A method for predicting the floor reaction spectrum of nuclear power plant structures based on static and dynamic information fusion

Abstract

A method for predicting floor response spectra of nuclear power plant structures based on static and dynamic information fusion belongs to the field of structural seismic safety analysis. This invention solves the problems of existing analysis methods failing to consider the relative dynamic characteristics between the structure and equipment, the uncertainty of the ground motion incident angle, and high computational costs. Specifically, this invention involves: conducting nonlinear dynamic time-history analysis on a finite element model of the nuclear power plant structure using various ground motion samples to extract the acceleration time-history response of each floor at different heights under each ground motion sample; combining different ground motion samples with structural static parameters to obtain the floor response spectrum corresponding to each floor height under each combination, thereby constructing a training sample set; then using the training sample set to train a constructed encoder-decoder network model based on conditional modulation and physical consistency constraints; and finally using the trained encoder-decoder network model to predict the floor response spectrum. This invention can be used for floor response spectrum prediction.

Description

Technical Field

[0001] This invention belongs to the field of structural seismic safety analysis, specifically involving a method for predicting the floor response spectrum of nuclear power plant structures based on static and dynamic information fusion. Background Technology

[0002] In recent years, against the backdrop of continuous advancements in energy structure optimization and low-carbon development goals, my country's nuclear power engineering construction has progressed steadily. Nuclear energy, as a low-carbon, high-energy-density, and stable energy source, holds significant strategic importance in ensuring national energy security and optimizing the energy structure. With the continuous improvement of nuclear power engineering design standards, the requirements for the seismic safety of nuclear power structures are also increasing. In the seismic analysis of nuclear power structures, the floor response spectrum is a crucial basis for the seismic design and safety assessment of internal equipment, reflecting the response requirements of each floor to auxiliary equipment with different dynamic characteristics under seismic loading. The accuracy of floor response spectrum prediction not only affects the reliability of equipment seismic performance but also influences the safety margin of the entire nuclear power system under extreme seismic conditions. Therefore, accurate prediction of the floor response spectrum can provide a reliable analytical basis for the seismic design and performance evaluation of nuclear power equipment and offer technical references for research on equipment seismic response under complex conditions, possessing significant theoretical and engineering application value.

[0003] Existing floor response spectrum analysis methods are typically based on the subsystem assumption, treating equipment as a secondary system with no significant feedback effect on the main structure, thus ignoring the dynamic coupling relationship between equipment and structure during the analysis. However, in practical engineering, when equipment accounts for a large proportion of the mass or its dynamic characteristics are similar to those of the structure, the interaction between equipment and structure will significantly alter the dynamic response characteristics of the system. For example, damping differences affect the energy dissipation process, and changes in mass ratio alter the distribution of vibration energy. Without considering these factors, traditional floor response spectra may underestimate or overestimate equipment response, thereby affecting the safety and economy of seismic design. Therefore, with the increasing demands on the seismic performance of nuclear power structures, it is necessary to incorporate the relative dynamic characteristics between the structure and equipment into the floor response spectrum prediction process to improve the accuracy of response assessment.

[0004] The randomness of the earthquake incident direction is also a significant factor affecting the seismic analysis results of structures. Changes in the incident direction alter the coupling relationship of vibration components in different directions, thus affecting the amplitude and spectral characteristics of the floor acceleration response. For irregularly shaped structures, their seismic response is typically more sensitive to changes in the incident direction, especially when the incident direction is close to the most unfavorable direction of the structure, where the structural response may be significantly amplified. Nuclear power plant structures generally exhibit complex planar layouts and uneven stiffness distributions, leading to significant directional sensitivity under earthquakes in different directions. However, in current engineering practice, floor response spectrum analysis typically uses fixed-direction input or simplified orthogonal combination methods to handle earthquakes. This approach fails to comprehensively reflect the most unfavorable response under different incident angles, especially for asymmetric structures, where this simplification may lead to insufficient assessment of the seismic requirements of critical equipment. Therefore, considering the uncertainty of the earthquake incident angle during floor response spectrum modeling is crucial for improving the reliability of the analysis results.

[0005] Traditional methods for obtaining floor response spectra typically rely on extensive seismic time-history analysis. This involves progressively calculating and extracting floor responses from different seismic inputs to construct the response spectrum. This process is computationally intensive and time-consuming, making it unsuitable for the practical needs of seismic analysis in nuclear power engineering. With the development of artificial intelligence, deep learning methods have demonstrated excellent performance in modeling complex nonlinear mappings, providing a new technical approach for efficiently predicting structural dynamic responses and floor response spectra. This technology can simultaneously consider the static properties of the equipment-structure and the dynamic characteristics of seismic excitation, while significantly reducing computational costs while maintaining analytical accuracy. Therefore, developing a deep learning-based floor response spectrum prediction method to achieve multi-source information fusion and rapid response assessment has significant engineering value and application prospects for improving the efficiency and accuracy of seismic analysis of nuclear power structures.

[0006] In summary, traditional analytical methods struggle to comprehensively reflect the combined impact of seismic incident direction effects and equipment-structure dynamic coupling on floor response spectra. This is especially true when considering multiple seismic conditions, incident direction variations, and equipment-structure parameters simultaneously, as the model input dimensions increase significantly, revealing complex nonlinear coupling relationships between various factors that traditional analytical methods or empirical formulas cannot effectively characterize. Furthermore, dynamic time-history analysis methods are computationally extremely costly under multi-condition scenarios, severely limiting the efficiency of seismic analysis in nuclear power engineering. Therefore, it is necessary to construct a predictive model that integrates dynamic seismic characteristics and static equipment-structure properties to achieve efficient prediction of floor response spectra for nuclear power structures. Summary of the Invention

[0007] This invention addresses the problems of existing floor response spectrum analysis methods failing to consider the relative dynamic characteristics between the structure and equipment, as well as the uncertainty of the ground motion incident angle, and having high computational costs. It proposes a method for predicting the floor response spectrum of nuclear power plant structures based on the fusion of static and dynamic information.

[0008] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a method for predicting the floor reaction spectrum of nuclear power plant structures based on static and dynamic information fusion, the method specifically includes the following steps:

[0009] Step 1: Construct a finite element analysis model based on the geometric information, material parameters and boundary conditions of the actual nuclear power plant structure; select several ground motion records as input excitations for the finite element analysis model, and then perform amplitude modulation processing on each ground motion record. Combine the ground motion records obtained by amplitude modulation processing with different incident angles, and use each combination of ground motion record and incident angle as a ground motion sample.

[0010] Then, nonlinear dynamic time history analysis was carried out on the finite element model using each ground motion sample, and the acceleration time history response of the nuclear power structure at different heights was extracted for each ground motion sample.

[0011] Step 2: Randomly sample several sets of structural static parameters, combine different ground motion samples with structural static parameters, and for each combination, calculate the spectral acceleration value of the floor height under different periods based on the single degree of freedom system, and obtain the floor response spectrum corresponding to the floor height under the current combination based on the spectral acceleration value.

[0012] A training sample is formed by combining ground motion samples, structural static parameters, floor acceleration time history response, and floor response spectrum. By iterating through each combination, a training sample set is obtained.

[0013] Step 3: Construct an encoder-decoder network model based on conditional modulation and physical consistency constraints;

[0014] Step 4: Train the encoder-decoder network model using the training sample set obtained in Step 2;

[0015] Step 5: Use the trained encoder-decoder network model to predict the floor response spectrum.

[0016] Furthermore, the structural static parameters include mass ratio, floor height, and relative damping.

[0017] Furthermore, the specific working process of the encoder-decoder network model is as follows:

[0018] Step 1: Construct a static information vector of the device-structure system based on training samples. ,vector This includes mass ratio, floor height, relative damping, and angle of incidence;

[0019] Acceleration time history of ground motion samples in the training samples Static information vector of equipment-structure system As input to the encoder, a conditional modulation mechanism is introduced into the encoder to explicitly embed the static information vector Z of the device-structure system into the feature extraction process of the encoder to obtain the features extracted by the encoder.

[0020] Within the encoder, the static information vector of the device-structure system is... After passing through the static information encoding module, the static information vector of the equipment-structure system is processed by the static information encoding unit. Perform nonlinear mapping:

[0021] (1)

[0022] in, Represents a static information encoding unit. This represents the implicit representation obtained from the nonlinear mapping;

[0023] implicit representation As input to the FiLM parameter generation module, parameters for modulating convolutional features are generated by the FiLM parameter generation module. ;

[0024] Within the encoder, the acceleration time history of the seismic motion sample is... After passing through the first convolutional block, we obtain the features output by the first convolutional block, and then use the parameters... and The features output by the first convolutional block are linearly modulated, and the linearly modulated result is downsampled. The downsampled result is then used as the input to the second convolutional block.

[0025] Reuse parameters and The features output by the second convolutional block are linearly modulated, and the linearly modulated result is downsampled. The downsampled result is then used as the input to the third convolutional block.

[0026] Reuse parameters and The features output by the third convolutional block are linearly modulated, and the linearly modulated result is downsampled. The downsampled result is then used as the input to the fourth convolutional block.

[0027] Reuse parameters and A linear modulation operation is performed on the features output by the fourth convolutional block to obtain the features h output by the encoder.

[0028] Step 2: Upsample the feature h output by the encoder and use the upsampling result as the input of the floor acceleration time history decoding unit. In the floor acceleration time history decoding unit, the input feature h is first passed through the first TCN residual module, then the output of the first TCN residual module is used as the input of the second TCN residual module, the output of the second TCN residual module is used as the input of the third TCN residual module, the output of the third TCN residual module is used as the input of the fourth TCN residual module, and the output of the fourth TCN residual module is passed through a linear convolution mapping layer to obtain the floor acceleration time history response prediction result of the floor acceleration time history decoding unit for the input floor height.

[0029] Step 3: The feature h output by the encoder is passed through the floor response spectrum decoding unit. Within the floor response spectrum decoding unit, global pooling is first performed on the feature h to compress it into a fixed-length vector. ;

[0030] Using a multilayer perceptron for a fixed-length vector A nonlinear transformation is performed to achieve the mapping from the characteristic space to the floor response spectrum space.

[0031] Furthermore, the first TCN residual module includes a first dilated causal convolutional layer and a second dilated causal convolutional layer, and each dilated causal convolutional layer is followed by a normalization layer and a nonlinear activation function layer.

[0032] Furthermore, within the first TCN residual module, the feature update process of the first dilated causal convolutional layer is as follows:

[0033] (2)

[0034] in, The parameters are the kernel parameters of the first dilated causal convolutional layer within the first TCN residual module. The expansion coefficient of the first TCN residual module. The kernel bias of the first dilated causal convolutional layer within the first TCN residual module. For normalization layer, It is a non-linear activation function layer. This is the input to the first dilated causal convolutional layer. This is the output of the first dilated causal convolutional layer within the first TCN residual module. Represents the first in the convolution kernel One element, Indicates the kernel size. For time;

[0035] Within the first TCN residual module, the feature update process of the second dilated causal convolutional layer is as follows:

[0036] (3)

[0037] in, The parameters are the kernel parameters of the second dilated causal convolutional layer within the first TCN residual module. The kernel bias of the second dilated causal convolutional layer within the first TCN residual module. The output of the second dilated causal convolutional layer within the first TCN residual module;

[0038] Will and Perform residual connections to obtain the output of the first TCN residual module.

[0039] Furthermore, the use of a multilayer perceptron for a fixed-length vector... Perform a nonlinear transformation, specifically:

[0040] (4)

[0041] in, and They represent the first Layer weights and bias parameters.

[0042] Furthermore, the total loss function used during the training of the encoder-decoder network model is:

[0043] (5)

[0044] in, For predicting losses based on floor acceleration time history, To predict loss based on floor response spectrum, For physical loss, The response spectrum loss was calculated using the predicted floor acceleration time history; , , and These are the weighting coefficients for each loss term.

[0045] Furthermore, the floor acceleration time history prediction loss for:

[0046] (6)

[0047] in, For the first The true floor acceleration time history of each training sample For response time, For the first The predicted floor acceleration time history corresponding to each training sample.

[0048] Furthermore, the floor response spectrum prediction loss for:

[0049] (7)

[0050] in, Represents the number of discrete periodic points. For the first The training sample at the th ... The true floor response spectrum value for each cycle For the first The training sample at the th ... Predicted floor response spectrum values ​​for each cycle.

[0051] Furthermore, the physical loss term for:

[0052] (8)

[0053] in, This indicates that, based on the dynamic equation and The calculated floor response spectrum values;

[0054] The response spectrum loss calculated using the predicted floor acceleration time history for:

[0055] (9)

[0056] in, This indicates that, based on the dynamic equation and The calculated floor response spectrum values.

[0057] The beneficial effects of this invention are:

[0058] This invention introduces static feature parameters as conditional information into the model and embeds them into the seismic motion feature extraction process using a feature modulation mechanism. This allows the model to explicitly characterize the relative dynamic characteristics between the structure and auxiliary equipment, thereby overcoming the error problem caused by neglecting coupling effects in traditional auxiliary system assumptions. Furthermore, by introducing the seismic motion incident angle as an important input variable into the model training process, this invention enables the network to learn the changing patterns of structural response under seismic loading from different directions. This comprehensively captures response characteristics under unfavorable incident angle conditions, significantly improving the applicability and analytical reliability for complex or asymmetric structures. At the implementation level, this invention utilizes a deep learning model to construct a direct mapping relationship from seismic motion input and structural parameters to the floor response spectrum. This avoids the process of gradually calculating the response spectrum through extensive time-history analysis, a common practice in traditional methods. This significantly reduces computational costs and time consumption, enabling efficient application in scenarios such as multi-condition analysis, parameter sensitivity studies, and structural life-cycle assessment. In addition, this invention introduces physical consistency constraints based on structural dynamics during model training, ensuring that the prediction results simultaneously meet the requirements of data-driven fitting and physical laws. This effectively avoids non-physical result problems that may arise from purely data-driven methods, further enhancing the stability and reliability of the model output. This invention, taking into account the dynamic coupling effect of structure-equipment, the uncertainty of the incident angle of ground motion, and computational efficiency, achieves high-precision and high-efficiency prediction of floor response spectrum. It has good physical interpretability and engineering applicability, and can provide reliable technical support for the seismic design and operational safety assessment of nuclear power plant structures. Attached Figure Description

[0059] Figure 1 This is a flowchart of a method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion, according to the present invention.

[0060] Figure 2 This is a schematic diagram of a nuclear power plant structure;

[0061] Figure 3 This is a schematic diagram of the earthquake incident direction;

[0062] Figure 4 This is a diagram illustrating the construction of the training dataset;

[0063] Figure 5 This is a schematic diagram of a floor response spectrum prediction network;

[0064] Figure 6 This is a comparison of floor response spectra under Chi-Chi earthquake action;

[0065] Figure 7 This is a comparison of floor response spectra under the Northridge earthquake. Detailed Implementation

[0066] Nuclear power plant structures mainly consist of two parts: the shielded building and the auxiliary buildings. Their main characteristics are as follows:

[0067] (1) The shielding building is a cylindrical reinforced concrete shear wall structure with a total height of 81.54m. It has a dome at the top, and gravity water tanks for the passive safety cooling system are arranged on the sloping surface of the dome. The shielding building provides radiation shielding for the reactor cooling system and related radioactive systems, and prevents the escape of radioactive materials in the event of an accident.

[0068] (2) The auxiliary plant adopts a reinforced concrete shear wall structure with an asymmetrical spatial layout. The transverse dimension is 77.4m, and the longitudinal dimension consists of two sections of 35.2m and 26.67m. The interior of the plant is clearly divided and has multiple functional areas. Its main function is to provide electromagnetic shielding and physical protection for the electrical and instrumentation systems outside the shielded plant, and to meet the spatial isolation requirements of systems with different safety levels.

[0069] The present invention is as follows Figure 2 The nuclear power plant structure shown is the research object. The shell element in Abaqus is used to perform finite element simulation on the concrete walls and floor slabs. The following section first establishes the finite element model of the nuclear power plant structure, and then describes the method of the present invention in detail based on the established finite element model.

[0070] Specific implementation method one: Combining Figure 1 This embodiment describes a method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion. The method specifically includes the following steps:

[0071] Step 1: Construct a finite element analysis model based on the geometric information, material parameters and boundary conditions of the actual nuclear power plant structure; select several ground motion records as input excitations for the finite element analysis model, and then perform amplitude modulation processing on each ground motion record. Combine the ground motion records obtained by amplitude modulation processing with different incident angles, and use each combination of ground motion record and incident angle as a ground motion sample.

[0072] Then, nonlinear dynamic time history analysis was carried out on the finite element model using each ground motion sample, and the acceleration time history response of the nuclear power structure at different heights was extracted for each ground motion sample.

[0073] Specifically,

[0074] The appropriate selection of seismic ground motion records as input excitation is a prerequisite for ensuring the reliability of seismic response analysis of nuclear power plant structures. This invention selects 40 natural seismic ground motion records from the Pacific Earthquake Engineering Research Center database for subsequent analysis. The selection of seismic ground motion records follows these principles:

[0075] (1) To ensure that the ground motion has sufficient energy to excite the dynamic response of the structure, the magnitude of the selected earthquake event shall not be less than 5.0;

[0076] (2) To avoid a large number of amplitude modulation operations, the PGA of the original seismic record should be greater than 0.1g;

[0077] (3) Considering that nuclear power plant sites are mostly located in hard soil or bedrock sites, the average shear wave velocity of the stations is limited to not less than 360 m / s;

[0078] (4) In order to reduce the influence of soil-structure interaction on the characteristics of ground motion records, free field or low-rise structure stations should be selected for recording.

[0079] In order to achieve accurate prediction of floor response spectrum, a dataset with good representativeness and sufficient sample size needs to be constructed. This invention selects 40 ground motion records as the basic ground motion samples and performs uniform amplitude modulation processing on all ground motion samples. The amplitude modulation range is 0.1g to 1.0g and the amplitude modulation step size is 0.1g to improve the coverage of different earthquake intensity levels by the sample.

[0080] This invention defines the earthquake incident angle as the angle between the earthquake input direction and the structure's x-axis, such as... Figure 3 As shown, changes in the incident direction alter the distribution of dynamic input to the structure in different directions, thus causing differences in the structure's seismic response. The seismic incident direction is taken starting from the structural principal axis x-axis and incremented counterclockwise in 15° steps, resulting in a total of 24 incident direction cases.

[0081] Step 2: Combining actual structural design information or engineering experience, randomly sample several sets of structural static parameters, combine different ground motion samples with structural static parameters, and for each combination, calculate the spectral acceleration value of the floor height under different periods based on the single degree of freedom system, and obtain the floor response spectrum corresponding to the floor height under the current combination based on the spectral acceleration value.

[0082] A training sample is formed by combining ground motion samples, structural static parameters, floor acceleration time history response, and floor response spectrum. By iterating through each combination, a training sample set is obtained.

[0083] The structural static parameters are equipment-structure coupling characteristic parameters. The structural static parameters used in this invention include mass ratio, floor height and relative damping. By setting different values ​​for the parameters, several sets of structural static parameters can be obtained.

[0084] Based on actual engineering information, the specific values ​​of the three equipment-structure coupling characteristic parameters are as follows: floor heights of 4.42m, 10.67m, 16m, 21.41m, 25.14m, 29.41m, and 81m; mass ratios of 0.1, 0.3, and 0.5; and relative damping values ​​of 0.5, 1.0, and 1.5. Equivalent single-degree-of-freedom systems are established for different combinations of static parameters, and the dynamic response of the single-degree-of-freedom system is analyzed using the floor acceleration time history at the target location. Floor response spectra for all working conditions are obtained, and a complete dataset is constructed (seismic acceleration and equipment-structure coupling characteristic parameters are inputs, and floor acceleration response and floor response spectra are outputs). Finally, the dataset is divided into training and testing sets in an 8:2 ratio to ensure the reliability of model training and generalization performance evaluation. The dataset construction process is as follows: Figure 4 As shown.

[0085] Step 3: Construct an encoder-decoder network model based on conditional modulation and physical consistency constraints. This model is used to simultaneously predict the story acceleration time history response and story response spectrum of the structure, given the seismic acceleration time history and the static characteristic parameters of the equipment-structure system. In other words, this model uses the seismic acceleration time history... and equipment-structure system static information vector As input, a nonlinear mapping from input to output is achieved by constructing a multi-branch deep learning network, and its overall functional relationship can be expressed as:

[0086] (10)

[0087] in, Indicates the first Predicted floor acceleration time history response of a multi-story structure Indicates the first Floor response spectrum values ​​of a multi-story structure For equipment cycle.

[0088] like Figure 5 As shown, the encoder section aims to construct an efficient mapping from seismic input to the latent feature space, while explicitly introducing the modulation effect of static characteristic parameters of the equipment-structure system on the dynamic response, thereby forming a physically meaningful conditional feature representation. The specific working process of the encoder-decoder network model is as follows:

[0089] Step 1: Construct a static information vector of the device-structure system based on training samples. ,vector This includes mass ratio, floor height, relative damping, and angle of incidence;

[0090] Because the coupling characteristics of the equipment-structure system and the incident direction effect can significantly affect the dynamic response, relying solely on seismic motion input is insufficient to characterize the complete process of structural response. Therefore, this invention uses the acceleration time history of seismic motion samples from the training samples... Static information vector of equipment-structure system As input to the encoder, a conditional modulation mechanism is introduced into the encoder to explicitly embed the static information vector Z of the device-structure system into the feature extraction process of the encoder to obtain the features extracted by the encoder.

[0091] Specifically,

[0092] Within the encoder, the static information vector of the device-structure system is... After passing through the static information encoding module, which adopts an MLP (Multilayer Perceptron) structure, the static information encoding unit processes the static information vector of the device-structure system. Perform nonlinear mapping:

[0093] (1)

[0094] in, Represents a static information encoding unit. This represents the implicit representation obtained from the nonlinear mapping;

[0095] implicit representation As input to the FiLM (Feature-wise Linear Modulation) parameter generation module, the FiLM parameter generation module is configured as an MLP network consisting of two fully connected layers, generating parameters for modulating convolutional features. ;

[0096] Within the encoder, the acceleration time history of the seismic motion sample is... After passing through the first convolutional block, we obtain the features output by the first convolutional block, and then use the parameters... and The features output by the first convolutional block are linearly modulated, and the linearly modulated result is downsampled. The downsampled result is then used as the input to the second convolutional block.

[0097] Reuse parameters and The features output by the second convolutional block are linearly modulated, and the linearly modulated result is downsampled. The downsampled result is then used as the input to the third convolutional block.

[0098] Reuse parameters and The features output by the third convolutional block are linearly modulated, and the linearly modulated result is downsampled. The downsampled result is then used as the input to the fourth convolutional block.

[0099] Reuse parameters and A linear modulation operation is performed on the features output by the fourth convolutional block to obtain the features h output by the encoder.

[0100] By stacking convolutional operations layer by layer, the model can progressively extract higher-level abstract features from local temporal features and expand the receptive field during downsampling, thereby achieving effective modeling of multi-scale features of seismic motion. Each convolutional block includes a convolutional layer and a nonlinear activation function layer. The above process can be represented as follows:

[0101] (11)

[0102] in, For the first The kernel weights within each convolutional block For the first Kernel bias within each convolutional block This represents the convolution operation. It is a non-linear activation function. Indicates the first The result of linearly modulating and downsampling the features output by each convolutional block in sequence. For the first Features output by each convolutional block;

[0103] right Perform linear modulation operation:

[0104] (12)

[0105] in, and These are used for scaling and translating the feature channels, respectively. This is the result of linear modulation.

[0106] This modulation process can be understood as a recalibration of "equivalent dynamic characteristics" in the latent feature space, that is, the differences in floor dynamic response corresponding to different equipment-structure system coupling characteristics or floor locations, which are reflected by adjusting the feature channel weights. This design not only improves the model's ability to express changes under multiple operating conditions, but also enhances the physical interpretability of the features, enabling the network's internal representation to reflect the modulation law of structural parameters on the dynamic response.

[0107] Ultimately, the entire encoder obtains a potential representation h that simultaneously contains input excitation characteristics and device-structure system attribute information, providing a sufficient information foundation for the subsequent decoder.

[0108] The decoder includes a story acceleration time history decoding unit and a story response spectrum decoding unit. The goal of the story acceleration time history decoding unit is to reconstruct the dynamic response process of the target story of the structure under seismic loading from the latent features h output by the encoder, that is, to establish a mapping relationship from the feature space to the time series space. Unlike encoders, which focus on local feature extraction, decoders need to characterize the continuous evolution of structural responses over time. The task of the floor response spectrum decoding unit is to establish a direct mapping from the latent feature representation h obtained from the encoder to the response spectrum space, i.e., to achieve... .

[0109] Step 2: Upsample the feature h output by the encoder (upsample the feature h to restore the time resolution consistent with the target time history). Use the upsampling result as the input of the floor acceleration time history decoding unit. In the floor acceleration time history decoding unit, the input feature h is first passed through the first TCN residual module. The first TCN residual module includes a first dilated causal convolution layer and a second dilated causal convolution layer. Each dilated causal convolution layer is followed by a normalization layer and a nonlinear activation function layer.

[0110] Within the first TCN residual module, the feature update process of the first dilated causal convolutional layer is as follows:

[0111] (2)

[0112] in, The parameters are the kernel parameters of the first dilated causal convolutional layer within the first TCN residual module. The expansion coefficient of the first TCN residual module. The kernel bias of the first dilated causal convolutional layer within the first TCN residual module. For normalization layer, It is a non-linear activation function layer. This is the input to the first dilated causal convolutional layer (i.e., the input to the first TCN residual module). This is the output of the first dilated causal convolutional layer within the first TCN residual module. Represents the first in the convolution kernel One element, Indicates the kernel size. For time;

[0113] Within the first TCN residual module, the feature update process of the second dilated causal convolutional layer is as follows:

[0114] (3)

[0115] in, The parameters are the kernel parameters of the second dilated causal convolutional layer within the first TCN residual module. The kernel bias of the second dilated causal convolutional layer within the first TCN residual module. The output of the second dilated causal convolutional layer within the first TCN residual module;

[0116] Will and Residual connections are performed to obtain the output of the first TCN residual module; then the output of the first TCN residual module is used as the input of the second TCN residual module, the output of the second TCN residual module is used as the input of the third TCN residual module, the output of the third TCN residual module is used as the input of the fourth TCN residual module, and the output of the fourth TCN residual module is passed through a linear convolution mapping layer to obtain the floor acceleration time history response prediction result of the floor acceleration time history decoding unit for the input floor height;

[0117] Dilated causal convolution expands the temporal receptive field of the network without significantly increasing the number of parameters by introducing a gap between the sampling points of the convolution kernel. The expansion coefficient of each TCN residual module is based on As the number of layers increases, the effective receptive field of the model grows exponentially, enabling it to capture the long-term effects of accumulated early input stimuli in the structural response. This characteristic is particularly crucial for structural dynamic responses, as the current response depends not only on the instantaneous input but also on the input history over a longer time span. Furthermore, to ensure that the model's prediction process conforms to the physical time evolution, the decoder employs a causal convolutional form, meaning that the output at any given time t depends only on the feature inputs from the current and previous times, without using future information.

[0118] To further improve the training stability and expressive power of deep networks, residual connection structures are introduced in each TCN residual module. Input features are first processed through dilated causal convolutions to extract long-range temporal dependencies. Then, these features are element-wise added to the TCN residual module input via residual connections to obtain the current TCN residual module output, which serves as the input to the next TCN residual module. The feature update form of the residual connections is as follows:

[0119] (13)

[0120] in, For the first The input of each TCN residual module, This indicates the first [unit / type] obtained through residual connection. The input of each TCN residual module, This indicates that the feature transformation, consisting of two layers of dilated causal convolution, a normalization layer, and a nonlinear activation function, can effectively alleviate the gradient vanishing problem in deep network training. Subsequently, the feature transformation result is added to the module input element by element to form the module output.

[0121] This decoding unit achieves high-precision reconstruction of the entire process of structural dynamic response by combining the long sequence modeling capability of dilated convolution, the physical consistency of causal structure, and the stable training characteristics of residual connections, providing a reliable foundation for subsequent response spectrum prediction and physical consistency constraints.

[0122] Step 3: The feature h output by the encoder is passed through the floor response spectrum decoding unit. Within the floor response spectrum decoding unit, global pooling is first performed on the feature h to compress it into a fixed-length vector. Through this operation, information in the time dimension is integrated into global statistical features, enabling subsequent mapping to focus on the overall dynamic response characteristics represented by different feature channels.

[0123] Using a multilayer perceptron for a fixed-length vector A nonlinear transformation is performed to achieve the mapping from the characteristic space to the floor response spectrum space;

[0124] (14)

[0125] in, and They represent the first The structure, with its layer weights and bias parameters, can approximate complex functional relationships through layer-by-layer nonlinear mapping, thereby enabling accurate prediction of the high-dimensional output of the floor response spectrum.

[0126] In summary, the floor response spectrum decoding unit achieves efficient modeling of the frequency domain characteristics of the device response through the design of "global feature compression + multi-layer nonlinear mapping".

[0127] The floor response spectrum prediction branch and the time history response prediction branch of this invention share encoder features, realizing information collaboration under a multi-task learning framework. On the one hand, the latent feature h serves both time history response and floor response spectrum prediction, which helps to improve feature utilization efficiency; on the other hand, combined with the subsequently introduced physical consistency constraints, the response spectrum prediction results can not only depend on the data-driven mapping relationship, but also be indirectly constrained by the dynamic response time history, thereby further enhancing the physical rationality and stability of the prediction results.

[0128] Step 4: Train the encoder-decoder network model using the training sample set obtained in Step 2;

[0129] During model training, this invention employs batch training, learning rate adjustment, and regularization strategies to improve the model's convergence speed and generalization ability. Validation data is used to evaluate and adjust model performance. The construction of the loss function in this invention not only measures the deviation between predicted results and real data, but more importantly, it introduces structural dynamics constraints to organically combine data-driven learning with physical laws, thereby improving the model's generalization ability and the physical rationality of the predicted results. To this end, based on traditional data loss, this invention further constructs a physical consistency loss based on response spectrum calculation relationships, enabling the model to simultaneously meet the requirements of data fitting accuracy and dynamic consistency during training; that is, the overall loss function of this invention can be expressed as:

[0130] (5)

[0131] in, For predicting losses based on floor acceleration time history, To predict loss based on floor response spectrum, For physical loss, The response spectrum loss was calculated using the predicted floor acceleration time history; , , and These are the weighting coefficients for each loss term, used to balance the relationship between data fitting and physical constraints.

[0132] By appropriately setting the weights of each component, the model's adherence to dynamic laws can be improved while ensuring prediction accuracy. This loss function system, through a multi-layered design of "data supervision + physical constraints + internal consistency," achieves a shift from purely data-driven to "data-physical fusion modeling."

[0133] The following is a detailed explanation of each loss function term:

[0134] The time-history prediction loss for floor acceleration is used to constrain the model's ability to fit the entire process of the floor's dynamic response, ensuring it can accurately reproduce the amplitude changes of the time-history response. for:

[0135] (6)

[0136] in, For the first The true floor acceleration time history of each training sample For response time, For the first The predicted floor acceleration time history corresponding to each training sample;

[0137] The floor response spectrum prediction loss is used to directly constrain the model's prediction accuracy of the target response spectrum and is a core indicator to ensure the model's engineering applicability. for:

[0138] (7)

[0139] in, Represents the number of discrete periodic points. For the first The training sample at the th ... The true floor response spectrum value for each cycle For the first The training sample at the th ... Predicted floor response spectrum values ​​for each cycle;

[0140] Relying solely on data loss can easily lead to models learning mappings inconsistent with physical laws, especially when training data is limited or the predicted operating conditions change. Therefore, this invention further introduces physical consistency loss, which constrains the model output by utilizing the deterministic theoretical derivation relationship between acceleration time history and response spectrum in structural dynamics. The role of the physical loss term is to align the predicted response spectrum with the physically consistent spectrum derived from the actual dynamic response, thereby guiding the model to learn a spectral mapping relationship consistent with dynamic laws and strengthening the model's dependence on physical mechanisms. for:

[0141] (8)

[0142] in, This indicates that, based on the dynamic equation and The calculated floor response spectrum values;

[0143] (15)

[0144] in, It is the angular frequency. For equipment damping ratio, It is the base of the natural logarithm. It is an integral variable.

[0145] To enhance the consistency among different outputs within the model, a self-consistent constraint based on the prediction results is constructed, that is, using the predicted floor acceleration time history. The corresponding response spectrum is calculated based on the dynamic equations and compared with the predicted spectrum. The response spectrum loss is calculated using the predicted floor acceleration time history. for:

[0146] (9)

[0147] in, This indicates that, based on the dynamic equation and The calculated floor response spectrum values.

[0148] This constraint on the model from the perspective of internal consistency ensures that the "time history prediction branch" and the "spectral prediction branch" satisfy a unified physical mapping relationship, avoiding the situation where the two branches fit the data separately but are inconsistent with each other.

[0149] Step 5: Use the trained encoder-decoder network model to predict the floor response spectrum. That is, given a new ground motion input and target characteristic parameters, the acceleration time history and corresponding response spectrum prediction results of the target floor location can be obtained simultaneously through forward calculation of the model.

[0150] The models of each part of this invention will be described in more detail below:

[0151] In the specific implementation of the model of this invention, the structural form and hyperparameter settings of each component module need to achieve a balance between expressive power, computational efficiency, and physical rationality. Firstly, in the encoder part, the number of layers and kernel size of the one-dimensional convolutional neural network are mainly used to control the extraction scale of seismic motion features. A four-layer convolutional structure is set, with the number of channels in each layer gradually increasing from 32, 64, 128 to 256, to achieve a step-by-step expression from low-level local waveforms to high-level abstract features. The kernel size is selected as 7, which can cover the typical short-time pulse features in seismic motion signals while avoiding redundant parameters caused by excessively large kernel sizes. The stride in each layer is set to 2 to achieve downsampling in the time dimension, thereby expanding the receptive field while reducing computational complexity. The nonlinear activation function used is ReLU to ensure the stability of the training process. For the conditional modulation module, its corresponding static information encoding unit is set as a three-layer fully connected network, with a hidden layer dimension of 64, to ensure expressive power while avoiding overfitting; the generated modulation parameters... and The dimension is consistent with the number of channels in the corresponding convolutional layer, thereby achieving channel-by-channel modulation.

[0152] Four TCN residual modules are configured in the floor acceleration time history decoding unit. To effectively cover the time scale of structural dynamic response, the dilation coefficients are exponentially increased, with the dilation coefficients of the four TCN residual modules set to 1, 2, 4, and 8, respectively. This configuration allows the receptive field of the model to expand rapidly with each layer, thereby capturing the long-term response effects caused by early inputs. Each TCN residual module includes two dilated causal convolutional layers with a one-dimensional convolutional kernel of length 3 to balance local detail capture with computational efficiency. To improve network training stability, layer normalization and ReLU activation functions are applied after each dilated convolutional layer. A Dropout layer is further introduced during the training phase with a parameter set to 0.2 to reduce the risk of network overfitting and improve the model's generalization ability. After completing the temporal modeling of the four TCN residual modules, a one-dimensional convolutional output layer is set at the end of the floor acceleration time history decoding unit. The convolutional kernel size is 1, and the number of output channels is set to 1. This layer is used to map high-dimensional temporal features to the target floor acceleration time history, achieving the final prediction of the floor acceleration sequence.

[0153] For the floor response spectrum decoding unit, since it is essentially a global mapping problem, a multilayer perceptron structure is sufficient. The number of hidden layers is set to 2, with a hidden dimension of 128, to ensure sufficient nonlinear expressive power. The number of output layer nodes is N. T Consistent with the number of discrete periodic points in the selected reaction spectrum, 50 periodic points were selected based on engineering requirements. To avoid overfitting, appropriate regularization techniques, such as dropout (with a value of 0.2), can be introduced between fully connected layers to enhance the model's generalization ability.

[0154] Regarding the weight settings of the loss function, the weight coefficients λ1, λ2, λ3, and λ4 of different loss terms directly affect the direction of model optimization. Generally speaking, response spectrum prediction, as the main engineering output, can have a higher weight λ2, such as 1.0; time history loss, as an auxiliary constraint, can have a slightly lower weight λ1, such as 0.5; the weight λ3 of physical consistency loss is usually between 0.1 and 0.5, used to introduce physical constraints without interfering with the convergence of the main task; the weight λ4 of internal consistency loss can be set to a smaller value (such as 0.1) to play a regularization role. In the early stages of training, the weight of physical loss can be appropriately reduced to allow the model to learn the basic mapping relationship first, and then the weight of physical constraints can be gradually increased to enhance the physical consistency of the prediction results.

[0155] Regarding the training strategy, the optimizer chosen is Adam, and the initial learning rate can be set to 10. -3A learning rate decay strategy was used to improve convergence. The batch size was 32, and the training epochs were 500. To prevent overfitting, an early stopping strategy was employed, dynamically terminating the training process based on changes in the validation set error.

[0156] To further verify the model's prediction accuracy under typical working conditions, the Chi-Chi ground motion from the CHY006 station and the Northridge ground motion from the City Terrace station were selected as input samples. Other parameters were set as follows: floor height 29.41m, mass ratio 0.1, relative damping 0.5, and incident direction 0°. Under these conditions, the floor response spectrum predicted by the model was compared with the reference floor response spectrum constructed through numerical calculation. The results are as follows: Figure 6 and Figure 7 As shown in the figure, the prediction results exhibit good fitting performance. The predicted spectrum and the actual calculated reference spectrum show high consistency in peak position, amplitude level, and overall spectral shape trend. When the Chi-Chi earthquake was used as input, the floor spectrum was around 0.3s period, with a reference response spectrum peak value of 17.9 m / s², and the model predicted value of 17.5 m / s², resulting in a relative error of 2.23%. Within the 0.4–0.6s interval, the relative error at each period point was controlled within 3%. For the medium and long period intervals of 1.0–4.0s, although there were some spectral value differences in individual intervals, the overall error did not exceed 3%, and the spectral shape did not show significant distortion or abnormal fluctuations. When the Northridge earthquake was used as input, the model still maintained good prediction accuracy. Around 0.3s period, the reference response spectrum peak value was 18.6 m / s², and the predicted value was 18.1 m / s², resulting in a relative error of 1.67%. Within the 0.4–0.6s interval, the error was less than 3%, and only a few period points showed slightly increased deviations in the medium and long period intervals. The above results show that the prediction model can effectively extract the temporal and static characteristics of ground motion and fully capture their coupling relationship, thereby accurately depicting the variation of the floor response spectrum under different earthquake records, incident directions, and equipment-structure coupling characteristics.

[0157] The above examples of this invention are merely illustrative of the computational model and process of this invention, and are not intended to limit the implementation of this invention. Those skilled in the art can make various variations or modifications based on the above description; it is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of this invention are still within the scope of protection of this invention.

Claims

1. A method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion, characterized in that, The method specifically includes the following steps: Step 1: Construct a finite element analysis model based on the geometric information, material parameters and boundary conditions of the actual nuclear power plant structure; select several ground motion records as input excitations for the finite element analysis model, and then perform amplitude modulation processing on each ground motion record. Combine the ground motion records obtained by amplitude modulation processing with different incident angles, and use each combination of ground motion record and incident angle as a ground motion sample. Then, nonlinear dynamic time history analysis was carried out on the finite element model using each ground motion sample, and the acceleration time history response of the nuclear power structure at different heights was extracted for each ground motion sample. Step 2: Randomly sample several sets of structural static parameters, combine different ground motion samples with structural static parameters, and for each combination, calculate the spectral acceleration value of the floor height under different periods based on the single degree of freedom system, and obtain the floor response spectrum corresponding to the floor height under the current combination based on the spectral acceleration value. A training sample is formed by combining ground motion samples, structural static parameters, floor acceleration time history response, and floor response spectrum. By iterating through each combination, a training sample set is obtained. Step 3: Construct an encoder-decoder network model based on conditional modulation and physical consistency constraints; Step 4: Train the encoder-decoder network model using the training sample set obtained in Step 2; Step 5: Use the trained encoder-decoder network model to predict the floor response spectrum.

2. The method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion according to claim 1, characterized in that, The static parameters of the structure include mass ratio, floor height, and relative damping.

3. The method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion according to claim 2, characterized in that, The specific working process of the encoder-decoder network model is as follows: Step 1: Construct a static information vector of the device-structure system based on training samples. ,vector This includes mass ratio, floor height, relative damping, and angle of incidence; Acceleration time history of ground motion samples in the training samples and equipment-structure system static information vector As input to the encoder, a conditional modulation mechanism is introduced into the encoder to explicitly embed the static information vector Z of the device-structure system into the feature extraction process of the encoder to obtain the features extracted by the encoder. Within the encoder, the static information vector of the device-structure system is... After passing through the static information encoding module, the static information vector of the equipment-structure system is processed by the static information encoding unit. Perform nonlinear mapping: （1） in, Represents a static information encoding unit. This represents the implicit representation obtained from the nonlinear mapping; implicit representation As input to the FiLM parameter generation module, parameters for modulating convolutional features are generated by the FiLM parameter generation module. ; Within the encoder, the acceleration time history of the seismic motion sample is... After passing through the first convolutional block, the features output by the first convolutional block are obtained, and then the parameters are used. and The features output by the first convolutional block are linearly modulated, and the linearly modulated result is downsampled. The downsampled result is then used as the input to the second convolutional block. Reuse parameters and The features output by the second convolutional block are linearly modulated, and the linearly modulated result is downsampled. The downsampled result is then used as the input to the third convolutional block. Reuse parameters and The features output by the third convolutional block are linearly modulated, and the linearly modulated result is downsampled. The downsampled result is then used as the input to the fourth convolutional block. Reuse parameters and A linear modulation operation is performed on the features output by the fourth convolutional block to obtain the features h output by the encoder. Step 2: Upsample the feature h output by the encoder and use the upsampling result as the input of the floor acceleration time history decoding unit. In the floor acceleration time history decoding unit, the input feature h is first passed through the first TCN residual module, then the output of the first TCN residual module is used as the input of the second TCN residual module, the output of the second TCN residual module is used as the input of the third TCN residual module, the output of the third TCN residual module is used as the input of the fourth TCN residual module, and the output of the fourth TCN residual module is passed through a linear convolution mapping layer to obtain the floor acceleration time history response prediction result of the floor acceleration time history decoding unit for the input floor height. Step 3: The feature h output by the encoder is passed through the floor response spectrum decoding unit. Within the floor response spectrum decoding unit, global pooling is first performed on the feature h to compress it into a fixed-length vector. ; Using a multilayer perceptron for a fixed-length vector A nonlinear transformation is performed to achieve the mapping from the characteristic space to the floor response spectrum space.

4. The method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion according to claim 3, characterized in that, The first TCN residual module includes a first dilated causal convolutional layer and a second dilated causal convolutional layer, and each dilated causal convolutional layer is followed by a normalization layer and a nonlinear activation function layer.

5. The method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion according to claim 4, characterized in that, Within the first TCN residual module, the feature update process of the first dilated causal convolutional layer is as follows: （2） in, The parameters are the kernel parameters of the first dilated causal convolutional layer within the first TCN residual module. The expansion coefficient of the first TCN residual module. The kernel bias of the first dilated causal convolutional layer within the first TCN residual module. For normalization layer, It is a non-linear activation function layer. This is the input to the first dilated causal convolutional layer. This is the output of the first dilated causal convolutional layer within the first TCN residual module. Represents the first in the convolution kernel One element, Indicates the kernel size. For time; Within the first TCN residual module, the feature update process of the second dilated causal convolutional layer is as follows: （3） in, The parameters are the kernel parameters of the second dilated causal convolutional layer within the first TCN residual module. The kernel bias of the second dilated causal convolutional layer within the first TCN residual module. The output of the second dilated causal convolutional layer within the first TCN residual module; Will and Perform residual connections to obtain the output of the first TCN residual module.

6. The method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion according to claim 5, characterized in that, The use of a multilayer perceptron for fixed-length vectors Perform a nonlinear transformation, specifically: （4） in, and They represent the first Layer weights and bias parameters.

7. The method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion according to claim 6, characterized in that, The total loss function used in the training process of the encoder-decoder network model is: （5） in, For predicting losses based on floor acceleration time history, To predict loss based on floor response spectrum, For physical loss, The response spectrum loss was calculated using the predicted floor acceleration time history; , , and These are the weighting coefficients for each loss term.

8. The method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion according to claim 7, characterized in that, The floor acceleration time history prediction loss for: （6） in, For the first The true floor acceleration time history of each training sample For response time, For the first The predicted floor acceleration time history corresponding to each training sample.

9. The method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion according to claim 8, characterized in that, The floor response spectrum prediction loss for: （7） in, Represents the number of discrete periodic points. For the first The training sample at the th ... The true floor response spectrum value for each cycle For the first The training sample at the th ... Predicted floor response spectrum values ​​for each cycle.

10. The method for predicting the floor reaction spectrum of a nuclear power plant structure based on static and dynamic information fusion according to claim 9, characterized in that, The physical loss item for: （8） in, This indicates that, based on the dynamic equation and The calculated floor response spectrum values; The response spectrum loss calculated using the predicted floor acceleration time history for: （9） in, This indicates that, based on the dynamic equation and The calculated floor response spectrum values.

Images