismic acceleration time history includes seismic accelerations sampled at least at one sampling time. In any given seismic acceleration time history, the first... i The ground motion acceleration during the sampling time is expressed as: ,in i It is a positive integer greater than 1.

3. The modeling method for calculating the seismic response of a structure using a cascaded neural network model according to claim 2, characterized in that, In step 2: The response time history includes the displacement, velocity, acceleration, and internal force calculated for each degree of freedom in the structural finite element model over at least one sampling time; specifically: In the structural finite element model, any degree of freedom at the 1st... i The displacement of the sampling time is Speed ​​is acceleration is and internal force The displacement at the 0th sampling time is =0, speed is =0, acceleration is =0, and internal force is =0; The equivalent load time history includes the equivalent load calculated for each degree of freedom in the structural finite element model at at least one sampling time; specifically: In the structural finite element model, any degree of freedom at the 1st... i The equivalent load of sampling time is .

4. The modeling method for calculating the seismic response of a structure using a cascaded neural network model according to claim 3, characterized in that, Step 3 is as follows: Step 3.1: Take any seismic acceleration time history, the corresponding response time history and equivalent load time history obtained when it is used as an external excitation, as a slice data source; Step 3.2: Divide all slice data sources into at least two groups, one group for training data sources and the other group for validation data sources; Step 3.3: Using data slicing method one, slice the data sources in the training data source group to obtain the pre-training set. In the pre-training set: Corresponding to any slice data source, any degree of freedom in the structural finite element model at the th... i Modeling data features of sampling time F q i , is represented as: F q i = ； Corresponding to any of the same slice data sources, any degree of freedom in the structural finite element model at the th... i Modeling data labels for sampling time L q i , is represented as: L q i = ； Step 3.4: Using data slicing method two, slice the data sources in the training data source group to obtain the post-training set. In the post-training set: Corresponding to any slice data source, any degree of freedom in the structural finite element model at the th... i Modeling data features of sampling time F h i , is represented as: F h i = ； Corresponding to any of the same slice data sources, any degree of freedom in the structural finite element model at the th... i Modeling data labels for sampling time L h i , is represented as: h i = ;in, The pre-defined target equivalent load; Step 3.5: Using data slicing method three, slice the data sources in the verification data source group to obtain a verification set. In the verification set: Corresponding to any slice data source, any degree of freedom in the structural finite element model at the th... i Modeling data features of sampling time F y i , is represented as: F y i = ； Corresponding to any of the same slice data sources, any degree of freedom in the structural finite element model at the th... i Modeling data labels for sampling time L y i , is represented as: L y i = 。 5. The modeling method for calculating the seismic response of a structure using a cascaded neural network model according to claim 4, characterized in that, Step 4 is as follows: Step 4.1: The initial cascaded neural network model includes a pre-neural network model and a post-neural network model, wherein the post-neural network model adopts a residual neural network; Step 4.2: Based on the finite element model of the structure, determine the construction parameters of the pre-neural network model and the post-neural network model respectively. The construction parameters include the model type, the number of network layers of the model, the number of neurons in each network layer, and the adjustable hyperparameters of the model. Step 4.3: The training parameters include pre-training parameters and post-training parameters; the value range of the training parameters is the value range of the pre-training parameters and the value range of the post-training parameters. Determine the pre-training parameters of the pre-neural network model, and the range of values ​​for the pre-training parameters; Determine the post-training parameters of the post-neural network model, and the range of values ​​for the post-training parameters; Step 4.4: Obtain all possible combinations of values ​​for the pre-training parameters and the post-training parameters, and construct the pre-neural network model and the post-neural network model in the corresponding initial concatenated neural network model based on each combination of values ​​and the construction parameters.

6. The modeling method for calculating the seismic response of a structure using a cascaded neural network model according to claim 5, characterized in that, Step 6 is as follows: Step 6.1: In each of the trained concatenated neural network models, the output of the trained pre-neural network model at the i-th sampling time is... And each degree of freedom in the finite element model of the structure at the 1st i- Displacement at sampling time 1 and internal strength As the trained post-neural network model in the first... i Input of sampling time; Step 6.2: In each of the trained cascaded neural network models, add a velocity and acceleration calculation module, and calculate any degree of freedom in the structural finite element model output by the trained post-neural network model in the 1st... i Displacement calculation value at sampling time , as the input to the velocity and acceleration calculation module; The velocity and acceleration calculation module is used to calculate the velocity and acceleration based on each degree of freedom in the structural finite element model at the 1st... i Displacement calculation value at sampling time and in the i- Displacement calculation value at sampling time 1 and calculated speed values To obtain the degree of freedom of each of the structural finite element models in the 1st... i Calculated value of sampling time speed , among which, when i When =1, the = =0, = =0; The velocity and acceleration calculation module is also used to calculate the velocity and acceleration based on each degree of freedom in the structural finite element model at the 1st... i Calculated value of sampling time speed and in the i -1 Sampling time velocity calculation value and acceleration calculation value To obtain the degree of freedom of each of the structural finite element models in the 1st... i Acceleration calculation value at sampling time , among which, when i When =1, the = =0; Step 6.3: In each of the trained concatenated neural network models: The input of the pre-trained neural network model is used as the input of each post-trained cascaded neural network model; the output of the post-trained neural network model and the velocity and acceleration calculation module are used as the output of each post-trained cascaded neural network model; after the structure of each post-trained cascaded neural network model is adjusted, the corresponding cascaded neural network model to be verified is obtained.

7. The modeling method for calculating the seismic response of a structure using a cascaded neural network model according to claim 6, characterized in that, Step 7 is described in detail below: Step 7: Using the validation set, simulate the time history analysis method to validate each of the serial neural network models to be validated, so as to obtain the optimal serial neural network model; the optimal serial neural network model is used to simulate the time history analysis method, and calculate the displacement, velocity, acceleration and internal force of each degree of freedom in the structural finite element model at the same sampling time based on the ground motion acceleration at any sampling time; Step 7.1: In the verification set, select any degree of freedom in the structural finite element model corresponding to any slice data source in the [missing information - likely a specific step or step]. i Modeling data features of sampling time F y i , which serves as the input to each of the aforementioned concatenated neural network models to be verified; Step 7.2: For each of the aforementioned concatenated neural network models to be verified, based on the features of the input modeling data... F y i Calculate the internal force values Calculated displacement values Calculated speed values And acceleration calculation values ; Based on the internal force calculation values ​​of each of the aforementioned serial neural network models to be verified at all sampling times. Calculated displacement values Calculated speed values and acceleration calculation values Obtain the response time history calculation result corresponding to any one of the slice data sources; Step 7.3: Compare the response time history calculation result with the data recorded in the modeling data label in any of the slice data sources; Based on the comparison results, an evaluation index is calculated for each of the cascaded neural network models to be verified. The evaluation index is used to evaluate the computational performance of the cascaded neural network models to be verified. Step 7.4: Based on the evaluation index, obtain the performance ranking of each of the concatenated neural network models to be verified when verifying any slice data source in the verification set, according to the calculation effect from best to worst; wherein, the better the calculation effect, the lower the performance ranking. Step 7.5: For each of the concatenated neural network models to be verified, sum the performance rankings when verifying all slice data sources in the verification set to obtain a comprehensive performance ranking; the concatenated neural network model with the smallest comprehensive performance ranking is the optimal concatenated neural network model.

8. A modeling apparatus for calculating a cascaded neural network model of structural seismic response, characterized in that, The device specifically includes: Module 1 is used to establish a structural finite element model, wherein the structural finite element model contains at least one degree of freedom; Module 2 is used to calculate the response time history and equivalent load time history of the finite element model of the structure when any seismic acceleration time history in the pre-acquired seismic acceleration record is used as the external excitation, using the time history analysis method. Module 3 is used to group the seismic acceleration time history, the response time history, and the equivalent load time history and then perform data slicing to obtain at least 3 sets of modeling datasets, namely, the pre-training set, the post-training set, and the validation set. Module 4 is used to determine the architecture, training parameters, and value range of the initial concatenated neural network model, and to construct at least one initial concatenated neural network model based on the architecture, training parameters, and value range of the training parameters. Module 5 is used to train each of the initial concatenated neural network models using the pre-training set and the post-training set to obtain the corresponding post-trained concatenated neural network model. Module 5 is described in detail below: The pre-training set is used to train the pre-neural network in each of the initial cascaded neural network models to obtain the trained pre-neural network models; the trained pre-neural network models are used to simulate time history analysis, according to the first... i Seismic acceleration during sampling time Calculate the degree of freedom of each degree of freedom in the finite element model of the structure at the 1st... i Equivalent load of sampling time ; The post-training set is used to train the post-neural network in each of the initial cascaded neural network models to obtain the trained post-neural network models; the trained post-neural network models are used to simulate time history analysis, based on each degree of freedom in the structural finite element model at the 1st... i Equivalent load of sampling time Calculate the degree of freedom of each degree of freedom in the finite element model of the structure at the 1st... i Displacement of sampling time ,speed acceleration and internal strength ; Module 6 is used to simulate the calculation process of time history analysis, adjust the structure of each trained cascaded neural network model, and obtain the cascaded neural network model to be verified. The cascaded neural network model to be verified is used to use an autoregressive mechanism to calculate the displacement, velocity, acceleration and internal force of each degree of freedom in the finite element model of the structure at the same sampling time based on the ground motion acceleration at any sampling time. Module 7 is used to verify each of the serial neural network models to be verified using the verification set, so as to obtain the optimal serial neural network model.

9. An electronic device, comprising: A processor and a memory, characterized in that the memory is used to store executable instructions of the processor, the processor being configured to execute the modeling method of a cascaded neural network model for calculating the seismic response of a structure as described in any one of claims 1-7 by executing the executable instructions.

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