Truss structure wind-induced dynamic response prediction method and system based on physical enhancement

Abstract

The invention discloses a truss structure wind-induced dynamic response prediction method and system based on physical enhancement. The method comprises the following steps: carrying out feature extraction and alignment fusion on input data containing condition parameters and wind speed time sequence data by utilizing a long short-term memory network and a physical enhancement attention mechanism; extracting multi-scale features from the fusion features through expansion convolution, and performing weighted aggregation on the multi-scale features; the physical priori knowledge of structural vibration is fused into position coding and a self-attention mechanism so as to carry out response prediction; and integrating physical model information of the truss structure and a dynamic control equation into a loss function, and calculating physical information residual loss so as to improve the physical interpretability of a prediction result. According to the method, data heterogeneity can be eliminated, complementary information can be fused, the multi-scale characteristic of wind-induced response is coped with, the accuracy and efficiency of wind-induced dynamic response prediction of the truss structure are effectively improved, and the physical interpretability and generalization ability are enhanced.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of structural engineering and artificial intelligence, and in particular to a method and system for predicting the wind-induced dynamic response of truss structures based on physical enhancement. Background Technology

[0002] Truss structures are widely used in public infrastructure such as long-span bridges, airport terminals, high-speed rail stations, and stadiums due to their high structural efficiency. However, with the increase in span and height, these structures become significantly more sensitive to wind loads due to their lightweight and flexible characteristics. Therefore, wind-induced dynamic response has become a key factor restricting their structural safety and reliability. Efficiently and accurately predicting the wind-induced dynamic response of truss structures is crucial for optimizing their wind-resistant design. However, this task faces significant technical challenges, particularly in developing high-fidelity real-time simulations for structural health monitoring (SHM) and digital twin systems in smart construction.

[0003] The traditional finite element method (FE) widely used in engineering practice can achieve high-precision analysis. However, when applied to complex multi-degree-of-freedom truss structures, single-condition dynamic time-history analysis still consumes a significant amount of time. On the other hand, traditional empirical prediction methods based on simplified formulas rely on idealized assumptions. These methods employ simplification strategies that sacrifice accuracy, have limited applicability, and struggle to account for the nonlinear dynamic effects of wind-structure coupling. The inherent multidimensional conflict between accuracy and efficiency in these two methods constitutes a major bottleneck hindering the development of digital twin systems.

[0004] Meanwhile, deep learning technology is driving a paradigm shift in the field of SHM (Wind-Induced Dynamic Response). Data-driven baseline models such as Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, and Transformers have been successfully applied to SHM, typically demonstrating significant improvements over traditional methods in both prediction accuracy and efficiency. However, despite the immense potential of purely data-driven methods, their performance remains heavily dependent on the quantity and quality of available data. Furthermore, these methods often exhibit limited physical interpretability and generalization ability when applied to physics-based problems. Therefore, there is an urgent need for a novel method for predicting the wind-induced dynamic response of trusses that balances prediction accuracy and computational efficiency while possessing good physical interpretability and generalization ability. Summary of the Invention

[0005] The purpose of this invention is to address the problems of high computational cost, insufficient accuracy, and limited applicability of traditional finite element methods and empirical prediction methods in the prior art, by providing a physically enhanced method and system for predicting the wind-induced dynamic response of truss structures. This invention solves the problems of high computational cost, insufficient accuracy, and limited applicability of traditional finite element methods and empirical prediction methods, and improves upon the poor physical interpretability, limited generalization ability, and sensitivity to data quality and distribution of purely data-driven deep learning methods.

[0006] The objective of this invention is achieved through the following technical solution: The first aspect of this invention provides a method for predicting the wind-induced dynamic response of truss structures based on physical enhancement, comprising the following steps: Step 1, Input Processing: Receive condition parameters of the truss structure and wind speed time series data as input data, and use a long short-term memory network and physically enhanced attention mechanism to extract and align the input data to generate fused features; Step 2, Multi-scale feature processing: Multi-scale features are extracted from the fused features by dilated convolution, and the routing weights of each scale feature are calculated by a curvature-sensitive routing network to perform weighted aggregation of the multi-scale features and obtain aggregated features. Step 3, Response Prediction: By embedding the physical prior knowledge of truss structure vibration into the position encoding of the Transformer architecture and incorporating the mass matrix constraint into the multi-head self-attention mechanism of the Transformer architecture, the Transformer architecture is improved. The aggregated features are then processed through the improved Transformer architecture to obtain shared features. The shared features are then processed to predict the dynamic response time series of the truss structure at different measurement points or coordinate axes. Step 4, Physical Information Constraints: Calculate the global physical parameters of the truss structure based on its physical model information to construct the structural dynamics equations, and calculate the physical information residual loss based on the structural dynamics equations and the predicted dynamic response time series. Step 5, Model Optimization: Calculate the total loss function by combining the physical information residual loss and the prediction error loss, and update the network parameters in the input processing, multi-scale feature processing and response prediction steps based on the total loss function.

[0007] Furthermore, the condition parameters refer to the static characteristics of the structure, including the structure's length, width, height, number of spans, material elastic modulus, yield strength, node coordinates, and member cross-sectional properties; the wind speed time series data are dynamic data recorded through high-frequency sampling. The physical model information includes node coordinates, topology, material properties, and cross-sectional properties; the global physical parameters include the global mass matrix, global stiffness matrix, and global damping matrix. The physical prior knowledge of the vibration of the truss structure includes information from the structural dynamics equations.

[0008] Furthermore, step 1 specifically includes: Wind speed time series data is denoising using wavelet and then input into a long short-term memory network. Temporal features are extracted through a gating mechanism to obtain the hidden state. The hidden state and physical prior information related to the conditional parameters are incorporated into the calculation of attention weights using a physically enhanced attention mechanism to obtain aligned temporal features. The aligned temporal features and conditional parameters are then fed into a fully connected layer for feature fusion to obtain fused features.

[0009] Furthermore, the computational process of the physically enhanced attention mechanism is expressed as follows:

[0010] In the formula, The temporal characteristics representing alignment, This represents the attention mechanism. The query vector Q is derived from the condition parameter P. The key vector K represents the hidden state output by the Long Short-Term Memory network. , The value vector V represents the hidden state output by the Long Short-Term Memory network. , This represents the softmax activation function. The dimension of the key vector is represented by the superscript T, which indicates the transpose of the matrix or vector, and E represents the physical prior information related to the condition parameter P.

[0011] Furthermore, step 2 specifically includes: First, dilated convolutions with different dilation rates are applied to extract multi-scale features from the fused features. Then, a curvature-sensitive routing network is used to calculate the dynamic routing weights of each scale feature. In this curvature-sensitive routing network, each scale feature and its second derivative representing the spatial curvature change are concatenated and fed into a multilayer perceptron for nonlinear mapping, and then passed through a softmax activation function to obtain the dynamic routing weights of each scale feature. Next, depthwise separable convolutions are applied independently to each scale feature to obtain the separated independent features. Finally, the dynamic routing weights are used to perform a weighted summation of the separated independent features to obtain the aggregated features.

[0012] Furthermore, the improvements to the Transformer architecture specifically include: First, the physical prior knowledge of truss structure vibration, including structural dynamics equation information, is embedded into the position encoding of the Transformer architecture to form a physically enhanced position encoding; then, the mass matrix constraints are integrated into the multi-head self-attention mechanism of the Transformer architecture to form a physically enhanced multi-head self-attention mechanism. The process of obtaining shared features by processing aggregated features using the improved Transformer architecture specifically includes: In this improved Transformer architecture, the aggregated features first pass through the input embedding layer, then are added to the physically enhanced positional encodings passed through the sigmoid layer. Subsequently, the data stream passes through multiple encoders, multiple decoders, linear layers, and softmax layers to obtain the shared output features. Each encoder contains a physically enhanced multi-head self-attention mechanism layer and a feedforward neural network layer, followed by residual connections and summation normalization layers. The decoder also employs the physically enhanced mechanism when used for sequence-to-sequence prediction.

[0013] Furthermore, the processing of shared features to predict the dynamic response time series of the truss structure at different measuring points or coordinate axes specifically includes: The dynamic response time series of different measuring points or coordinate axes is predicted by dynamically weighting the correlation between tasks and decoupling the output layer parameters. Specifically, the output layer parameters are decomposed into shared components and task-specific components using the task correlation matrix to calculate the output layer weight matrix for each task. Then, the predicted values ​​of the dynamic response time series of the truss structure in different tasks are predicted based on the shared features and the output layer weight matrices of each task.

[0014] Furthermore, step 4 specifically includes: First, the physical model information of the truss structure is defined, including the node coordinates, topology, material properties, and section properties. Then, the length of each member is calculated based on the node coordinates and topology, and the physical parameters of each node, including mass, stiffness, and damping, are calculated based on the member length, material properties, and section properties. Subsequently, the mass, stiffness, and damping of each node are assembled into a global physical parameter matrix of the truss structure using finite element assembly technology, including a global mass matrix, a global stiffness matrix, and a global damping matrix. Then, the structural dynamics equations are constructed using the global physical parameter matrix and external loads. Finally, the predicted dynamic response time series and its corresponding velocity and acceleration are substituted into the structural dynamics equations, and the weighted sum of the L2 norm of the unbalance in the structural dynamics equations and the smoothing term is calculated to obtain the physical information residual loss.

[0015] Further, step 5 specifically includes: firstly, calculating the mean square error between the predicted dynamic response time series and its corresponding true value as the prediction error loss, and combining the prediction error loss with the physical information residual loss to calculate the single-task loss; then, using a heteroscedastic uncertainty weighting method, introducing a learnable noise parameter for each single-task loss to dynamically adjust the weight of the single-task loss for each task, and calculating the sum of all single-task losses as the total loss function based on this weight; finally, with minimizing the total loss function as the optimization objective, simultaneously updating and optimizing the network parameters and noise parameters in the input processing, multi-scale feature processing, and response prediction steps until the preset training rounds are reached.

[0016] A second aspect of this invention provides a system for implementing the above-described method for predicting the wind-induced dynamic response of truss structures based on physical enhancement, comprising: The physics-first multimodal input alignment module receives conditional parameters of the truss structure and wind speed time series data as input data, and uses a long short-term memory network and a physically enhanced attention mechanism to extract and align the input data to generate fused features. The dynamic multi-scale feature routing and aggregation module is used to extract multi-scale features from the fused features through dilated convolution, and to calculate the routing weights of each scale feature using a curvature-sensitive routing network, so as to perform weighted aggregation of multi-scale features to obtain aggregated features. The Physically Enhanced Transformer module is used to improve the Transformer architecture by embedding the physical prior knowledge of truss structure vibration into the position encoding of the Transformer architecture, integrating mass matrix constraints into the multi-head self-attention mechanism of the Transformer architecture, and processing aggregated features through the improved Transformer architecture to obtain shared features. An adaptive correlation-aware multi-task output module is used to process shared features to predict the dynamic response time series of the truss structure at different measurement points or coordinate axes. The physical information constraint module is used to calculate the global physical parameters of the truss structure based on the physical model information to construct the structural dynamics equations, and to calculate the physical information residual loss based on the structural dynamics equations and the predicted dynamic response time series. The model optimization unit is used to calculate the total loss function by combining the physical information residual loss and the prediction error loss, and to update and optimize the network parameters in the physical-first multimodal input alignment module, the dynamic multi-scale feature routing and aggregation module, the physically enhanced Transformer module, and the adaptive correlation-aware multi-task output module based on the total loss function.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The present invention can improve prediction accuracy and efficiency: through the powerful fitting ability of deep learning models and optimized network architecture (such as Transformer), combined with multi-scale feature processing, it can more accurately capture the complex dynamic characteristics of wind-induced response. At the same time, the inference stage of deep learning is usually more efficient than traditional FE analysis.

[0018] (2) This invention can enhance physical interpretability and consistency: by explicitly integrating physical model information (such as node coordinates, topology, mass, stiffness, damping matrix, etc.) and dynamic control equations into the model's position encoding, self-attention mechanism and loss function, the model's prediction results are more in line with physical laws, reducing the "black box" characteristics and non-physical interpretation of pure data-driven models.

[0019] (3) The present invention can improve the ability to process data heterogeneity: through physical priority multimodal input alignment, it can effectively process and fuse data from different sources with different characteristics (such as static condition parameters and dynamic wind speed time series).

[0020] (4) The present invention can effectively handle multi-scale effects: through the dynamic multi-scale feature routing and aggregation mechanism, it can adaptively learn and fuse response features of different spatiotemporal scales, thereby reducing the impact of scale aliasing on prediction accuracy.

[0021] (5) The present invention can improve the generalization ability of the model: due to the integration of physical constraints, the model not only learns statistical laws from the data, but also learns the underlying physical mechanism. This helps the model maintain good prediction performance under working conditions or small structural changes outside the training data, and overcomes the shortcomings of pure data-driven methods in terms of poor generalization ability when facing unseen scenarios.

[0022] (6) This invention can promote the development of intelligent construction and digital twin systems: by providing high-fidelity and high-efficiency real-time simulation capabilities, it provides key technical support for the construction of structural health monitoring and digital twin systems. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the overall architecture of the truss structure wind-induced dynamic response prediction method and system based on physical enhancement of the present invention; Figure 2 This is a flowchart illustrating the architecture of the physical-priority multimodal input alignment module of the present invention. Figure 3 This is a flowchart illustrating the architecture of the dynamic multi-scale feature routing and aggregation module of the present invention. Figure 4 This is a flowchart illustrating the architecture of the physically enhanced Transformer module of this invention. Figure 5 This is a flowchart illustrating the architecture of the physical information constraint module of this invention. Detailed Implementation

[0024] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims. It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not intended to limit this application.

[0025] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0026] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "in response to determination," or "includes." Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process or method that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process or method. Without further limitations, an element defined by the phrase "comprising a..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0027] The present invention will now be described in detail with reference to the accompanying drawings. Unless otherwise specified, the features of the following embodiments and implementations can be combined with each other.

[0028] This invention provides a PhysScaleFormer method and system for predicting the wind-induced dynamic response of truss structures, which is based on physical enhancement and can be used to accurately predict the wind-induced dynamic response of truss structures.

[0029] See Figure 1The PhysScaleFormer method described in this invention specifically includes the following steps: Step 1, Input Processing: Receive the condition parameters of the truss structure and wind speed time series data as input data, and use Long Short-Term Memory (LSTM) network and physically enhanced attention mechanism to extract and align the input data to generate fused features.

[0030] The input data consists of two parts: the conditional parameter P and the wind speed time series data. The condition parameter P refers to the static characteristics of the structure, including but not limited to its length, width, height, number of spans, material elastic modulus, yield strength, node coordinates, and member cross-sectional properties; wind speed time series data. It is dynamic data recorded through high-frequency sampling.

[0031] In this embodiment, the input data includes the conditional parameter P of the truss structure and the wind speed time series data. Because these two data modalities have different characteristics, a long short-term memory network architecture is needed, combined with a physically enhanced attention mechanism, to extract features from the heterogeneous input data and effectively align and fuse them, in order to process and resolve the conditional parameter P and wind speed time series data. The issue of differences in data modalities and scale characteristics between them. Specifically, such as... Figure 2 As shown, firstly, the wind speed time series data... Wavelet denoising was performed to obtain the denoised wind speed time series data. Then, the denoised wind speed time series data The input is fed into a Long Short-Term Memory (LSTM) network, where temporal features are extracted through its gating mechanism to obtain the hidden states. Next, a physically enhanced attention mechanism is used to hide the state. Furthermore, physical prior information related to the conditional parameter P is incorporated into the calculation of attention weights to enhance the physical interpretability of feature alignment, thereby obtaining aligned temporal features. Finally, the aligned temporal features The conditional parameter P is fed into a fully connected layer for feature fusion to obtain the fused features. .

[0032] Furthermore, the Long Short-Term Memory (LSTM) network includes a forget gate, an input gate, and an output gate. The forget gate contains a sigmoid activation function, the input gate contains both sigmoid and tanh activation functions, and the output gate contains both sigmoid and tanh activation functions. Its cell state... and hidden state Calculated according to the standard method, specifically as follows: Figure 2As shown, the denoised wind speed time series data Temporal features can be extracted and hidden states obtained through the gating mechanism of Long Short-Term Memory (LSTM) networks. .

[0033] Furthermore, in the physically-enhanced attention mechanism, the query vector is composed of conditional parameters P or their transformed forms, and the key and value vectors are composed of hidden states. The key lies in incorporating prior physical information related to the conditional parameter P into the calculation of attention weights. For example, when the prior physical information related to the conditional parameter P is the method for processing the material's elastic modulus, it can be achieved through... This adjustment of attention weights allows the model to dynamically adjust its approach to wind speed time series data based on material properties. The level of attention. This physically enhanced attention mechanism can be expressed by the following formula:

[0034] In the formula, The temporal characteristics representing alignment, This represents the attention mechanism. The query vector Q is derived from the condition parameter P. The key vector K represents the hidden state output by the Long Short-Term Memory network. , The value vector V represents the hidden state output by the Long Short-Term Memory network. , This represents the softmax activation function. The dimension of the bond vector is indicated by the superscript T, which indicates the transpose of the matrix or vector, and E represents the physical prior information (such as the elastic modulus of the material) related to the condition parameter P.

[0035] It should be understood that when using physically enhanced attention mechanisms to compute attention weights, incorporating physical prior information related to conditional parameters can effectively enhance the physical interpretability of feature alignment.

[0036] Step 2, Multi-scale feature processing: Multi-scale features are extracted from the fused features by dilated convolution, and the routing weights of each scale feature are calculated using a curvature-sensitive routing network to perform weighted aggregation of the multi-scale features and obtain aggregated features.

[0037] In this embodiment, considering that the response of truss structures under complex wind fields typically exhibits multi-scale characteristics, it is necessary to effectively handle these multi-scale features to mitigate scale aliasing effects and address issues such as system bias and gradient stiffness that may exist in existing deep learning methods (such as Physical Information Neural Networks (PINN)) when dealing with such problems. Specifically, as... Figure 3 As shown, firstly, dilated convolutions with different dilation rates are applied to extract multi-scale features from the fused features. ,in Let represent the i-th scale feature, and n represent the total number of scale features. Applying dilated convolutions with different dilation rates can increase the receptive field without increasing the number of parameters. Then, a curvature-sensitive routing network is used to compute the features at each scale. The dynamic routing weights quantify the importance of features at each scale. The curvature-sensitive routing network is a small subnetwork centered on a multilayer perceptron (MLP) and explicitly incorporating curvature information, which quantifies the importance of features at each scale. and the second derivative used to represent its spatial curvature change. (The spatial curvature changes used to represent features) are concatenated and then fed into an MLP for nonlinear mapping, followed by a softmax activation function to obtain features at each scale. Dynamic routing weights This can enhance sensitivity to local responses and dynamically adjust the importance of features at each scale. The softmax activation function ensures that the sum of dynamic routing weights across all scales is 1. It can be represented as:

[0038] In the formula, Represents the i-th scale feature Dynamic routing weights To represent the i-th scale feature The second derivative of the spatial curvature change, Indicates feature splicing, This represents a multilayer perceptron. This represents the softmax activation function. Subsequently, for each scale feature... Independently applying depthwise separable convolutions yields separate, independent features. This reduces computational complexity while maintaining feature independence. Finally, dynamic routing weights are used. Independent features after separation Perform weighted summation to obtain aggregated features. , can be represented as:

[0039] In the formula, Indicates aggregation features, This represents the independent feature at the i-th scale.

[0040] Step 3, Response Prediction: By embedding the physical prior knowledge of truss structure vibration into the position encoding of the Transformer architecture, and integrating the mass matrix constraint into the multi-head self-attention mechanism of the Transformer architecture, the Transformer architecture is improved. The aggregated features are then processed through the improved Transformer architecture to obtain shared features. The shared features are then processed to predict the dynamic response time series of the truss structure at different measuring points or coordinate axes (such as the displacement time series at different measuring points).

[0041] The physical prior knowledge of truss structure vibration includes information from the structural dynamics equations.

[0042] In this embodiment, the Transformer architecture needs to be improved first, and then the improved Transformer architecture is used to process the aggregated features to obtain shared features. The Transformer architecture can capture aggregated features. The global time dependency in the structure is used to obtain shared features for predicting dynamic responses. The core of this approach is to integrate the physical prior knowledge of truss structure vibration into the two key components of the Transformer architecture: positional encoding and multi-head self-attention mechanism.

[0043] Furthermore, improvements are made to the Transformer architecture, specifically including: the traditional Transformer uses a sine function to generate positional encoding, as shown in the following equation:

[0044] In the formula, Indicates the position encoding matrix at time step Dimensions The value at that location, Indicates the time step index. Indicates a dimension index. Indicates even-numbered dimensions. This represents the embedding dimension of the Transformer architecture. In this invention, the vibration of the truss structure follows specific structural dynamics equations, typically expressed as a second-order ordinary differential equation as shown below:

[0045] In the formula, M represents the global mass matrix of the truss structure, K represents the global stiffness matrix of the truss structure, and C represents the global damping matrix of the truss structure. Represents the time series of dynamic response (such as displacement vector). and These represent the velocity and acceleration corresponding to the time series of the dynamic response, respectively. This represents the external load. Therefore, to enhance the physical consistency of the model, the prior physical knowledge governing the wind-induced vibration response of the truss structure, namely the specific structural dynamics equations, is first embedded into the positional encoding of the Transformer architecture, forming a physically enhanced positional encoding, which can be expressed as:

[0046] In the formula, This represents a physically enhanced positional encoding that combines time t and velocity terms derived from the structural dynamics equations. And parameters related to M, C, and K, which are used as part of the physical augmentation location coding; Indicates an embedded function; This represents the velocity term derived from the structural dynamics equations. This represents the set of physical parameters (such as natural frequencies, modal damping ratios, etc.) calculated or extracted by M, C, and K. As can be seen from the above, embedding the structural dynamics equations into the location encoding involves using the solutions to the structural dynamics equations or their transformed forms as part of the location encoding. Then, the mass matrix constraints are integrated into the multi-head self-attention mechanism of the Transformer architecture, forming a physically enhanced multi-head self-attention mechanism as shown in the following equation, to further enhance physical consistency:

[0047] In the formula, This indicates a physically enhanced multi-head self-attention mechanism. This represents a quality matrix constraint. When introducing a quality matrix constraint into a multi-head self-attention mechanism, it can be achieved by adjusting the calculation method of the attention score; for example, by multiplying certain attributes of the quality matrix or certain forms of its inverse matrix by... On the item, or as part of the attention weight scaling factor.

[0048] Furthermore, the aggregated features are processed using the improved Transformer architecture to obtain shared features, specifically including: Figure 4 As shown, in this improved Transformer architecture, aggregated features First, the data passes through an input embedding layer, then is added to the physically augmented positional encoding from a sigmoid layer. The data then flows through multiple encoders, multiple decoders, linear layers, and a softmax layer to obtain the shared output features. Each encoder contains a physically enhanced multi-head self-attention mechanism layer and a feedforward neural network layer, followed by residual connections and summation normalization layers. When the decoder is used for sequence-to-sequence prediction, it will also adopt a physically enhanced mechanism, similar to the encoder, namely physically enhanced positional encoding, physically enhanced multi-head self-attention mechanism and physically enhanced cross self-attention mechanism.

[0049] It should be understood that the standard Transformer decoder has one more cross-self-attention mechanism layer than the encoder, and its own self-attention layer is masked. The physical enhancements described in this invention primarily apply to the positional encoding and self-attention mechanism components; therefore, these physical enhancements are also applied to the corresponding components of the decoder, specifically to the cross-attention mechanism layer. Furthermore, in the decoder, to generate the next word, the currently generated sequence needs to be converted back into a vector; the embedding layer used in this process is called the "output embedding layer."

[0050] Furthermore, shared features are processed to predict the dynamic response time series of the truss structure at different measuring points or coordinate axes. Specifically, this includes improving the flexibility and accuracy of multi-task prediction through multi-task output, especially when it is necessary to simultaneously predict the dynamic response time series of different measuring points or coordinate axes on the truss structure (i.e., displacement output). When these outputs are processed, their magnitudes and noise levels may differ. Prediction of dynamic response time series at different measurement points or along different coordinate axes is achieved by dynamically weighting the correlation between tasks and decoupling the output layer parameters. Let the number of tasks be *s*, and the shared features be... Using the task relevance matrix Decompose the output layer parameters into shared components. and task-specific components During decomposition, matrix multiplication is first used to guide how the basic weights are mixed based on the similarity between tasks, thereby "distilling" out the shared components. Then, the task's personalized information is extracted through masking operations as a task-specific component. And then utilize shared components and task-specific components Calculate the output layer weight matrix for each task , can be represented as:

[0051] In the formula, This represents the output layer weight matrix of the s-th task. Indicates a shared component. This represents a task-specific component of the s-th task. The relevance weight of the s-th task can be dynamically determined using the Spearman rank correlation coefficient, expressed as:

[0052] In the formula, This represents the Spearman rank correlation coefficient. This represents the actual measured value of the time series of the dynamic response of the s-th task. Indicates the use of shared features The predicted values ​​of the time series of dynamic responses to the task. Finally, based on shared features... The predicted values ​​of the dynamic response time series of different tasks are obtained by combining the output layer weight matrices of each task, and can be expressed as:

[0053] In the formula, This represents the predicted value of the dynamic response time series of the s-th task.

[0054] Step 4, Physical Information Constraints: Calculate the global physical parameters of the truss structure based on its physical model information to construct the structural dynamics equations, and calculate the physical information residual loss based on the structural dynamics equations and the predicted dynamic response time series.

[0055] The physical model information includes node coordinates, topology, material properties, and cross-sectional properties. Global physical parameters include the global mass matrix, global stiffness matrix, and global damping matrix.

[0056] In this embodiment, the physical model information and structural dynamics equations of the truss structure are integrated into the loss function through a physical information constraint step to calculate the physical information residual loss, thereby enhancing the physical interpretability of the prediction results and reducing non-physical oscillations. The process is as follows: Figure 5 The diagram illustrates the specific process of calculating the physical information residual loss from the physical model information of a truss structure. The core of the physical information constraint step is to introduce known physical laws (i.e., structural dynamic equations) as constraints into the model's learning process, and then use the calculated physical information residual loss to guide subsequent model optimization.

[0057] Specifically, such as Figure 5 As shown, the physical model information of the truss structure is first defined, including the node coordinates of the truss structure. Topology (such as the connection relationship between unit nodes), material properties (such as elastic modulus E, density, etc.) And cross-sectional properties (such as cross-sectional area S, etc.), among which Represents a node The three-dimensional coordinates.

[0058] Then, the length of each member is calculated based on the node coordinates and topology. The specific calculation formula is as follows:

[0059] In the formula, This represents the length of member e, which is the connection node. and nodes The method for calculating the length of member e, Represents a node The three-dimensional coordinates Represents a node The three-dimensional coordinates are used. The physical parameters of each node, including mass, stiffness, and damping, are calculated based on the length, material properties, and cross-sectional properties of the member. Specifically, ① for mass: assuming the mass is uniformly distributed throughout the member and equivalently allocated to its two end nodes, the mass of member e is... ,in Indicates the mass of member e. This indicates the material density of the truss structure. This indicates the cross-sectional properties and nodal mass of member e. The sum of contributions from adjacent members, i.e., nodes quality It is all nodes related to this node Half the sum of the masses of the connected rods can be expressed as:

[0060] In the formula, Represents nodes Connected rods; ② Regarding stiffness: First calculate the axial stiffness of rod e as follows: ,in This indicates the axial stiffness of member e. The elastic modulus of member e is represented by the coordinate transformation matrix. Convert it to the stiffness matrix of the element in the global coordinate system. , can be represented as:

[0061] In the formula, This represents the stiffness matrix of the element containing member e. ③ For damping: Rayleigh damping model is used for nodal damping, i.e., the nodal damping matrix is ​​denoted by . With node quality matrix and nodal stiffness matrix Proportional, which can be expressed as ,in and This is the Rayleigh damping coefficient, which needs to be determined based on the structural characteristics. In this embodiment, the nodal damping can be calculated using the following formula:

[0062] In the formula, Represents a node Damping, Represents a node quality Represents a node The stiffness (which can be represented by the stiffness matrix of the element containing the node). and These represent the Rayleigh damping coefficients for mass and stiffness, respectively.

[0063] Subsequently, based on the physical parameters of each node, a global physical parameter matrix is ​​assembled using finite element assembly technology. Specifically, this technology assembles the mass, stiffness, and damping of each node into the global mass matrix, global stiffness matrix, and global damping matrix of the truss structure. In particular, the global mass matrix M is a diagonal matrix in the lumped mass model, with the diagonal elements representing the mass of each node. The global stiffness matrix K is obtained by superimposing the stiffness matrices of each element, specifically derived from the stiffness matrices of each element. It is formed by superimposing the corresponding degrees of freedom; the global damping matrix C is usually obtained through the Rayleigh damping formula, expressed as: In calculating nodal mass, element stiffness, and nodal damping, element length, material density, interface area, elastic modulus, and Rayleigh damping model were utilized.

[0064] Then, using the global physical parameter matrix (i.e., the global mass matrix M, the global stiffness matrix K, and the global damping matrix C) and external loads... (The external load here refers to the equivalent nodal load caused by wind load.) Construct the structural dynamics equations, i.e., the aforementioned formula. .

[0065] Finally, the predicted dynamic response time series and its corresponding velocities and accelerations are substituted into the structural dynamics equations. By calculating the weighted sum of the L2 norm of the unbalance quantities and the smoothing term in the structural dynamics equations, the physical information residual loss is obtained, which can be expressed as:

[0066] In the formula, This represents the physical information residual loss, which penalizes predictions that do not satisfy the dynamic equilibrium equations. Global physical constraints can be applied; Represents the square of the L2 norm; This represents the predicted dynamic response time series. This represents the velocity corresponding to the predicted dynamic response time series. This represents the acceleration corresponding to the predicted dynamic response time series. and Numerical differentiation methods (such as the central difference method) can be used to obtain... The calculations show that M represents the global mass matrix, K represents the global stiffness matrix, and C represents the global damping matrix. This represents a smoothing term, used to penalize non-physical high-frequency oscillations in the prediction results and prevent non-physical abrupt changes in the prediction results; This represents the weight of the smoothing term.

[0067] Step 5, Model Optimization: Calculate the total loss function by combining the physical information residual loss and the prediction error loss, and update the network parameters in the input processing, multi-scale feature processing and response prediction steps based on the total loss function.

[0068] In this embodiment, to aggregate the total loss function used for model training and adaptively optimize the weights of different loss components (i.e., physical information residual loss and prediction error loss), the mean squared error (MSE) between the predicted dynamic response time series and its corresponding true value is first calculated as the prediction error loss. The prediction error loss is then combined with the physical information residual loss to calculate the single-task loss, which can be expressed as:

[0069]

[0070] In the formula, This represents the single-task loss of the s-th task. This represents the prediction error loss for the s-th task. This represents the predicted dynamic response time series for the s-th task. This represents the true dynamic response time series of the s-th task. This represents the physical information residual loss of the s-th task. The weighting coefficients representing the physical information residual loss can be preset or adaptively optimized. Then, to balance the impact of losses with different properties during multi-task learning or combining different types of losses, a heteroscedastic uncertainty weighting method is used for each single-task loss. Introduce a learnable noise parameter The weights of the individual task losses for each task are dynamically adjusted, and the sum of all individual task losses is calculated based on these weights as the total loss function, expressed as:

[0071] In the formula, Represents the total loss function. Let represent the learnable noise parameter corresponding to the s-th single-task loss. These represent the weighting coefficients for the noise parameter components. Finally, the goal is to minimize the total loss function. To optimize the objective, backpropagation and gradient descent optimizers (such as the Adam optimizer) are used to simultaneously update network parameters and noise parameters in the input processing, multi-scale feature processing, and response prediction steps. This allows the model to accurately predict wind-induced dynamic responses while satisfying physical constraints, until the preset training epochs are reached. Larger tasks contribute less to the total loss function, and vice versa; the regularization term is used to prevent... If it becomes too small, ensure numerical stability.

[0072] It should be noted that when the model training is complete, all its network parameters (referring to the network parameters in the input processing, multi-scale feature processing, and response prediction steps) are frozen. Afterward, only the trained model needs to be used for prediction. During prediction, the input data only needs to pass through step 1 (input processing), step 2 (multi-scale feature processing), and step 3 (response prediction) sequentially to obtain the predicted dynamic response time series; the training processes in steps 4 and 5 are no longer required.

[0073] It is worth mentioning that this invention also provides a PhysScaleFormer system for predicting the wind-induced dynamic response of truss structures, which is based on physical enhancement, to implement the PhysScaleFormer method in the above embodiments. Figure 1 As shown, the PhysScaleFormer system includes a Physics-prioritized multimodal input alignment module, a Dynamic multiscale feature routing and aggregation module, a Physics-enhanced Transformer module, an Adaptive correlation-aware multitask output module, a Physics-informed constraint module, and a Model Optimization Module.

[0074] In this embodiment, the physics-first multimodal input alignment module receives condition parameters of the truss structure and wind speed time series data as input data. It then utilizes a Long Short-Term Memory (LSTM) network and a physically-enhanced attention mechanism to extract and align the input data, generating fused features. The specific process is as follows: Figure 2 As shown.

[0075] In this embodiment, the dynamic multi-scale feature routing and aggregation module is connected to the output of the physical-first multimodal input alignment module, inputting the fused features output by the physical-first multimodal input alignment module into the dynamic multi-scale feature routing and aggregation module. The dynamic multi-scale feature routing and aggregation module extracts multi-scale features from the fused features through dilated convolutions and uses a curvature-sensitive routing network to calculate the routing weights of each scale feature, thereby weighted aggregation of the multi-scale features to obtain aggregated features. The specific process is as follows: Figure 3 As shown.

[0076] In this embodiment, the physically enhanced Transformer module is connected to the output of the dynamic multi-scale feature routing and aggregation module, inputting the aggregated features output by the multi-scale feature routing and aggregation module into the physically enhanced Transformer module. The physically enhanced Transformer module is used to improve the Transformer architecture by embedding prior physical knowledge of truss structure vibration into the position encoding of the Transformer architecture and incorporating mass matrix constraints into the multi-head self-attention mechanism of the Transformer architecture. The improved Transformer architecture is then used to process the aggregated features to obtain shared features. The specific process is as follows: Figure 4 As shown.

[0077] In this embodiment, the adaptive correlation-aware multi-task output module is connected to the output of the physically enhanced Transformer module, inputting the shared features output by the physically enhanced Transformer module into the adaptive correlation-aware multi-task output module. The adaptive correlation-aware multi-task output module processes the shared features to predict the dynamic response time series of the truss structure at different measurement points or coordinate axes. The specific process is as follows: Figure 1 As shown.

[0078] In this embodiment, the physical information constraint module is used to calculate the global physical parameters of the truss structure based on its physical model information, in order to construct the structural dynamics equations, and to calculate the physical information residual loss based on the structural dynamics equations and the predicted dynamic response time series. The specific process is as follows: Figure 5 As shown.

[0079] In this embodiment, the model optimization unit is used to calculate the total loss function by combining the physical information residual loss and the prediction error loss, and to update the network parameters in the physical-first multimodal input alignment module, the dynamic multi-scale feature routing and aggregation module, the physically enhanced Transformer module, and the adaptive correlation-aware multi-task output module based on the total loss function. The specific process is as follows: Figure 1 As shown.

[0080] Furthermore, once model training is complete, all network parameters (referring to the network parameters in the physics-first multimodal input alignment module, the dynamic multi-scale feature routing and aggregation module, the physically enhanced Transformer module, and the adaptive correlation-aware multi-task output module) are frozen. Afterward, only the trained model needs to be used for prediction. During prediction, the input data only needs to pass through the physics-first multimodal input alignment module, the dynamic multi-scale feature routing and aggregation module, the physically enhanced Transformer module, and the adaptive correlation-aware multi-task output module sequentially to obtain the predicted dynamic response time series; the training process of the physical information constraint module and the model optimization unit is no longer required.

[0081] In summary, the PhysScaleFormer method and system described in this invention, through the collaborative work of the above modules, first aligns and fuses the heterogeneous input data, then extracts and aggregates multi-scale features, next uses the Transformer module incorporating physical priors for response prediction, and finally optimizes the network parameters in the physics-prioritized multimodal input alignment module, dynamic multi-scale feature routing and aggregation module, physics-enhanced Transformer module, and adaptive correlation-aware multi-task output module through physical information constraints and the adaptively adjusted total loss function in the model optimization unit. This achieves accurate, efficient, and physically interpretable prediction of the wind-induced dynamic response of truss structures.

[0082] The preferred embodiments of the present invention have been described above with reference to the accompanying drawings. However, those skilled in the art should understand that various modifications or improvements can be made to the specific embodiments described above without departing from the concept of the present invention, and such modifications or improvements should also be considered to fall within the protection scope of the present invention. For example, specific variants of LSTM, the number of layers and heads of the Transformer, the selection of activation functions, and the specific type of optimizer can all be adjusted according to actual applications. In addition, the embedding method of physical priors and the specific form of physical constraints can also be implemented in various equivalent ways.

[0083] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the wind-induced dynamic response of a truss structure based on physical enhancement, characterized in that, Includes the following steps: Step 1, Input Processing: Receive condition parameters of the truss structure and wind speed time series data as input data, and use a long short-term memory network and physically enhanced attention mechanism to extract and align the input data to generate fused features; Step 2, Multi-scale feature processing: Multi-scale features are extracted from the fused features by dilated convolution, and the routing weights of each scale feature are calculated by a curvature-sensitive routing network to perform weighted aggregation of the multi-scale features and obtain aggregated features. Step 3, Response Prediction: By embedding the physical prior knowledge of truss structure vibration into the position encoding of the Transformer architecture and incorporating the mass matrix constraint into the multi-head self-attention mechanism of the Transformer architecture, the Transformer architecture is improved. The aggregated features are then processed through the improved Transformer architecture to obtain shared features. The shared features are then processed to predict the dynamic response time series of the truss structure at different measurement points or coordinate axes. Step 4, Physical Information Constraints: Calculate the global physical parameters of the truss structure based on its physical model information to construct the structural dynamics equations, and calculate the physical information residual loss based on the structural dynamics equations and the predicted dynamic response time series. Step 5, Model Optimization: Calculate the total loss function by combining the physical information residual loss and the prediction error loss, and update the network parameters in the input processing, multi-scale feature processing and response prediction steps based on the total loss function.

2. The method for predicting the wind-induced dynamic response of truss structures based on physical enhancement according to claim 1, characterized in that, The condition parameters refer to the static characteristics of the structure, including the structure's length, width, height, number of spans, material elastic modulus, yield strength, node coordinates, and member cross-sectional properties; the wind speed time series data are dynamic data recorded through high-frequency sampling. The physical model information includes node coordinates, topology, material properties, and cross-sectional properties; the global physical parameters include the global mass matrix, global stiffness matrix, and global damping matrix. The physical prior knowledge of the vibration of the truss structure includes information from the structural dynamics equations.

3. The method for predicting the wind-induced dynamic response of truss structures based on physical enhancement according to claim 1, characterized in that, Step 1 specifically includes: Wind speed time series data is denoising using wavelet and then input into a long short-term memory network. Temporal features are extracted through a gating mechanism to obtain the hidden state. The hidden state and physical prior information related to the conditional parameters are incorporated into the calculation of attention weights using a physically enhanced attention mechanism to obtain aligned temporal features. The aligned temporal features and conditional parameters are then fed into a fully connected layer for feature fusion to obtain fused features.

4. The method for predicting wind-induced dynamic response of truss structures based on physical enhancement according to claim 3, characterized in that, The computational process of the physically enhanced attention mechanism is expressed as follows: ； In the formula, The temporal characteristics representing alignment, This represents the attention mechanism. The query vector Q represents the condition parameter P. The key vector K represents the hidden state output by the Long Short-Term Memory network. , The value vector V represents the hidden state output by the Long Short-Term Memory network. , This represents the softmax activation function. The dimension of the key vector is represented by the superscript T, which indicates the transpose of the matrix or vector, and E represents the physical prior information related to the condition parameter P.

5. The method for predicting wind-induced dynamic response of truss structures based on physical enhancement according to claim 1, characterized in that, Step 2 specifically includes: First, dilated convolutions with different dilation rates are applied to extract multi-scale features from the fused features. Then, a curvature-sensitive routing network is used to calculate the dynamic routing weights of each scale feature. In this curvature-sensitive routing network, each scale feature and its second derivative representing the spatial curvature change are concatenated and fed into a multilayer perceptron for nonlinear mapping, and then passed through a softmax activation function to obtain the dynamic routing weights of each scale feature. Next, depthwise separable convolutions are applied independently to each scale feature to obtain the separated independent features. Finally, the dynamic routing weights are used to perform a weighted summation of the separated independent features to obtain the aggregated features.

6. The method for predicting the wind-induced dynamic response of truss structures based on physical enhancement according to claim 1, characterized in that, The improvements to the Transformer architecture specifically include: First, the physical prior knowledge of truss structure vibration, including structural dynamics equation information, is embedded into the position encoding of the Transformer architecture to form a physically enhanced position encoding; then, the mass matrix constraints are integrated into the multi-head self-attention mechanism of the Transformer architecture to form a physically enhanced multi-head self-attention mechanism. The process of obtaining shared features by processing aggregated features using the improved Transformer architecture specifically includes: In this improved Transformer architecture, the aggregated features first pass through the input embedding layer, then are added to the physically enhanced positional encodings passed through the sigmoid layer. Subsequently, the data stream passes through multiple encoders, multiple decoders, linear layers, and softmax layers to obtain the shared output features. Each encoder contains a physically enhanced multi-head self-attention mechanism layer and a feedforward neural network layer, followed by residual connections and summation normalization layers. The decoder also employs the physically enhanced mechanism when used for sequence-to-sequence prediction.

7. The method for predicting wind-induced dynamic response of truss structures based on physical enhancement according to claim 1, characterized in that, The process of processing shared features to predict the dynamic response time series of the truss structure at different measuring points or coordinate axes specifically includes: The dynamic response time series of different measuring points or coordinate axes is predicted by dynamically weighting the correlation between tasks and decoupling the output layer parameters. Specifically, the output layer parameters are decomposed into shared components and task-specific components using the task correlation matrix to calculate the output layer weight matrix for each task. Then, the predicted values ​​of the dynamic response time series of the truss structure in different tasks are predicted based on the shared features and the output layer weight matrices of each task.

8. The method for predicting the wind-induced dynamic response of truss structures based on physical enhancement according to claim 1, characterized in that, Step 4 specifically includes: First, the physical model information of the truss structure is defined, including the node coordinates, topology, material properties, and section properties. Then, the length of each member is calculated based on the node coordinates and topology, and the physical parameters of each node, including mass, stiffness, and damping, are calculated based on the member length, material properties, and section properties. Subsequently, the mass, stiffness, and damping of each node are assembled into a global physical parameter matrix of the truss structure using finite element assembly technology, including a global mass matrix, a global stiffness matrix, and a global damping matrix. Then, the structural dynamics equations are constructed using the global physical parameter matrix and external loads. Finally, the predicted dynamic response time series and its corresponding velocity and acceleration are substituted into the structural dynamics equations, and the weighted sum of the L2 norm of the unbalance in the structural dynamics equations and the smoothing term is calculated to obtain the physical information residual loss.

9. The method for predicting the wind-induced dynamic response of truss structures based on physical enhancement according to claim 1, characterized in that, Step 5 specifically includes: First, calculating the mean square error between the predicted dynamic response time series and its corresponding true value as the prediction error loss, and combining the prediction error loss with the physical information residual loss to calculate the single-task loss; then, using a heteroscedastic uncertainty weighting method, introducing a learnable noise parameter for each single-task loss to dynamically adjust the weight of the single-task loss for each task, and calculating the sum of all single-task losses as the total loss function based on this weight; finally, with minimizing the total loss function as the optimization objective, simultaneously updating and optimizing the network parameters and noise parameters in the input processing, multi-scale feature processing, and response prediction steps until the preset training rounds are reached.

10. A system for implementing the method for predicting the wind-induced dynamic response of a truss structure based on physical enhancement as described in any one of claims 1-9, characterized in that, include: The physics-first multimodal input alignment module receives conditional parameters of the truss structure and wind speed time series data as input data, and uses a long short-term memory network and a physically enhanced attention mechanism to extract and align the input data to generate fused features. The dynamic multi-scale feature routing and aggregation module is used to extract multi-scale features from the fused features through dilated convolution, and to calculate the routing weights of each scale feature using a curvature-sensitive routing network, so as to perform weighted aggregation of multi-scale features to obtain aggregated features. The Physically Enhanced Transformer module is used to improve the Transformer architecture by embedding the physical prior knowledge of truss structure vibration into the position encoding of the Transformer architecture, integrating mass matrix constraints into the multi-head self-attention mechanism of the Transformer architecture, and processing aggregated features through the improved Transformer architecture to obtain shared features. An adaptive correlation-aware multi-task output module is used to process shared features to predict the dynamic response time series of the truss structure at different measurement points or coordinate axes. The physical information constraint module is used to calculate the global physical parameters of the truss structure based on the physical model information to construct the structural dynamics equations, and to calculate the physical information residual loss based on the structural dynamics equations and the predicted dynamic response time series. The model optimization unit is used to calculate the total loss function by combining the physical information residual loss and the prediction error loss, and to update and optimize the network parameters in the physical-first multimodal input alignment module, the dynamic multi-scale feature routing and aggregation module, the physically enhanced Transformer module, and the adaptive correlation-aware multi-task output module based on the total loss function.

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