Large-span space structure nonlinear dynamic response prediction method based on deep learning

Abstract

The invention discloses a large-span space structure nonlinear dynamic response prediction method based on deep learning, and the method constructs a bidirectional gated recurrent neural network (Att-BiGRU) prediction model fused with an attention mechanism for the complex nonlinear behavior of a large-span space structure considering a lower support structure under a strong earthquake. The method comprises the following steps: firstly, preprocessing a three-way seismic oscillation acceleration time history, and performing multichannel time sequence feature extraction by using a bidirectional gating recurrent neural network; then, an attention mechanism layer is introduced to endow the extracted features with dynamic weights so as to accurately capture key local nonlinear features of structural dynamic response; and finally, performing nonlinear mapping through a full connection layer, and directly outputting a dynamic response time history of the structure node. According to the method, traditional time-consuming nonlinear finite element time-history analysis can be partially replaced, the calculation efficiency is greatly improved on the premise that the prediction precision is guaranteed, and an efficient scientific basis is provided for anti-seismic performance evaluation and optimization design of a large-span space structure.

Description

Technical Field

[0001] This invention relates to the field of seismic analysis technology in structural engineering, and in particular to a method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning. Background Technology

[0002] Large-span spatial structures, represented by spherical reticulated shells, cylindrical reticulated shells, and flat plate space frames, have been widely used in large-scale public projects such as stadiums and transportation hubs due to their excellent span and spatial efficiency. Damage to these structures under seismic loading often leads to extremely serious consequences, including significant casualties, huge economic losses, and difficulties in structural repair or even complete failure. Damage to critical transportation hubs will also severely impact post-disaster relief efficiency. Therefore, seismic analysis and design for these structures are of great importance. With the continuous development of seismic design concepts, behavior-based seismic design methods have become the mainstream direction in the field of seismic engineering. This method requires structures to meet predetermined performance targets under seismic excitation at different intensity levels, thus necessitating multi-level, multi-condition seismic response analysis, including dynamic responses in both linear and nonlinear ranges. This directly leads to a significant increase in the demand for seismic response calculations for large-span spatial structures, especially nonlinear dynamic response analysis, which is particularly crucial because it more accurately reflects the behavior of structures under major earthquakes.

[0003] Currently, research on the nonlinear response mechanism of such structures under strong earthquakes mainly relies on the finite element method. This method, by establishing a detailed finite element model and combining it with dynamic time history analysis, can obtain the seismic response of the structure relatively accurately. However, it still faces significant challenges in engineering applications: First, the complex geometry and node construction of the structure make high-precision modeling difficult; second, although the traditional nonlinear finite element method has high analytical accuracy in theory, its computational cost is extremely high. This computational burden is further exacerbated when the interaction of the substructure and its dynamic amplification effect need to be considered simultaneously. These limitations make the traditional method unsuitable for the urgent needs of rapid assessment (such as the establishment of real-time health monitoring and early warning systems) and large-scale parametric analysis (such as using incremental dynamic analysis for structural vulnerability assessment) in practical engineering.

[0004] In recent years, deep learning-based methods for analyzing the performance of large-span spatial structures have developed rapidly. Takuchi et al. proposed a novel method for calculating seismic forces in large-span spatial structures using machine learning, and its effectiveness was verified by comparison with the response spectrum method. Chai et al. developed a time-span network model integrating a global contextual attention mechanism, successfully identifying the dynamic stability of large-span spatial structures. Zhang et al. systematically compared the performance of nine machine learning algorithms in predicting the ultimate bearing capacity of large-span spatial structures, pointing out that artificial neural networks have the best performance and accuracy. Guo et al. proposed an implicit parameterized modeling method based on generative adversarial neural networks, achieving rapid response generation for large-span spatial structures, which was verified in numerical models and real structures. However, when applied to the nonlinear response analysis of large-span spatial structures under seismic loading, existing deep learning models still have certain limitations: convolutional neural networks struggle to effectively capture long-sequence global temporal dependencies; unidirectional recurrent neural networks, utilizing only historical information, cannot fully characterize the reciprocating oscillations and bidirectional dynamic coupling effects of the structure, thus affecting the prediction accuracy of hysteresis and peak responses; and physical information neural networks need to simultaneously optimize data loss and physical equation residuals, often facing training challenges such as gradient vanishing, slow convergence, or even non-convergence. Summary of the Invention

[0005] The purpose of this invention is to provide a deep learning-based method for predicting the nonlinear dynamic response of large-span spatial structures. By integrating a bidirectional recurrent neural network (BRN) and an attention mechanism, the nonlinear dynamic analysis capability of the model is significantly enhanced. The BRN can extract and analyze time-series features from both positive and negative directions, thereby improving the model's prediction accuracy of the overall dynamic response trend of the structure. The attention mechanism enables the model to adaptively focus on segments with significant local nonlinear responses, further improving the prediction accuracy of key nonlinear stages (such as peak response segments). Compared with traditional dynamic response analysis methods, this method achieves higher prediction accuracy while possessing superior computational efficiency, thus solving the problems mentioned in the background section.

[0006] To achieve the above objectives, the present invention provides the following technical solution: Deep learning-based methods for predicting the nonlinear dynamic response of large-span spatial structures include: The seismic excitation-structural nonlinear response time series dataset of the large-span spatial structure was obtained by analyzing a refined finite element model of the large-span spatial structure. The finite element model takes into account the contributions of floor slabs, roof slabs, infill walls and lower supporting structures to the overall stiffness, and introduces initial geometric imperfections based on the eigenvalue buckling analysis results. A deep learning-based nonlinear dynamic response prediction model for large-span spatial structures was built and trained. The optimal model parameters were then loaded and solidified into the model. The seismic excitation time series was preprocessed using a standardization method consistent with the training phase. The preprocessed data was then input into the deep learning-based nonlinear dynamic response prediction model. Through forward propagation calculations using the deep learning-based nonlinear dynamic response prediction model, the nonlinear dynamic response time history of the large-span spatial structure under the corresponding seismic excitation was directly output.

[0007] Furthermore, the steps for obtaining the seismic excitation-structural nonlinear response time series dataset of the established refined finite element model of the large-span spatial structure include: Three-dimensional natural seismic waves are selected as input, and peak ground acceleration amplitude modulation (PGA) is applied to the 3D natural seismic waves to cover the entire process of structural development from elastic to elastoplastic. The amplitude-modulated seismic records are used as excitation input for finite element nonlinear dynamic time history analysis. Seismic wave input data and corresponding structural key node response data are extracted to construct original sample pairs. The original sample pairs are then subjected to sequence filling, pruning, and standardization to divide them into training, validation, and test sets, generating a standardized time series dataset.

[0008] Furthermore, the construction method for the nonlinear dynamic response prediction model of large-span spatial structures based on deep learning includes: The three-dimensional ground motion time series is first input into the data preprocessing module, where it is filled to form input data with uniform dimensions, and a corresponding filling mask is generated. The preprocessed data is input into the feature extraction layer of a bidirectional gated recurrent neural network to extract the temporal dependence features of seismic excitation from both the forward and reverse directions, respectively, to obtain high-dimensional encoded features. The high-dimensional encoded features are further input into the attention mechanism layer to capture the local concentrated characteristics of the nonlinear damage evolution of large-span spatial structures under seismic action, and output attention-weighted deep features. Decoding and dimension mapping are performed through a fully connected feature mapping layer to output the predicted acceleration dynamic response values ​​of key nodes in a large-span spatial structure.

[0009] Furthermore, training methods for deep learning-based nonlinear dynamic response prediction models for large-span spatial structures include: Standardized time-series datasets are input into a deep learning-based prediction model for the nonlinear dynamic response of large-span spatial structures for iterative training and parameter optimization. A mean squared error loss function is constructed to calculate the difference between the predicted and actual responses. The Adam optimizer is used to perform gradient descent and parameter updates, and the parameter learning step size is dynamically adjusted by adaptively estimating the first and second moments of the gradient. Simultaneously, the Noam learning rate scheduling strategy is used, linearly increasing the learning rate in the early stages of training to stabilize gradient updates, and then gradually decreasing the learning rate by the inverse square root of the training steps to improve convergence efficiency and stability. Furthermore, a Bayesian optimization framework is introduced into the training process for automatic hyperparameter search: a joint search space for key hyperparameters is constructed based on prior knowledge, and a mapping relationship between hyperparameters and model performance is established through a Gaussian process surrogate model. The coefficient of determination R² on the validation set is used as the objective function, and iterative search is performed based on the expected improvement of the acquisition function to obtain the optimal hyperparameter combination.

[0010] Furthermore, the deep learning-based nonlinear dynamic response prediction model for large-span spatial structures includes a data preprocessing module. This module comprises a sequence fixed-length padding function, a padding mask generator, and a sequence packing and unpacking processor. The data preprocessing module performs uniform-length padding on the input seismic motion sequence, generates a corresponding padding mask, and packs the data into a tensor format suitable for network computation. The padding mask is used to shield the influence of the padding portion during subsequent attention mechanism and loss function calculations, ensuring that the deep learning-based nonlinear dynamic response prediction model for large-span spatial structures performs feature extraction and error backpropagation only based on valid data.

[0011] Furthermore, the deep learning-based prediction model for the nonlinear dynamic response of large-span spatial structures also includes an encoder and a decoder. The encoder is composed of a bidirectional gated recurrent neural network feature extraction layer and an attention mechanism processing layer in sequence. The decoder is composed of a fully connected feature mapping layer. The fully connected feature mapping layer contains three linear layers, with a nonlinear activation function embedded between each linear layer. The activation function is the ReLU function. Through the alternating stacking of the linear layers and activation functions, the fully connected feature mapping layer gradually maps the input feature dimension to a higher feature dimension, then down to a lower feature dimension, and finally maps to the output response dimension.

[0012] Furthermore, the bidirectional gated recurrent neural network feature extraction layer consists of a bidirectional gated recurrent neural network module and an attention mechanism calculation module; the bidirectional gated recurrent neural network module consists of two independent recurrent neural networks based on gated recurrent units, one forward and one backward, wherein each gated recurrent unit includes a reset gate and an update gate composed of σ activation function, tanh activation function and Hadamard product operation; the attention mechanism calculation module includes a sliding window sampling unit, a linear key-value query calculation unit, a padding masking unit, a SoftMax normalization unit and a full-scale stitching unit.

[0013] Furthermore, the bidirectional gated recurrent neural network module consists of a forward gated recurrent unit network and a backward gated recurrent unit network. The forward network processes the input sequence step by step in chronological order. At each time step, it receives the input at the current moment and the hidden state at the previous time step. It regulates the information flow through update gates and reset gates, outputs the feature representation and hidden state at the current moment, and passes them to the next time step. The backward network processes the same sequence step by step in reverse chronological order. At each time step, it receives the input at the current moment and the hidden state at the next time step. After being regulated by the gating mechanism, it outputs the feature representation and hidden state at the current moment and passes them to the previous time step. Finally, the outputs of the forward and backward networks at each time step are concatenated to achieve the extraction and fusion of temporal features from both directions, forming a high-dimensional encoded feature representation.

[0014] Furthermore, the attention mechanism layer includes a sliding window sampling module, an in-window attention score calculation module, and a full-dimensional attention score concatenation module. The encoded feature sequence is first divided into several continuous time intervals by the sliding window sampling module. For each time interval, a corresponding key matrix, value matrix, and query matrix are generated through linear transformation, and the attention score within that interval is calculated. Subsequently, the attention scores of all time intervals are integrated by the full-dimensional concatenation module to obtain a complete sequence attention distribution. Finally, the value matrix is ​​weighted and fused based on the attention distribution to generate the attention-encoded feature sequence.

[0015] Furthermore, the fully connected feature mapping layer includes a nonlinear activation function module and a linear transformation module. The fully connected feature mapping layer receives high-dimensional temporal encoded features from the output of the previous layer. First, a nonlinear transformation is introduced through the nonlinear activation function module to enhance the feature representation capability. Then, through a multi-layer linear transformation module, the high-dimensional features are gradually mapped to the output dimension corresponding to the dynamic response of the key nodes of the structure, thereby realizing feature decoding and dimension mapping.

[0016] Compared with the prior art, the beneficial effects of the present invention are: This invention constructs a deep learning model that deeply integrates a bidirectional gated recurrent neural network and a multi-head attention mechanism. This deep learning model captures the global time-history evolution of structural responses through bidirectional network layers and adaptively focuses on key nonlinear abrupt changes, such as peak acceleration responses, using the attention mechanism to accurately characterize complex dynamic behaviors. To train this deep learning model, this invention generates a high-fidelity dataset based on refined finite element analysis. During modeling, the system considers the stiffness and initial geometric defects of actual components such as floor slabs and infill walls. During training, the Noam learning rate scheduling strategy and Bayesian optimization framework are innovatively integrated to achieve stable convergence and intelligent optimization of hyperparameters. Compared to traditional nonlinear time-history analysis methods, this method can predict responses to new seismic excitations in just seconds after training, ensuring extremely high computational efficiency while improving the prediction accuracy of key indicators such as peak responses. This provides a new technical tool for rapid seismic performance assessment of engineering structures. Attached Figure Description

[0017] Figure 1 A logical diagram of a deep learning-based nonlinear dynamic response prediction model for large-span spatial structures. Figure 2 A schematic diagram of a bidirectional recurrent neural network based on gated recurrent units; Figure 3 This is a schematic diagram of the calculation unit for the gated loop unit; Figure 4 This is a schematic diagram of sliding window sampling; Figure 5 This is a diagram illustrating the calculation of attention scores. Figure 6 This is a schematic diagram of the feature mapping layer structure; Figure 7 A flowchart of the model training process; Figure 8 This is a flowchart of a method for predicting the nonlinear dynamic response of large-span spatial structures. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described 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.

[0019] Example 1: This example uses the nonlinear dynamic response of a Kelwit 8 type single-layer spherical reticulated shell structure under seismic excitation as an example to illustrate the technical solution of the present invention in detail. The main contents include three parts: training data acquisition, construction and training of the nonlinear dynamic response prediction model. (1) Training data acquisition To obtain the nonlinear dynamic response of a large-span spatial structure under seismic excitation, this embodiment first establishes a refined finite element model. The finite element model consists of the upper spatial roof structure and the lower support system. The upper spatial roof structure works collaboratively with the lower structure through a ring transfer beam. Its member system is optimized and determined based on the full stress design method, including three types of sections: main ribs, ring members, and diagonal members. Analytical rigid shell elements are used to simulate welded hollow spherical nodes in the node domain, and multi-point constraints are used to achieve rigid connections between the rod ends and the node spheres, considering the corrective effect of the spherical nodes on the local stiffness of the upper spatial roof structure. Roof loads are applied using the equivalent mass method, and initial geometric imperfections are introduced using the consistent modal method. The lower support system consists of a steel frame, concrete floor slabs, and masonry infill walls. The support frame uses variable cross-section square steel columns, which, together with the steel beams, form a spatial lateral force resisting system. To reasonably reflect the influence of the floor slabs and infill walls on the stiffness of the lower structure, corresponding concrete floor slab and masonry infill wall elements are also established in the model.

[0020] Subsequently, three-dimensional natural seismic waves were selected as the seismic excitation input. The time history records of the seismic waves used were first subjected to linear interpolation upsampling or step-size sampling downsampling to unify their sampling frequency, then the peak ground acceleration (PGA) was normalized, and the PGA ratio of the three axes was corrected to X:Y:Z = 1:0.85:0.65. Finally, PGA amplitude modulation was applied to ensure that the seismic intensity could cover the entire process of the structure's development from elastic to elastoplastic. The resulting time history data can be used for subsequent finite element analysis and also as training input for a nonlinear dynamic response prediction model for large-span spatial structures.

[0021] The amplitude-modulated seismic records were used as excitation input for finite element nonlinear dynamic time history analysis. Seismic wave input data and corresponding structural key node response data were extracted to construct original sample pairs. The original sample pairs were subjected to sequence filling, pruning and standardization processing to divide them into training set, validation set and test set, generating a standardized time series dataset for subsequent training of nonlinear dynamic response prediction model for large-span spatial structures.

[0022] (2) Construction of a nonlinear dynamic response prediction model for large-span spatial structures See Figure 1The nonlinear dynamic response prediction model for large-span spatial structures employs a bidirectional gated recurrent neural network architecture with an attention mechanism. The main body of the nonlinear dynamic response prediction model comprises: a data preprocessing module, a bidirectional gated recurrent neural network feature extraction layer, an attention mechanism layer, and a fully connected feature mapping layer. The specific process is as follows: First, the three-dimensional seismic motion time series is input to the data preprocessing module, where it undergoes padding to form input data with uniform dimensions, and a corresponding padding mask is generated. Then, the preprocessed data enters the bidirectional gated recurrent neural network feature extraction layer, which extracts the temporal dependence features of seismic excitation from both forward and reverse directions, obtaining high-dimensional encoded features. These encoded features are further input to the attention mechanism layer to capture the localized concentrated characteristics of the nonlinear damage evolution of the structure under seismic loading, outputting attention-weighted deep features. Finally, the fully connected feature mapping layer performs decoding and dimension mapping, outputting the predicted acceleration dynamic response values ​​of key nodes in the large-span spatial structure. The following sections will provide a detailed introduction to each module.

[0023] First, the data preprocessing module includes a fixed-length sequence padding function, a padding mask generator, and a sequence packing and unpacking processor. Addressing the constraint of non-uniform length characteristics of sequence data during seismic acceleration on the input dimension of deep learning models, this study proposes a multi-stage data standardization processing scheme. First, based on the maximum duration criterion, a zero-value forward padding strategy is used to unify the sequence to 10,000 dimensions, constructing a tensor structure that meets the model input requirements. To avoid interference from padding data on temporal modeling, a dynamic sequence packing mechanism is introduced in the gated recurrent neural network module to achieve adaptive sequence length compression, effectively reducing unnecessary computation. In the attention mechanism module, this work designs a three-dimensional Boolean matrix based on a position mask, strictly limiting the model to focus only on effective seismic segments during self-attention computation. Simultaneously, to address the loss calculation bias caused by the linear layer output deviating from zero in the padding region, a mask matrix is ​​used to mask the output in the padding region.

[0024] Secondly, see Figure 2-3 The feature extraction layer of the bidirectional gated recurrent neural network consists of forward-gated recurrent units and backward-gated recurrent units. The forward network processes the input sequence sequentially over time: at each time step, it receives the current input and the hidden state from the previous time step, regulates the information flow through update and reset gates, outputs the feature representation and hidden state at the current moment, and passes them to the next time step. The backward network processes the same sequence in reverse order over time: at each time step, it receives the current input and the hidden state from the next time step, regulates the information flow through a gating mechanism, outputs the current feature and hidden state, and passes them to the previous time step. Finally, the outputs of the forward and backward networks at each time step are concatenated to achieve the extraction and fusion of temporal features in both directions, forming a high-dimensional encoded feature representation. For any time step... tThe gated loop unit regulates the information flow by updating and resetting the gate, and its calculation process is shown in equations (1) to (4):

[0025] in: x(l) t For time steps t Next l Layer-gated recurrent unit network layer input, r(l) t , z(l) t , n(l) t These are the outputs for the reset gate, update gate, and candidate hidden states, respectively. h(l) t The hidden state of the final output. W(l) ir , b (l) ir and W(l) hr , b(l) hr These represent the learning weights and biases for the input corresponding to the reset gate and the hidden state at the previous time step, respectively. W(l) iz , b(l) iz and W(l) hz , b(l) hz These represent the learning weights and biases for the input corresponding to the update gate and the hidden state at the previous time step, respectively. W(l) in、b(l) in and W(l) hn、b(l) hn σ(·) and tanh(·) are the inputs corresponding to the candidate hidden state and the learning weights and biases of the hidden state at the previous time step, respectively. σ(·) and tanh(·) are the activation functions, and ☉ is the Hadamard product.

[0026] See Figure 4 The attention mechanism layer consists of a sliding window sampling module, a window-based attention score calculation module, and a full-dimensional attention score concatenation module. To address the low computational efficiency of the global attention mechanism in seismic motion time-history response analysis, this invention proposes an improved local multi-head attention method based on a sliding window. This method leverages the stronger dynamic correlation between adjacent time steps of seismic motions, constraining attention calculations within a fixed-length local window, ensuring that each time step only establishes a correlation with its immediate and neighboring regions. By introducing the sliding window mechanism, the processing efficiency of long-sequence data is significantly improved while maintaining local feature extraction capabilities.

[0027] Specifically, the encoded feature sequence is first divided into multiple consecutive time windows by a sliding window sampling module. For each window, a corresponding key matrix is ​​generated through a linear transformation. k ), value matrix ( v ) and query matrix ( q ), and calculate the attention score within its window according to equation (5). Subsequently, the attention scores of all windows (attention scores are calculated as follows) Figure 5(As shown) The attention matrix is ​​integrated through a full-dimensional stitching module to form a complete sequence attention distribution. Finally, the value matrix is ​​weighted and fused based on this attention distribution to output the attention-weighted feature representation.

[0028]

[0029] Where: Attention is the attention-weighted output, and softmax(·) is the activation function. d k Key matrix k Dimensions.

[0030] See Figure 6 The fully connected feature mapping layer consists of five layers, comprising alternating stacked nonlinear activation function modules and linear transformation modules. It is used to progressively map the data output from the feature extraction layer from high-dimensional temporal encoded features to the output dimension corresponding to the dynamic responses of key structural nodes. This layer first performs a nonlinear transformation on the input features using a ReLU-based nonlinear activation module to enhance the model's expressive power. Subsequently, through multiple layers of linear transformation modules, it progressively completes the mapping from the high-dimensional feature space to the target output dimension, thereby achieving feature decoding and dimension adaptation.

[0031] (3) Training of the nonlinear dynamic response prediction model for large-span spatial structures See Figure 7 First, standardized time-series data is used as input for iterative training and parameter optimization of the deep learning model. To effectively evaluate the model's training performance and generalization ability, a phased, multi-dimensional evaluation system is adopted: firstly, the mean squared error loss function (MSE) is introduced at the model training level; secondly, the coefficient of determination (R²) is used at the model performance evaluation level. 2 Perform global accuracy analysis.

[0032] During the parameter optimization stage, the MSE loss function with clear mathematical and physical meaning is used to guide the model parameter update, and its mathematical expression is shown in equation (6):

[0033]

[0034]

[0035] The model's parameter updates employ the Adam optimizer, which dynamically adjusts the learning step size of each parameter by adaptively estimating the first and second moments of the gradient, thereby improving the adaptability of the training process. Furthermore, to improve training convergence efficiency and stability, this invention introduces the Noam learning rate scheduling strategy. This strategy linearly increases the learning rate in the early stages of training to stabilize the gradient update direction; subsequently, as the number of training steps increases, the learning rate gradually decreases by the reciprocal of the square root of the number of steps, facilitating fine-tuning of the model in the later stages. The specific learning rate calculation formula is shown in equation (8):

[0036]

[0037] In the training process of deep learning models, the reasonable configuration of hyperparameters has a significant impact on the convergence speed and generalization performance of the model. To systematically determine the optimal combination of hyperparameters, a Bayesian optimization framework is also incorporated into the training process. First, a joint search space for key hyperparameters is defined based on prior knowledge; then, a mapping relationship between hyperparameter configuration and model performance is established through a Gaussian process surrogate model; finally, the coefficient of determination on the validation set is used to determine the optimal hyperparameter configuration. R ² As an optimization objective, iterative search and evaluation are performed based on the expected improvement of the acquisition function, thereby efficiently obtaining the hyperparameter combination that optimizes model performance. Through the coordinated design and optimization of the above-mentioned steps, this invention can effectively improve the accuracy, convergence speed, and generalization ability of time series prediction models.

[0038] Furthermore, to prevent model overfitting, this invention introduces a dual regularization mechanism: First, Dropout layers are embedded in key nodes of the model architecture (including fully connected layers and attention modules) to reduce the network's excessive dependence on specific local features by randomly blocking connection paths between neurons (with a dropout rate of 0.1); Second, an early stopping strategy based on validation loss is adopted, terminating the training process when the validation set loss function value does not show a significant decrease for 200 consecutive training epochs. This mechanism can effectively prevent the model from falling into an overfitting state in the later stages of training, while reducing unnecessary consumption of computational resources.

[0039] Based on the aforementioned method, this invention trains a large number of training samples to predict the nonlinear dynamic response of a large-span spatial structure, and verifies the feasibility and prediction accuracy of the trained model using test set data. The verification results are shown in Tables 1 and 2: Table 1 presents the overall accuracy of the model in the overall three-dimensional response output; Table 2 further provides the specific accuracy indicators of the three-dimensional response in each direction.

[0040]

[0041] Implementation of Column 2 This application provides a method for predicting the nonlinear dynamic response of large-span spatial structures, including the following steps: Obtain the time series of earthquake excitations to be predicted; See Figure 8 The optimal model parameters obtained based on the above training method will be loaded and solidified into the constructed nonlinear dynamic response prediction model for large-span spatial structures. In the prediction phase, the input seismic excitation time series is first preprocessed using the same standardization method as in the training phase. Then, the preprocessed data is input into the prediction model, and through forward propagation calculations, the nonlinear dynamic response time history of the large-span spatial structure under the corresponding seismic excitation is directly output. This method replaces the traditional finite element nonlinear iterative solution with a fully trained deep learning model, achieving rapid and efficient prediction of the structural dynamic response.

[0042] Based on the above prediction method, the acceleration response of the mid-span node of a typical large-span spatial structure, a spherical reticulated roof, under the action of the El Centro seismic wave was predicted, and the accuracy was compared and analyzed based on the finite element calculation results. The results are shown in Table 3.

[0043]

[0044] Table 3 quantifies the prediction performance from three aspects: regression equation, mean squared error loss, and coefficient of determination. The results show that this method performs well in predicting the nonlinear dynamic response of spherical reticulated shell structures under seismic loading, and the output three-dimensional structural response is close to the actual response, especially exhibiting high accuracy in the vertical response.

[0045] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning, characterized in that, include: The seismic excitation-structural nonlinear response time series dataset of the large-span spatial structure was obtained by analyzing the refined finite element model of the large-span spatial structure. The finite element model takes into account the contributions of floor slabs, roof panels, infill walls and lower supporting structures to the overall stiffness during modeling, and introduces initial geometric imperfections based on the eigenvalue buckling analysis results. A deep learning-based nonlinear dynamic response prediction model for large-span spatial structures was built and trained. The optimal model parameters were then loaded and solidified into the built deep learning-based nonlinear dynamic response prediction model for large-span spatial structures. The seismic excitation time series was preprocessed using a standardized method consistent with the training phase. The preprocessed data is input into the deep learning-based nonlinear dynamic response prediction model for large-span spatial structures. Through forward propagation calculation of the deep learning-based nonlinear dynamic response prediction model for large-span spatial structures, the nonlinear dynamic response time history of the large-span spatial structure under the corresponding seismic excitation is directly output.

2. The method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning as described in claim 1, characterized in that, The steps for obtaining the seismic excitation-structural nonlinear response time series dataset of a large-span spatial structure through the analysis of a refined finite element model include: Three-dimensional natural seismic waves are selected as input, and peak ground acceleration amplitude modulation (PGA) is applied to the 3D natural seismic waves to cover the entire process of structural development from elastic to elastoplastic. The amplitude-modulated seismic records are used as excitation input for finite element nonlinear dynamic time history analysis. Seismic wave input data and corresponding structural key node response data are extracted to construct original sample pairs. The original sample pairs are then subjected to sequence filling, pruning, and standardization to divide them into training, validation, and test sets, generating a standardized time series dataset.

3. The method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning as described in claim 1, characterized in that, Methods for constructing nonlinear dynamic response prediction models for large-span spatial structures based on deep learning include: The three-dimensional ground motion time series is first input into the data preprocessing module, where it is filled to form input data with uniform dimensions, and a corresponding filling mask is generated. The preprocessed data is input into the feature extraction layer of a bidirectional gated recurrent neural network to extract the temporal dependence features of seismic excitation from both the forward and reverse directions, respectively, to obtain high-dimensional encoded features. The high-dimensional encoded features are further input into the attention mechanism layer to capture the local concentrated characteristics of the nonlinear damage evolution of large-span spatial structures under seismic action, and output attention-weighted deep features. Decoding and dimension mapping are performed through a fully connected feature mapping layer to output the predicted acceleration dynamic response values ​​of key nodes in a large-span spatial structure.

4. The method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning as described in claim 1, characterized in that, Training methods for deep learning-based nonlinear dynamic response prediction models for large-span spatial structures include: Standardized time-series datasets are input into a deep learning-based prediction model for the nonlinear dynamic response of large-span spatial structures for iterative training and parameter optimization. A mean squared error loss function is constructed to calculate the difference between the predicted and actual responses. The Adam optimizer is used to perform gradient descent and parameter updates, and the parameter learning step size is dynamically adjusted by adaptively estimating the first and second moments of the gradient. Simultaneously, the Noam learning rate scheduling strategy is used, linearly increasing the learning rate in the early stages of training to stabilize gradient updates, and then gradually decreasing the learning rate by the inverse square root of the training steps to improve convergence efficiency and stability. Furthermore, a Bayesian optimization framework is introduced into the training process for automatic hyperparameter search: a joint search space for key hyperparameters is constructed based on prior knowledge, and a mapping relationship between hyperparameters and model performance is established through a Gaussian process surrogate model. The coefficient of determination R² on the validation set is used as the objective function, and iterative search is performed based on the expected improvement of the acquisition function to obtain the optimal hyperparameter combination.

5. The method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning as described in claim 1, characterized in that, The deep learning-based prediction model for the nonlinear dynamic response of large-span spatial structures includes a data preprocessing module. This module comprises a fixed-length padding function, a padding mask generator, and a sequence packing and unpacking processor. The data preprocessing module pads the input ground motion sequence to a uniform length, generates a corresponding padding mask, and packs the data into a tensor format suitable for network computation. The padding mask is used to shield the influence of the padding portion during subsequent attention mechanism and loss function calculations, ensuring that the deep learning-based prediction model for the nonlinear dynamic response of large-span spatial structures performs feature extraction and error backpropagation based solely on valid data.

6. The method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning as described in claim 5, characterized in that, The deep learning-based prediction model for the nonlinear dynamic response of large-span spatial structures also includes an encoder and a decoder. The encoder is composed of a bidirectional gated recurrent neural network feature extraction layer and an attention mechanism processing layer in sequence. The decoder is composed of a fully connected feature mapping layer. The fully connected feature mapping layer contains three linear layers, with a nonlinear activation function embedded between each linear layer. The activation function is the ReLU function. The fully connected feature mapping layer gradually maps the input feature dimension to a higher feature dimension, then down to a lower feature dimension, and finally maps to the output response dimension through the alternating stacking of the linear layers and activation functions.

7. The method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning as described in claim 6, characterized in that, The bidirectional gated recurrent neural network feature extraction layer consists of a bidirectional gated recurrent neural network module and an attention mechanism calculation module. The bidirectional gated recurrent neural network module consists of two independent recurrent neural networks based on gated recurrent units, one in the forward direction and one in the reverse direction. Each gated recurrent unit includes a reset gate and an update gate composed of a σ activation function, a tanh activation function, and a Hadamard product operation. The attention mechanism calculation module includes a sliding window sampling unit, a linear key-value query calculation unit, a padding mask unit, a SoftMax normalization unit, and a full-scale stitching unit.

8. The method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning as described in claim 7, characterized in that, The bidirectional gated recurrent neural network module consists of a forward gated recurrent unit network and a backward gated recurrent unit network. The forward network processes the input sequence step by step in chronological order. At each time step, it receives the input at the current moment and the hidden state at the previous time step. It regulates the flow of information through update gates and reset gates, outputs the feature representation and hidden state at the current moment, and passes them to the next time step. The backward network processes the same sequence step by step in reverse chronological order. At each time step, it receives the input at the current moment and the hidden state at the next time step. After being regulated by the gating mechanism, it outputs the feature representation and hidden state at the current moment and passes them to the previous time step. Finally, the outputs of the forward and backward networks at each time step are concatenated to achieve the extraction and fusion of temporal features from both directions, forming a high-dimensional encoded feature representation.

9. The method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning as described in claim 6, characterized in that, The attention mechanism layer includes a sliding window sampling module, an in-window attention score calculation module, and a full-dimensional attention score concatenation module. The encoded feature sequence is first divided into several continuous time intervals by the sliding window sampling module. For each time interval, the corresponding key matrix, value matrix, and query matrix are generated by linear transformation, and the attention score in that interval is calculated. Subsequently, the attention scores for all time intervals are integrated by the full-dimensional splicing module to obtain the complete sequence attention distribution; Finally, the value matrix is ​​weighted and fused based on the attention distribution to generate an attention-encoded feature sequence.

10. The method for predicting the nonlinear dynamic response of large-span spatial structures based on deep learning as described in claim 6, characterized in that, The fully connected feature mapping layer includes a nonlinear activation function module and a linear transformation module. The fully connected feature mapping layer receives high-dimensional temporal encoded features from the output of the previous layer. First, a nonlinear transformation is introduced through the nonlinear activation function module to enhance the feature representation capability. Then, through a multi-layer linear transformation module, the high-dimensional features are gradually mapped to the output dimension corresponding to the dynamic response of the key nodes of the structure, realizing feature decoding and dimension mapping.

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