Structural dynamic response prediction method based on graph attention and selection state space network
Through the method of graph attention and selection of state space networks, graph representation and information aggregation of structures is achieved, dynamic response prediction of complex structures is solved, the challenges of accuracy and computing efficiency in the prior art are solved, and the generalization ability of the model is improved.
Patent Information
- Application Number
- CN202411886172.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-20
- Publication Date
- 2025-04-04
AI Technical Summary
The prior art has the dual challenges of accuracy and computational efficiency in structural dynamic response prediction, especially when facing complex and variable structural geometry and parameters, the model has poor generalization ability.
The structure is represented by a method based on graph attention and selecting state space networks. Through the graph attention mechanism and the LSTM network, aggregating the structure physical information and load dynamic information, forming a load-bearing structure characteristic sequence that can reflect the structure static and load dynamics, and input it into the state space module of structural dynamic analysis for prediction.
On the basis of no secondary training, the dynamic response of any geometric topology can be accurately predicted, which improves the generalization ability and computing efficiency of the model, and solves the problem of traditional methods dependence on specific structural configurations and parameters.
Smart Images
Figure CN119760840A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the intersection of civil structural engineering and computer science, and in particular to a structural dynamic response prediction method based on graph attention and selection state space network. Background Art
[0002] Structural dynamic analysis provides a theoretical basis for structural design. The obtained structural dynamic response data can be used to evaluate the bearing capacity and safety of structures under natural disasters such as earthquakes and hurricanes. However, as structures become larger and more complex, traditional structural dynamics numerical analysis methods face the dual challenges of accuracy and computational efficiency.
[0003] Although the early finite element proxy model method improved the computational efficiency, it relied on a large number of parameters to ensure the accuracy of the calculation, and the effect was not good in practical applications. In the past decade, deep learning has become a powerful tool for modeling structural static and dynamic analysis due to its superb ability in modeling nonlinear functions. However, most of the current work is trained for specific structural systems or structural types, resulting in generally poor generalization ability of the model and its own limitations. Because, in the face of different structural geometries and parameters, the existing technology still needs to be improved and developed. Summary of the invention
[0004] The problem to be solved by the present invention is to provide a structural dynamic response prediction method based on graph attention and selective state space network, which can accurately predict the height, span, unit section and other structural parameters of any geometric topological structure without the need for secondary training. The technical solution adopted is as follows: A structural dynamic response prediction method based on graph attention and selection state space network, characterized by comprising the following steps: Step (1): Represent the structure as a graph, convert the complex physical model into graph data, and store the features related to the structure nodes and the features related to the structure units as graph nodes V and edges E respectively; Step (2): Use the graph attention mechanism to further aggregate the physical information of the structure and embed it into the relevant nodes V and edges E respectively, forming a static feature sequence D that integrates the physical information of the structure; Step (3): The static feature sequence D of the fusion structure physical information is merged with the input load dynamic time series sequence, and input into the LSTM network to form a loaded structure feature sequence h that can reflect the static state of the structure and the dynamic state of the load. Step (4): According to the order of the load dynamic time series, the loaded structure characteristic sequence h is merged with the load sub-step, and input into the state space module of the structural dynamic analysis. The graph attention mechanism, LSTM and the state space model of the structural dynamic analysis are used to repeatedly learn and train the data set, and finally the structural dynamic response sequence is output.
[0005] As a preferred solution of the present invention, the step (1) of graphically representing the structure specifically includes: discretizing the structure by a node method, taking the connection points of the structural components as the nodes V of the graph, taking the topological spatial relationship between the nodes as the edges E of the graph, and the discretized structure is a graph G = (V, E). For various structures, they can be simply discretized into particles and units between the particles. Therefore, for any type of structure, the structure can be graphically represented by a similar method.
[0006] As a further preferred embodiment of the present invention, in step (2), the physical information includes structural node characteristics, as well as spatial geometric relationships between nodes or unit-related attributes. The structural node characteristics are embedded into the node V, and the spatial geometric relationships between nodes or unit-related attributes are embedded into the edge E. Thus, the complex and diverse structures are uniformly represented as a discrete graph with nodes and edges as the main elements.
[0007] As a further preferred embodiment of the present invention, the spatial geometric relationship between the nodes or the unit-related properties include unit length, unit cross-sectional parameters, unit material parameters and their combinations; the structural node characteristics include node coordinates, node mass and the frequency, mode, damping, restoring force and their combinations of the structure.
[0008] As a preferred embodiment of the present invention, in step (4), the method for constructing the state space module of the structural dynamic analysis comprises the following steps: Step (4-1): For any structure, its differential equation of motion can be expressed as:
[0009] in, , , are the displacement, velocity and acceleration response vectors of the structure, M and C are the mass and damping matrices, respectively. is the restoring force vector, is the external force vector.
[0010] Step (4-2): Define the state vector of the structure as:
[0011] Step (4-3): Rewrite the differential equation: Step (4-3-1): Assume the restoring force vector is the total elastic response force The force that produces plastic displacement The difference between , the restoring force vector is expressed as: , where the external force vector is the inertia force vector, and K is the stiffness matrix of the structure; Step (4-3-2): Rewrite the differential equation of motion of the structure as:
[0012] in, , and Output position matrices for displacement, velocity, and acceleration respectively; Step (4-4): Convert to discrete state space equation: Under the zero-order hold assumption, the continuous state space equation is converted into a discrete state space equation: in is the time step of structural dynamic analysis, where A and P are defined as learnable parameters, B, C, and for The fully connected output of Step (4-5): Calculate the response of the structure by combining data inversion learning and physical modeling .
[0013] Since the stiffness and damping matrix of the real structure are difficult to calculate accurately, the discrete state space equation is improved by combining data inversion learning with physical model, and the response of the structure is obtained by calculating equation (4): .
[0014] As a further preferred solution of the present invention, the algorithm flow corresponding to the discrete state space equation is as follows: enter: Characteristic sequence h of the loaded structure and the load substep f Merge and output y; 1. ; 2. ; 3. ; 4. ; 5. ; ; 6. ; 7. Calculate formula (4) and formula (3) to get ; 8. ; 9. .
[0015] Compared with the prior art, the present invention has the following advantages: The present invention achieves graph embedding of structural information by combining a multi-layer graph attention network to aggregate the features of the nodes and edges of the graph, thereby extracting the complex spatial correlation features between the discrete nodes of the structure, and splicing this feature with the load on the structure, and inputting it into the selective state space neural network to predict the dynamic time course of the structure. This method can accurately predict any geometric topological structure and structural parameters such as height, span, unit section, etc. without the need for secondary training. It solves the problem of artificial neural network model dependence on specific training structure configuration and parameters. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] Figure 1 is a flow chart of a preferred embodiment 1 of the present invention; Figure 2 It is a schematic diagram represented by the figure in the preferred embodiment 1 of the present invention; Figure 3 It is a schematic diagram of the displacement prediction results of each layer of the structure in the first preferred embodiment of the present invention; Figure 4 It is a schematic diagram of acceleration prediction results in the first preferred embodiment of the present invention; Figure 5 It is a schematic diagram of the bending moment prediction result in the first preferred embodiment of the present invention; Figure 6 is a schematic diagram of shear force prediction results in the first preferred embodiment of the present invention; Figure 7 is a schematic diagram of a simple harmonic vibration system with a single degree of freedom according to a second embodiment of the present invention; Figure 8 This is the nonlinear displacement response time history curve of the second embodiment of the present invention. DETAILED DESCRIPTION
[0017] The following is a further description of the preferred embodiments of the present invention in conjunction with the accompanying drawings.
[0018] Example 1: Predict the structural displacement, acceleration, velocity and other responses of 1,000 steel frame structures.
[0019] Example introduction: 1000 steel frame structures are randomly generated, including 4 to 7 random floors, 2 to 5 random horizontal spans, and 6 to 8 meters random span lengths. The first floor height is 4.2 meters, and the heights of the remaining floors are all 3.2 meters. The frame beams are I-beams, which are selected from 9 preset cross-sections. The columns are square steel, and 5 cross-sections are preset. The Young's modulus of steel is MPa, Poisson's ratio is 0.3, and density is 7900 , the yield strength is 270MPa. To ensure that the generated steel frame structure is practical, three basic conditions need to be met: A. The strength of the low-rise section is higher than that of the high-rise section to enhance the overall stability; B. The beams and columns are divided into inner and outer groups to ensure that the sections on the same floor and within the group remain consistent; C. The structure is designed using the design concept of strong columns and weak beams.
[0020] According to the above example requirements, Figure 1 As shown in FIG, this structural dynamic response prediction method based on graph attention and selection state space network includes the following steps: Step (1) Diagram representation: Figure 2 As shown, the steel frame structure is represented by a graph, the complex physical model of the steel frame structure is uniformly converted into graph data, and the features related to the structural nodes and the features related to the structural units are stored as nodes V and edges E of the graph respectively; specifically, the structure is discretized by the node method, the connection points of the steel frame structure components are taken as the nodes V of the graph, and the topological spatial relationship between the nodes is taken as the edges E of the graph, and the discretized structure is a graph G=(V,E); all points can be represented as V=[v1, v2,……, v12], and the edges can be represented as E=[e1, e2,……, e16], thus forming a graph G=(V,E); Step (2) The physical information of the steel frame structure is further aggregated by using the graph attention mechanism and embedded into the relevant nodes V and edges E respectively, forming a static feature sequence D that integrates the physical information of the structure; wherein the physical information includes the structural node characteristics, as well as the spatial geometric relationship between nodes or unit-related attributes. The steel frame structure node characteristics are embedded into the node V, and the spatial geometric relationship between nodes or unit-related attributes are embedded into the edge E. The steel frame structure node characteristics include the mass, coordinates, frequency, etc. of this point, represented by v1, v2, ..., v12; the spatial geometric relationship between nodes or unit-related attributes include unit length, unit section parameters, etc., represented by e1, e2, ..., e16; For example, the information transmission process of node embedding using a layer of graph attention mechanism is as follows:
[0021] Among them, a, , , is the weight of the graph attention network, , and is a universal activation function. Represented as a node j Belongs to Node i The multi-layer graph attention mechanism is the iteration of the above two calculation formulas on the layer; Step (3) combines the static feature sequence D of the fusion structural physical information with the input load dynamic time series The data are merged and input into the LSTM network to form a loaded structural feature sequence h that can reflect the static state of the structure and the dynamic state of the load. Step (4) In the order of the load dynamic time series, the loaded structure characteristic sequence h is merged with the load sub-step, input into the state space module of the structural dynamic analysis and use the graph attention mechanism, LSTM and the state space model of the structural dynamic analysis; 1000 groups of earthquake motions are randomly selected from the NGA-West 2 and ChiChi-Earthquake databases, and all earthquake motions are modulated according to the code with three types of site effects and a return period of 50 years. The mean value of the earthquake motion response spectrum after amplitude modulation is consistent with the code response spectrum. The finite element method is used to analyze these 1000 frame structures, construct the data set of the method of the present invention, and divide the training set, validation set and test set into a ratio of 7:2:1; through repeated learning and training of the data set, the structural dynamic response sequence is finally output.
[0022] In the above step (4), the method for constructing the state space module for structural dynamic analysis includes the following steps: Step (4-1): For any structure, its differential equation of motion can be expressed as: in, , , are the displacement, velocity and acceleration response vectors of the structure, M and C are the mass and damping matrices, R(t) is the restoring force vector, is the external force vector.
[0023] Step (4-2): Define the state vector of the structure as: Step (4-3): Rewrite the differential equation: Step (4-3-1): Assume the restoring force vector is the total elastic response force The difference between the force that produces plastic displacement , then the restoring force vector is expressed as: , where the external force vector is the inertia force vector, and K is the stiffness matrix of the structure; Step (4-3-2): Rewrite the differential equation of motion of the structure as: in, , and Output position matrices for displacement, velocity, and acceleration respectively; Step (4-4): Convert to discrete state space equation: Under the zero-order hold assumption, the continuous state space equation is converted into a discrete state space equation:
[0024] in is the time step of structural dynamic analysis, where A and P are defined as learnable parameters, B, C, and for The fully connected output of Step (4-5): Calculate the structural response y(t) by combining data inversion learning with physical models.
[0025] Since the stiffness and damping matrix of the real structure are difficult to calculate accurately, the discrete state space equation is improved by combining data inversion learning with physical model, and the response y(t) of the structure is obtained by calculating equation (4).
[0026] In the above step (4-4), the discrete state space equation can adopt the following algorithm flow: enter: Characteristic sequence h of the loaded structure and the load substep f Merge and output y; 1. ; 2. ; 3. ; 4. ; 5. ; ; 6. ; 7. Calculate formula (4) and formula (3) to get ; 8. ; 9. .
[0027] In this example, input: graph G and load , output structural displacement, acceleration, velocity and other responses, the test results are as follows Figure 3-Figure 6 shown.
[0028] Example 2: Predict the displacement response of a simple harmonic vibration system with any single degree of freedom under load, as follows: (1) Any simple harmonic vibration system with a single degree of freedom such as Figure 7 As shown; (2) Since the model of a single-degree-of-freedom simple harmonic vibration system has only one point, the diagram is omitted here, and its diagram G = (V); Its differential equation of motion is: The system's resilience , Cyclic Loading , c is the system damping, the damping ratio is 0.02, and the system damping , where k is the system stiffness; (3) Randomly generate 3600 pairs of angular velocity ω and mass m, thus forming 3600 single-degree-of-freedom systems and corresponding 3600 loads; (4) Using the Newmark-beta method, we can obtain the displacement responses of the 3,600 single-degree-of-freedom systems. We can then construct a data set using these numbers. To repeatedly train the model, we need to supervise the model using the data set. For this purpose, we need a supervised data set. The data set consists of two parts: input and output. Generally, we call the output a label. That is to say, during the training process, you need to tell the model what the correct output is for the graph G and the load you input, and then you can adjust the model so that the output of the model is consistent with the expected result. Here, we can get 3600 input (load + single degree of freedom graph G) and output pairs through the calculation in step (4), so we have obtained 3600 data samples. This data set sample is divided according to function. One part is used for training, one part is used to test whether the model is correct during training, which is called verification, and the other part is used to evaluate the performance of your method after training. So there is a ratio division here, and we divide the number according to the ratio of 7:2:1. (5) Training the model: As mentioned above, during the training process, we actually know the correct output under the current input conditions. To this end, we first need to measure the error between the current model output and the true label. The quantification of this error is called the loss function. Here we use a variety of loss function definitions, such as MSE mean square error and RMSE. After determining the size of the error, the back-propagation algorithm can be used to iteratively update (adjust) the parameters of the deep learning model (neural network model) so that under certain specific parameters, the input graph G and load can get the corresponding response.
[0029] For this reason, after training, the corresponding prediction model is actually obtained; (6) Prediction conclusion Predicted structure such as Figure 8 As shown in Figure G of load + single degree of freedom, the predicted nonlinear displacement response time history curve of single degree of freedom is consistent with the actual curve, and the error is very small.
[0030] In addition, it should be noted that the names of the various parts of the specific embodiments described in this specification may be different, and any equivalent or simple changes made based on the structure, features and principles described in the patent concept of the present invention are included in the protection scope of the patent of the present invention. The technicians in the technical field of the present invention can make various modifications or supplements to the specific embodiments described or replace them in a similar manner, as long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they should all fall within the protection scope of the present invention.
Claims
1. A structural dynamic response prediction method based on graph attention and selection state space network, characterized by The steps include: Step (1): Represent the structure as a graph, convert the complex physical model into graph data, and store the features related to the structure nodes and the features related to the structure units as graph nodes V and edges E respectively; Step (2): Use the graph attention mechanism to further aggregate the physical information of the structure and embed it into the relevant nodes V and edges E respectively, forming a static feature sequence D that integrates the physical information of the structure; Step (3): The static feature sequence D of the fusion structure physical information is merged with the input load dynamic time series sequence, and input into the LSTM network to form a loaded structure feature sequence h that can reflect the static state of the structure and the dynamic state of the load. Step (4): According to the order of the load dynamic time series, the loaded structure characteristic sequence h is merged with the load sub-step, and input into the state space module of the structural dynamic analysis. The graph attention mechanism, LSTM and the state space model of the structural dynamic analysis are used to repeatedly learn and train the data set, and finally the structural dynamic response sequence is output.
2. The structural dynamic response prediction method according to claim 1, characterized in that: The step (1) of representing the structure by graph specifically comprises: discretizing the structure by using a node method, taking the connection points of the structural components as nodes V of the graph, taking the topological spatial relationships between the nodes as edges E of the graph, and the discretized structure is a graph G=(V,E).
3. The structural dynamic response prediction method according to claim 2, characterized in that: In step (2), the physical information includes structural node characteristics, and spatial geometric relationships between nodes or unit-related attributes. The structural node characteristics are embedded in the node V, and the spatial geometric relationships between nodes or unit-related attributes are embedded in the edge E.
4. The structural dynamic response prediction method according to claim 3, characterized in that: The spatial geometric relationship between the nodes or the unit-related properties include unit length, unit section parameters, unit material parameters and their combinations; the structural node characteristics include node coordinates, node mass, and the frequency, mode, damping, restoring force and their combinations of the structure.
5. The structural dynamic response prediction method according to claim 1, characterized in that: In step (4), the method for constructing the state space module of the structural dynamic analysis comprises the following steps: Step (4-1): For any structure, its differential equation of motion can be expressed as: ， in, , , are the displacement, velocity and acceleration response vectors of the structure, M and C are the mass and damping matrices, R(t) is the restoring force vector, is the external force vector. Step (4-2): Define the state vector of the structure as: Step (4-3): Rewrite the differential equation: Step (4-3-1): Assume the restoring force vector is the total elastic response force The force that produces plastic displacement The difference between , the restoring force vector is expressed as: ; Among them, the external force vector is the inertia force vector, is the stiffness matrix of the structure; Step (4-3-2): Rewrite the differential equation of motion of the structure as: ； in, , and Output position matrices for displacement, velocity, and acceleration respectively; Step (4-4): Convert to discrete state space equation: Under the zero-order hold assumption, the continuous state space equation is converted into a discrete state space equation: ； in is the time step of structural dynamic analysis, where A and P are defined as learnable parameters, B, C, and for The fully connected output of Step (4-5): Calculate the response of the structure by combining data inversion learning and physical modeling .
6. The structural dynamic response prediction method according to claim 5, characterized in that: The algorithm flow corresponding to the discrete state space equation is as follows: enter: Characteristic sequence h of the loaded structure and the load substep f Merge and output y; 1. ； 2. ； 3. ； 4. ； 5. ； ； 6. ； 7. Calculate formula (4) and formula (3) to get ; 8. ； 9. 。