Agent Model and Finite Element Fusion Method and System for Bridge Safety Early Warning

Abstract

The present invention belongs to the technical field of bridge engineering, and specifically discloses a method and system for fusing a surrogate model and a finite element for bridge safety warning. The method includes: using a finite element model with structural multi-scale to simulate the real load of the bridge to calculate the bridge structure response, constructing a finite element surrogate model, and training the finite element surrogate model with a data set to extract the relationship between the weight matrix analysis of the neural network and the output items; at the refined mesh division part, considering the damage directly observed in the structure, dividing the model parameters extracted from the monitoring points by the model parameters directly corrected by the damage to obtain the finally corrected model. The present invention tightly combines sensor signal processing, model correction, and finite element calculation through neural network analysis, provides a method basis for the dynamic evolution of the numerical-physical fusion model, and provides technical support for subsequent bridge structure safety assessment and health warning.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge engineering, and more specifically, relates to a method and system for fusing a proxy model and a finite element for bridge safety warning. Background Art

[0002] The concept of digital twin is in an increasingly important position with the progress of science and technology and the growing transportation construction. Subsequently, it is the improvement of complementing the last link of the bridge health monitoring system using the technology of integrating digital and physical entities. In the construction of the concept of integrating digital and physical entities, dynamically updating and correcting the structural model based on on-site sensor signals is an effective means in the technical construction, and it can also timely reflect the real condition of the structure.

[0003] In the process of integrating digital and physical entities, how to reasonably design the information description method of the model for the twin object and improve the structural information included in the model establishment process is a very important link. For a finite element model with perfect physical and mechanical relationships, the current structural analysis needs to update the current information based on sensors in a timely manner. Using a multi-scale finite element model can not only display the structural behavior changes and predictions at the full-bridge scale, but also use the refined simulation at the component scale to carefully analyze the stress evolution trend. Therefore, calculating and predicting the health state of the bridge structure by establishing a finite element model is a method with high calculation efficiency and high operation accuracy.

[0004] In the finite element model correction, there are three common methods, mainly analyzing the sensitivity matrix of the structural correction parameters, sampling the Bayesian probability method by the Monte Carlo method to deduce the likelihood function expression of the structure, and establishing a proxy model to directly calculate the appropriate adjustment parameters of the model for rapid correction; and the indicator parameter for participating in the model correction process to judge whether the structure is damaged is the frequency response function. Through the existing model correction methods, it is difficult to use the frequency response function of the structure to judge the damage information of the structure in practical engineering applications, and the generated model correction cannot verify whether its correction results are reasonable in long-term applications. Correcting the structural model based on the static response of the structure through a proxy model can effectively solve this problem. Summary of the Invention

[0005] In view of the above deficiencies or improvement requirements of the prior art, the present invention provides a proxy model and finite element fusion method and system for bridge safety early warning. By establishing a multi-scale finite element model, simulated loads are applied at the excitation monitoring points to obtain the response monitoring point signals. The excitation and response information of each node is integrated as the input, and the calculation information of the multi-scale finite element model is extracted as the output, serving as the input data set of the neural network. A proxy model is established and trained to analyze the relationship between [excitation signal - response signal] and [finite element model parameters]. The proxy model is used to analyze the on-site excitation monitoring point signals and response monitoring point signals to obtain the finite element model parameters (material properties and geometric parameters of the elements) extracted from the monitoring point signals. For the refined mesh division part, the directly observed damage needs to be corrected. The model parameters extracted from the monitoring points are divided by the model parameters directly corrected for damage to obtain the finally corrected model. By establishing a proxy model of PINN, the on-site sensor excitation-response signals are quickly processed, and the calculation parameters of the finite element model are directly output, quickly correcting the multi-scale finite element model. Further, real-time dynamic correction results of the finite element model can be obtained through limited time series signals. It provides a method basis for the dynamic evolution of the numerical-physical fusion model and technical support for subsequent bridge structure safety assessment and health early warning.

[0006] To achieve the above object, according to one aspect of the present invention, a proxy model and finite element fusion method for bridge safety early warning is proposed, including the following steps:

[0007] Step 1, using a multi-scale finite element model of the structure to simulate the real load of the bridge to calculate the bridge structure response, and constructing a data set based on the real load and the structure response;

[0008] Step 2, constructing a finite element proxy model, and training the finite element proxy model with the data set to extract the relationship between the weight matrix analysis and the output items of the neural network;

[0009] Step 3, directly correcting the finite element model with the on-site monitored structural damage information for damage correction;

[0010] Step 4, using the trained finite element proxy model to analyze the on-site monitored excitation monitoring point signals and response monitoring point signals to obtain the model correction parameters based on data analysis;

[0011] Step 5, obtaining a corrected multi-scale finite element model according to the damage correction and the model correction parameters based on data analysis;

[0012] Step 6, using the corrected multi-scale finite element model to generate a data set for training and updating the finite element proxy model.

[0013] As a further preferred option, Step 1 includes the following steps:

[0014] Establish a refined component model according to the division of component positions and structures of sensors, divide the parts that need to establish a refined model according to the sensor network and key monitoring points of the structure, analyze the degradation models selected for different parts and different materials of the model, and then establish a multi-scale finite element model of the structure based on the bridge design drawings;

[0015] By applying an excitation signal or generating a simulated excitation to the multi-scale finite element model, generate a dataset for training the neural network, which contains the signals of excitation monitoring points and response monitoring points.

[0016] As a further preference, in step two, the finite element surrogate model is any one of polynomial response surface, BP neural network, radial basis function, and Kriging model.

[0017] As a further preference, in step two, in the finite element surrogate model, the virtual work principle equation is used as the physical constraint for the loss function part:

[0018] ,

[0019] In the formula, represents the variation of the total virtual work, , are the stress tensor component and body force density component in the i direction respectively, is the surface force per unit area in the i direction, is the direction vector of the i end of the element to be solved, is the strain component at the i end, V is the volume of the element for integrating the body force, and S is the area of the element for integrating the surface force;

[0020] The loss function also includes:

[0021] ,

[0022] In the formula, , , , are the acceleration, velocity, displacement, and external force time series of the structural space nodes, and M, C, and K are the mass, damping, and stiffness distributions of the system.

[0023] As a further preference, in step three, damage correction is performed on the finite element model according to the damage type of the structure, specifically including:

[0024] If the structural damage is a crack in the concrete part, damage correction is performed on the finite element model by increasing the number of nodes in the finite element model and modifying the boundary conditions, and it is necessary to recalculate the influence matrix a of the overall structural calculation parameters of the added and subtracted nodes ij;

[0025] If the structural damage is the deterioration of material properties, the model correction parameters are calculated through the equivalent property correction parameters obtained by sensor signal analysis. After that, as the physical constraint of the neural network, the finite element model is directly corrected for damage;

[0026] If the structural damage is the change of structural geometric parameters, the relevant cross-section property parameters of the structure are recalculated, and the model correction parameters are calculated. After that, as the physical constraint of the neural network, the finite element model is directly corrected for damage.

[0027] As a further optimization, in step four, the trained finite element surrogate model is used to analyze the signals of the excitation monitoring points and the response monitoring points monitored on site. By comparing the neural network calculation parameters of each node with the calculation parameters of the initial model, the model correction parameter β based on data analysis is obtained:

[0028] ,

[0029] In the formula, represents the model parameters of the structure in the current state, represents the model parameters of the bridge structure in the initial state, is the model parameter of the structure calculated from the sensor data.

[0030] As a further optimization, step five specifically includes the following steps:

[0031] If the model correction parameter is consistent with the model correction parameter β in terms of the correction target but inconsistent in terms of the correction time, then the model correction parameter is directly used as the physical constraint to train the neural network;

[0032] If the model completes health monitoring at this time and the model correction parameter directly obtained through monitoring can explain the state of the structure, then the model correction parameter represents the refined component adjustment parameter γ;

[0033] If the model correction parameter will cause an adjustment of the overall model, or a new physical constraint is generated when monitoring the bridge structure at this time, then the model correction parameter β and the model correction parameter are used to construct the refined component adjustment parameter γ, and the refined component adjustment parameter γ is used to complete the update of the finite element model to obtain the corrected multi-scale finite element model.

[0034] As a further optimization, the calculation process of the refined component adjustment parameter γ is as follows:

[0035] If the direct correction object can be solved through data analysis but has not been obtained through tests at the present stage, then = ;

[0036] If the correction object has completed tests and obtained accurate data that can be directly used for correction, then = ;

[0037] If the data obtained through on-site tests or direct monitoring cannot fully describe the structural state, then = ;

[0038] Among them, , are the model correction parameters directly obtained through on-site monitoring of the damage at the position of node j of the model and the model correction parameters obtained through calculating data by the surrogate model respectively, is the refined component adjustment parameter for the finite element model of node j, are the model correction parameters directly obtained through on-site monitoring of the damage at the position of node i of the model and the model correction parameters obtained through calculating data by the surrogate model, a ij is the influence matrix of the changes in all node calculation parameters after the changes in the calculation parameters related to node i of the structure.

[0039] As a further preference, it further includes performing bridge safety early warning by using the updated multi-scale finite element model.

[0040] According to another aspect of the present invention, there is also provided a bridge safety early warning system based on the fusion of a surrogate model and a finite element model, including:

[0041] The first main control module is used to simulate the real load of the bridge by using the finite element model of the structural multi-scale to calculate the bridge structure response, and construct a data set based on the real load and the structure response;

[0042] The second main control module is used to construct a finite element surrogate model and train the finite element surrogate model by using the data set to extract the relationship between the weight matrix analysis of the neural network and the output items;

[0043] The third main control module is used to directly correct the finite element model by using the structural damage information monitored on site for damage correction;

[0044] The fourth main control module is used to analyze the excitation monitoring point signal and the response monitoring point signal monitored on site by using the trained finite element surrogate model to obtain the model correction parameters based on data analysis;

[0045] The fifth main control module is used to obtain a corrected multi-scale finite element model according to the damage correction and the model correction parameters of the data analysis.

[0046] The sixth main control module is used to generate a data set for training and updating the finite element surrogate model by using the corrected multi-scale finite element model.

[0047] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the following technical advantages are mainly possessed:

[0048] 1. The model fusion method provided by the present invention quickly analyzes the excitation-response signal through the surrogate model, obtains the corrected calculation parameters of the finite element model, and directly corrects the finite element model by using the damage obtained by the sensor. It takes into account the defect information obtained by on-site sensor monitoring and the data information of the excitation-response monitoring points, realizes the dynamic evolution of the digital model, and improves the risk assessment efficiency and accuracy.

[0049] 2. The model fusion method provided by the present invention can identify structural damage by using information such as the stiffness and geometric features of the structure based on the updated finite element model. Compared with the frequency response characteristic function often used in the current model correction, it has the advantages of high response accuracy and can be directly applied to subsequent finite element calculations.

[0050] 3. The present invention uses the vectorized finite element as the finite element model for model correction, which can not only avoid the integration of the stiffness matrix during the calculation process, reduce the finite element analysis time for integrating the overall stiffness matrix due to structural parameter changes, but also optimize the establishment of the updated model during the analysis process of the multi-scale finite element model. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a flowchart of a surrogate model and finite element fusion method for bridge safety warning according to an embodiment of the present invention;

[0052] Figure 2 is a convergence graph of the calculated MSE of the surrogate model according to the number of iteration steps in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0053] As Figure 1 shown, a surrogate model and finite element fusion method for bridge safety warning provided by an embodiment of the present invention analyzes the on-site sensor signals and uses a neural network to replace the multi-scale finite element model to analyze the dynamic evolution information of the bridge in real time, including the following steps:

[0054] S1: Establish a structural multi-scale finite element model based on the bridge design drawings. Here, the multi-scale means that the model grid sizes are non-uniform under the same finite element model, especially at the positions where the excitation sensors and response sensors are arranged. The finite element model is divided into refined grids at these positions to facilitate the comparison of calculation results at different monitoring positions in the same cross-section. The multi-scale finite element model can use the excitation data collected in advance or stored in the database. The macroscopic damage that can be reflected in the finite element model is corrected by directly adding or subtracting nodes, and other numerical aspects are achieved by modifying the model calculation parameters. After the initial multi-scale finite element model is established, according to the requirements of model training, different model parameters are used to generate bridge structure models corresponding to different safety states, and the excitation-response pairs of the neural network are generated as the pre-training dataset.

[0055] In this step, the surrogate model is established based on the neural network. Especially compared with the traditional neural network surrogate model, using PINN (Physics-Informed Neural Networks) to establish the surrogate model can ensure the physical prior characteristics of the generated data, reduce the data requirements, and optimize the solution process of complex models.

[0056] The finite element model used is a multi-scale finite element model, especially a multi-scale vector finite element. In the vector finite element, the structural response caused by external excitation is described by the nodal behavior instead of the element analysis method of the traditional finite element. Using the element stiffness analysis instead of the integrated stiffness matrix in the traditional finite element can effectively accelerate the finite element analysis process, and it has good compatibility with the model correction process without the need for an integrated stiffness matrix.

[0057] S2: Establish a neural network surrogate model for quickly solving the current structural model information based on the signals of the excitation monitoring points - response monitoring points. The input variables of the neural network are the signals of the bridge excitation monitoring points - response monitoring points. The structural node connection information is determined by setting the weight functions of the first few connection layers. The model calculation parameters required for structural calculation are obtained through the analysis of the surrogate model.

[0058] S3: Directly correct the structural model based on the structural damage monitored by on-site sensors, and calculate the model correction parameters for the preliminary adjustment of the structure. When the damage monitored by on-site sensors requires adding or subtracting finite element model nodes, such as crack propagation, etc., the material properties and geometric parameters of the structure need to be adjusted, including cross-sectional area, moment of inertia of the cross-section for bending, moment of inertia of the cross-section for torsion, etc. When the damage information only involves adjusting the material properties of the structure, such as concrete carbonation, steel bar corrosion, etc., the cross-sectional area is corrected in this step. The specific structural parameters to be adjusted are related to the type of sensor monitoring data and the type of structure. The formula here only shows the adjustment calculation of stiffness. The adjustment parameter calculation of the structural model stiffness is as follows:

[0059]

[0060] wherein, represents the stiffness of the structure in the current state, represents the stiffness of the bridge structure in the initial state, is the equivalent model property adjustment parameter directly corrected based on the damage data directly monitored by the on-site sensors of the structure. Different types of parameters are distinguished by subscripts, such as represents the correction parameter of Young's modulus.

[0061] S4: Use the surrogate model processor to analyze the excitation monitoring point information - response monitoring point information, output the model information obtained from the [excitation signal - response signal] data analysis, compare the model calculation parameters (such as Young's modulus E, cross-sectional calculation area A, moment of inertia I, etc.) of each finite element model node with the information of the initial finite element model to obtain the model correction parameter β based on the data analysis. Derive the inverse function of the weight matrix of the neural network for the model calculation information, improve the physical relationship between the excitation and response revealed by the established surrogate model, and improve the rationality of the model. For example, analyze the relevant relationship between the information of a certain neuron node and the final output, and whether its calculation process can be reflected in the specific calculation formula of the finite element. Or by analyzing the connections between multiple neuron nodes, calculate how to deduce the relationship between the weight matrix and the final output through the inter-layer connections of these neurons.

[0062]

[0063] wherein, represents the model parameters of the structure in the current state, represents the model parameters of the bridge structure in the initial state, is the model parameter of the structure under the calculation of the sensor data.

[0064] S5: The update of the final finite element model not only includes direct damage correction, but also includes model correction information at the data level obtained from the analysis of on-site sensor signals. If the corresponding calculation parameters (such as properties like Young's modulus characterizing concrete deterioration) can be directly obtained through on-site sensor monitoring of damage, it indicates that the direct correction parameter α should be consistent with the data-driven correction parameter β, and then the direct correction parameter α can be used as a physical constraint for neural network training. If the direct correction parameter α causes an adjustment of the overall model (such as local cracks in a concrete member resulting in a change in cross-sectional area, etc.), or when the state of the bridge structure is monitored at this time (generating new physical constraints), then accurate model adjustment parameters for describing the current state of the model cannot be obtained only through the direct correction parameter α or the data-driven correction parameter β. At this time, subtracting the influence of the change in the structural model parameter α obtained through on-site sensor analysis in S3 from the data-driven model correction parameter β at the relevant nodes can obtain a more accurate correction result. The refined component adjustment parameter in this step is This process requires several time-step iterations until the structural calculation response is less than a predetermined range from the sensor on-site monitoring response; if the calculation result error is greater than the preset range, the neural network surrogate model needs to be retrained and then return to S4 to recalculate the adjustment parameters of the structure.

[0065] The calculation process of the refined component adjustment parameter γ is as follows:

[0066] If the direct correction object can be solved through data analysis and has not been obtained through experiments at the present stage, then = ;

[0067] If the correction object has completed experiments and accurate data that can be directly used for correction are obtained, then = ;

[0068] If the data obtained through on-site experiments or direct monitoring cannot fully describe the structural state, then = ;

[0069] Among them, , are the model correction parameters directly through on-site monitoring damage at the position of node j of the model and the model correction parameters obtained through calculating data by the surrogate model respectively, is the refined component adjustment parameter for the finite element model of node j, is the model correction parameter directly through on-site monitoring damage at the position of node i of the model and the model correction parameters obtained through calculating data by the surrogate model, a ij is the influence matrix of the change in all node calculation parameters after the change in the relevant model calculation parameters of node i of the structure.

[0070] The method further includes the following steps:

[0071] S6: Generating a dataset of [excitation signal - response signal] and [finite element model calculation parameters] using the corrected finite element model in S5 for updating the neural network surrogate model.

[0072] Embodiment 2

[0073] In this embodiment, the neural network surrogate model is used to quickly update the model based on the on-site sensor signals. The finite element model information and the on-site sensor monitored excitation - response information are input into the surrogate model, and the calculation information of the structural finite element model is directly output.

[0074] The surrogate model is established using PINN. Since PINN requires constraints to be imposed during the calculation process, the constraints are not only the structural mechanics equations as hard constraints, but also the value range of the signal adjustment parameters and the boundary conditions of the finite element model can be used as soft constraints.

[0075] Structural model adjustment parameter represents the ratio of the current structural parameters to the initial state. The value range of the structural model adjustment parameter is between 0 and 1 because the performance of the structure is in a degraded state during use. Under regular maintenance of the structure, the structural model adjustment parameter may exceed 1, and in this case, the neural network needs to be redesigned.

[0076] The data input into PINN varies according to the model adjustment parameters that need to be corrected. For example, if the cross-section adjustment parameter of the structure needs to be adjusted, the tensile response information of the structure under excitation needs to be input; if the torsional section moment of inertia of the structure needs to be adjusted, the monitoring information of the torque sensor of the structure needs to be input.

[0077] A multi-scale finite element model is established, and different finite element parts are established using elements with different mesh division precisions. For the parts that need to finely simulate the behavior of components, the modeling scale is smaller than that of other units. Through fine modeling, not only can the detailed damage be simulated on the entire finite element model, but also the local analysis of the fine model can isolate the damage input by the on-site sensors.

[0078] The structural types of the established bridge structure model include, but are not limited to: beam bridges, arch bridges, suspension bridges, and cable-stayed bridges.

[0079] According to the established finite element structure model, the sensor monitoring points are reasonably arranged and the fine simulation parts are divided. The detailed component models are set according to the structural monitoring requirements. The fine components include, but are not limited to, the sensor monitoring points, and in addition, some parts that are prone to performance degradation are also involved.

[0080] The established and corrected finite element model can not only be used for structural calculation, but also generate a neural network training set.

[0081] Based on the above, the method in this embodiment includes:

[0082] S1: Establish a structural multi-scale finite element model based on the bridge design drawings, and establish a refined component model according to the sensor layout position and the component division of the structure. Divide the parts that need to establish a refined model according to the sensor network and the key monitoring points of the structure. Analyze the degradation models selected for different parts and different materials of the model. By applying the excitation signal stored in the cloud server or the generated simulated excitation to the multi-scale finite element model, generate the excitation monitoring point - response monitoring point signal pair of the pre-training data set for the neural network.

[0083] S2: Establish a PINN proxy model processor for quickly solving the correction parameters of the current structure model information based on the excitation monitoring point - response monitoring point signal. The input variable of the neural network is the excitation monitoring point - response monitoring point signal pair of the bridge at the previous time step, and the calculation parameters of the structural finite element model are obtained. . The structural parameter adjustment information is extracted and the weight matrix between the fully connected layers is verified by back-calculation, which is then used for subsequent structure correction. In this step, only the neural network is pre-trained, and the generated adjustment parameters need to be verified through the subsequent verification of the structure correction results.

[0084] Among them, PINN is a network model that adds an equation of physical relationship as a soft constraint or a hard constraint in the calculation process of the neural network loss function. It takes into account the physical relationship between the output variables and makes it meet the prior conditions. In the establishment of the PINN model in structural mechanics, the virtual work principle equation is usually used as the physical constraint for the loss function part, and the loss function of the model can be calculated through the above formula and participate in the training process of the neural network. As shown in the following formula:

[0085] .

[0086] This formula describes the structural state variables in the space coordinates, where represents the variation of the total virtual work of the system, , is the variable on the volume of the system in the i direction, which are the stress tensor component and the body force density component respectively, is the surface force per unit area of the system in the i direction.

[0087] Similarly, there is also a case where the motion equation is used as the physical constraint for the loss function part. This physical constraint relationship is well compatible with the calculation parameter verification of the vectorized finite element to be used in the present invention.

[0088] 。

[0089] This equation describes the time-state variables in space coordinates. In the equation, , , , are the acceleration, velocity, displacement, and external force time series of the structural space nodes, and M, C, and K are the mass, damping, and stiffness distributions of the system.

[0090] S3: Directly modify the structural model based on the structural damage monitored by sensors. According to the main damage types of the structure, different damage correction methods for the finite element model are designed. If the structural damage is a crack in the concrete part, the finite element model is damaged and corrected by increasing the number of nodes in the finite element model and modifying the boundary conditions, and it is necessary to recalculate the influence matrix a of the overall structural calculation parameters of the added and reduced nodes ij ; if the structural damage is the deterioration of material properties, the model correction parameters are calculated through the equivalent property correction parameters obtained from the sensor signal analysis and used as the physical constraints of the neural network to directly correct the damage of the finite element model; if the structural damage is the change of structural geometric parameters, the relevant cross-sectional property parameters of the structure are recalculated, and the model correction parameters are calculated and used as the physical constraints of the neural network to directly correct the damage of the finite element model. The model correction parameters of the remaining parts without damage correction are all 1, indicating that the ratio of the relevant parameters before and after model correction is 1.

[0091] S4: Use the surrogate model processor to analyze the excitation monitoring point-response monitoring point signal pairs monitored by on-site sensors, directly obtain the calculation parameters of the finite element using the PINN surrogate model, and analyze the rationality of the neural network analysis results using the significance analysis of the weight matrix between the fully connected layers proposed in S2. Finally, by comparing the neural network calculation parameters of each node with the calculation parameters of the initial model, the model correction parameter β based on data analysis is obtained.

[0092]

[0093] In the equation, represents the model parameters of the structure in the current state, represents the model parameters of the bridge structure in the initial state, is the model parameter of the structure calculated from the sensor data.

[0094] S5: The update of the final finite element model not only includes direct damage correction, but also includes model correction information at the data level obtained from the analysis of on-site sensor signals. If the corresponding calculation parameters (such as properties like Young's modulus characterizing concrete deterioration) can be directly obtained by monitoring damage through on-site sensors, it indicates that the direct correction parameter α should be consistent with the data-driven correction parameter β, and then the direct correction parameter α can be used as a physical constraint for neural network training. If the direct correction parameter α causes an adjustment of the overall model (such as local cracks in a concrete member resulting in a change in the cross-sectional area, etc.), then accurate model adjustment parameters for describing the current state of the model cannot be obtained only through the direct correction parameter α or the data-driven correction parameter β. At this time, subtracting the influence of the change in the structural model parameter α obtained through on-site sensor analysis in S3 from the data-driven model correction parameter β at the relevant nodes can obtain a more accurate correction result. This process requires several time-step iterations until the structural calculation response is less than a predetermined range compared with the on-site sensor monitoring response; if the calculation result error is greater than the preset range, the neural network surrogate model needs to be retrained and then return to S4 to recalculate the adjustment parameters of the structure. Finally, use Multiply by the calculation parameters of the corresponding nodes of the finite element model to complete the update of the finite element model based on sensor signals using the surrogate model. The calculation process of

[0095] If the direct correction object can be solved through data analysis and has not been obtained through experiments at this stage, then = ;

[0096] If the correction object has completed the experiment and obtained accurate data that can be directly used for correction, then = ;

[0097] If the data obtained through on-site experiments or direct monitoring cannot fully describe the structural state, then = ;

[0098] Among them, , are the model correction parameters directly obtained from on-site monitoring damage at the position of node j of the model and the model correction parameters obtained through surrogate model calculation data respectively, is the refined component adjustment parameter for the finite element model of node j, a ij is the influence matrix of the changes in the calculation parameters of all nodes after the change in the calculation parameters of the relevant model of node i of the structure.

[0099] The method further includes the following steps:

[0100] S6: Generate excitation-response data pairs using the corrected finite element model in S5 for updating the PINN surrogate model.

[0101] Furthermore, for simple geometric boundary conditions, the loss function of the displacement at the boundary condition can be constrained through calculation; for the boundary conditions of the load, it can be achieved by establishing the calculation relationship of the mechanical parameters in this node (for example, the equivalent shear spring stiffness can be obtained by calculating the ratio of the node shear force to the displacement and then making a comparison), which further reflects the use of physical constraints in the neural network established in the present invention.

[0102] Furthermore, compared with the traditional finite element model, the finite element model can effectively reduce the storage space of the model, avoid the integrated calculation of the stiffness matrix during the calculation process, and improve the calculation efficiency of the finite element structural model in the time series. Improve the efficiency and convergence speed of the finite element calculation process.

[0103] Furthermore, based on the established finite element model, combined with traditional finite element simulation of the structural elastic state, a linear analysis is performed on the structure.

[0104] Example 3

[0105] In this example, a method for fusing a PINN surrogate model and a finite element structural model for bridge safety warning is described in detail.

[0106] It should be noted that the finite element surrogate model is used in the present invention to find the model calculation parameters that can be calculated by comparison to reflect the mapping relationship between the sensor excitation-response signals. The finite element surrogate model can be a polynomial response surface (P-RSM), a BP neural network, a radial basis function (RBF), a Kriging model, etc., and this example does not make specific limitations on this.

[0107] It should be noted that except for the parts where the nonlinear behavior or the stiffness changes and need to be established by the finite element method, the traditional finite element can be used for the parts where the structural calculation parameters do not change.

[0108] The embodiments described herein are specific specific embodiments of the present invention for explaining the concept of the present invention, and are all explanatory and exemplary, and should not be construed as limiting the embodiments of the present invention and the scope of the present invention. Except for the embodiments described herein, those skilled in the art can also adopt other obvious technical solutions based on the content disclosed in the claims and the description of the present application. These technical solutions include technical solutions that make any obvious substitutions and modifications to the embodiments described herein.

[0109] This example proposes a method for fusing a PINN surrogate model and a finite element structural model for bridge safety warning, in order to Figure 2Taking the model fusion step diagram shown as an example, it includes the following steps:

[0110] S1: Establish a structural multi-scale finite element model based on the bridge design drawings, and establish a refined component model according to the sensor layout positions and component divisions of the structure. In this case, a simply supported beam model with eight nodes is used for calculation, and only the model correction at the full-bridge scale is shown. It is assumed that the sensors are arranged at nodes 4 and 5. The external excitation is a downward impact load of 1000 kN applied at the monitoring points.

[0111] Furthermore, under simple load conditions, the main information of the structural model is: the elastic modulus, cross-sectional area, and flexural moment of inertia of the elements, and the length of the elements. The main information provided by the nodes is the mass of the nodes. In the simple model listed, only planar motion is involved. When solving for a complex model and involving three-dimensional space calculations, the calculation space needs to be extended, mainly the structural information and external excitation information of the model to three-dimensional space. The response information of the structural sensor signals also needs to be extended to three-dimensional space.

[0112] Furthermore, since the data dimensions of the node information and element information are different during the finite element calculation process, but they provide descriptive features of the structural information, information preprocessing is required (such as filling 0 at the end or in the middle of the data, using a 1D CNN to process the model data) to solve the problem of different numbers of neural network sample features.

[0113] S2: Establish a PINN proxy model processor for quickly solving the correction parameters of the current structural model information based on the excitation-response signals at the sensor points. The input to the neural network is [excitation signal - response signal] at each node at a certain time, and the main information of the structural model at this time as the output of the neural network is: the elastic modulus, cross-sectional area, and flexural moment of inertia of the elements, and the length of the elements. The main information provided by the nodes is the mass of the nodes. Extract the relationship between the weight matrix analysis of the neural network and the output items.

[0114] Furthermore, in this case, the input and output of the neural network are classified according to the finite element model nodes. That is to say, first, the excitation-response monitoring point data needs to be sorted to the corresponding node positions as the input. Similarly, the types of input data can be classified, with the excitation monitoring point signals grouped into one category and the response monitoring point signals grouped into one category.

[0115] Furthermore, in the preprocessing of the data, for the input and output of complex data types, a custom preprocessing method needs to be designed independently, and the neural network code is integrated according to the task requirements. For example, if it is necessary to input the model data of the multi-scale finite element model into the proxy model for other analysis purposes, a preprocessing program needs to be written or the inter-layer connections of the first few layers of neurons need to be set.

[0116] Similarly, in the output of data, the relationship of the output values and the rationality of the output data can be determined by analyzing the units of each parameter. Among the output parameters, the units of the cross-sectional area and the moment of inertia of the cross-section in terms of geometric dimensions are m 2 and m 4 , respectively. The rationality of the output parameters can be verified by analyzing the derivatives of the two with respect to length.

[0117] S3: Directly correct the structural model based on the structural damage monitored by on-site sensors. This model is a simple simply supported beam model, and no refined component model is established. Therefore, only the calculation and update of the material adjustment parameters are carried out. Assume model damage through code setting of random numbers to obtain the model correction parameters obtained from sensor data . If the damage is a change in the geometric parameters of the structure, recalculate the parameters such as the cross-sectional properties of the structure and directly correct the corresponding parameters.

[0118] As a further supplement to the above scheme, the correction of the calculation parameters involved in this case will not affect the total number of nodes. If the situation of adding finite element model nodes appears during the model correction process, it is necessary to return to S1, re-establish a model with added nodes, and retrain the surrogate model.

[0119] S4: Use the surrogate model processor to analyze the excitation monitoring point - response monitoring point signals monitored by on-site sensors, output the calculation parameters of the multi-scale finite element model, and extract the weight matrix of the neural network to analyze the rationality of the calculation results. Input the data of the sensor excitation monitoring points collected into the finite element model established by calculating the parameters of the neural network, and compare the response monitoring points data to analyze the rationality of the corrected model.

[0120] S5: The correction of the final finite element model needs to exclude the influence of directly corrected damage. However, in this case, there is no model damage that needs to be directly corrected in the structure. Therefore, the calculation results in S4 are used as the calculation parameters of the updated finite element model. This process requires several time-step iterations until the structural calculation response is consistent with the on-site sensor monitoring response.

[0121] The method further includes the following steps:

[0122] S6: Use the finite element model corrected in S5 to generate excitation - response data pairs for updating the PINN surrogate model. Since the finite element model has been determined to be damaged after calculation, the model adjustment parameters calculated by the PINN surrogate model in the next time step are based on the damaged model corrected in S5.

[0123] Further, the cumulative damage information of the model can be obtained by dividing the relevant parameters of the nodes by the calculation parameters of the original model. By making a chart of the cumulative damage parameters obtained at different times, a deterioration model of the relevant parameters can be obtained. Comparing the deterioration model proposed through experiments can determine the rationality of the correction process.

[0124] Specifically, the bridge to be evaluated is a physical bridge to be evaluated for building safety. In this embodiment, there are no restrictions on the structure and material properties of the bridge to be evaluated. The bridge to be evaluated includes, but is not limited to, ancient building bridges, cross-sea bridges and other bridges of various architectural forms and uses. The original bridge design drawing is a drawing that reflects various building data of the bridge obtained by drawing according to the built bridge or according to the historical building information of the bridge. The original bridge design drawing is marked with building data and building material information. The bridge connection point is the splicing site of multiple bridge components for the purpose of constructing the bridge body and achieving balanced load-bearing force.

[0125] Of course, based on any of the above embodiments or a combination of multiple embodiments, the present invention also provides a system for bridge safety warning using the above method.

[0126] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A proxy model and finite element fusion method for bridge safety warning, characterized in that, It includes the following steps: Step 1: Use a finite element model with structural multi-scale to simulate the real load of the bridge to calculate the bridge structure response, and construct a data set based on the real load and the structure response; Step 2: Construct a finite element surrogate model, and use the data set to train the finite element surrogate model to extract the relationship between the weight matrix analysis of the neural network and the output items; Step 3: Directly correct the finite element model using the structural damage information monitored on site for damage correction, and calculate the model correction parameter α for the preliminary adjustment of the structure; Step 4: Use the trained finite element surrogate model to analyze the excitation monitoring point signal and the response monitoring point signal monitored on site to obtain the model correction parameter β based on data analysis; Step 5: Obtain the corrected multi-scale finite element model according to the model correction parameters of damage correction and data analysis; Step 5 specifically includes the following steps: If the model correction parameter α and the model correction parameter β have the same correction target but different correction times, directly use the model correction parameter α as a physical constraint to train the neural network; If the model completes health monitoring at this time, and the model correction parameter α directly obtained through monitoring can explain the state of the structure, then the model correction parameter α represents the refined component adjustment parameter γ; If the model correction parameter α will cause an adjustment of the overall model, or if a new physical constraint is generated when monitoring the bridge structure at this time, then use the model correction parameter β and the model correction parameter α to construct the refined component adjustment parameter γ, and use the refined component adjustment parameter γ to complete the update of the finite element model to obtain the corrected multi-scale finite element model; Step 6: Use the corrected multi-scale finite element model to generate a data set for training and updating the finite element surrogate model.

2. The proxy model and finite element fusion method for bridge safety warning according to claim 1, characterized in that Step 1 includes the following steps: Establish a refined component model according to the sensor layout position and the component division of the structure, divide the part that needs to establish a refined model according to the sensor network and the key monitoring points of the structure, analyze the degradation models selected for different parts and different materials of the model, and then establish a structural multi-scale finite element model based on the bridge design drawings; By applying an excitation signal or generating a simulated excitation to the multi-scale finite element model, generate a data set containing the excitation monitoring point and response monitoring point signals for training the neural network.

3. A proxy model and finite element fusion method for bridge safety warning according to claim 1, characterized in that, In Step 2, the finite element surrogate model is any one of a polynomial response surface, a BP neural network, a radial basis function, and a Kriging model.

4. A proxy model and finite element fusion method for bridge safety warning according to claim 3, characterized in that, In Step 2, in the finite element surrogate model, the virtual work principle equation is used as a physical constraint for the loss function part: where δΠ represents the variation of the total virtual work, σ ij,j , f j are the stress tensor component and body force density component in the i direction respectively, is the surface force per unit area in the i direction, n j is the direction vector at the i end of the element to be determined, u i is the strain component at the i end, V is the volume of the element for body force integration, and S is the area of the element for surface force integration; The loss function also includes: In the formula, u, F are the time series of acceleration, velocity, displacement and external force of the structural space nodes, and M, C, K are the mass, damping and stiffness distributions of the system.

5. A proxy model and finite element fusion method for bridge safety warning according to claim 1, characterized in that In Step 3, damage correction is performed on the finite element model according to the damage type of the structure, specifically including: If the structural damage is a crack in the concrete part, the finite element model is corrected for damage by increasing the number of nodes in the finite element model and modifying the boundary conditions, and it is necessary to recalculate the influence matrix a of the overall structural calculation parameters of the added and subtracted nodes ij ; If the structural damage is the deterioration of material properties, after calculating the model correction parameter α using the equivalent property correction parameter obtained by analyzing the sensor signals, use it as a physical constraint of the neural network to directly perform damage correction on the finite element model; If the structural damage is the change of structural geometric parameters, recalculate the relevant cross-sectional property parameters of the structure, calculate the model correction parameter α, and use it as a physical constraint of the neural network to directly perform damage correction on the finite element model.

6. A proxy model and finite element fusion method for bridge safety warning according to claim 1, characterized in that In Step 4, the trained finite element surrogate model is used to analyze the signals of the excitation monitoring points and the response monitoring points monitored on site. By comparing the neural network calculation parameters of each node with the calculation parameters of the initial model, the model correction parameter β based on data analysis is obtained: In the formula, represents the model parameters of the structure in the current state, represents the model parameters of the bridge structure in the initial state, and β is the model parameter of the structure calculated from the sensor data.

7. A proxy model and finite element fusion method for bridge safety warning according to claim 1, characterized in that, The calculation process of the refined component adjustment parameter γ is shown in the following formula: If the direct correction object can be solved through data analysis and has not been obtained through experiments at the present stage, then γ j = β j ; If the object to be corrected has completed the test and obtained accurate data that can be directly used for correction, then γ j = α i ; If the data obtained through on-site tests or direct monitoring cannot fully describe the structural state, then γ j = β j - (α i - β j ) × a ij , where α j , β j are the model correction parameters directly obtained from on-site monitored damage at the node position of model j and the model correction parameters obtained from the surrogate model calculation data respectively, and γ j is the refined component adjustment parameter for the finite element model of node j, and a ij is the influence matrix of the changes in the calculation parameters of all nodes after the calculation parameters related to node i of the structure change.

8. A surrogate model and finite element fusion method for bridge safety warning according to claim 1, further comprising using the updated multi-scale finite element model for bridge safety warning.

9. A bridge safety early warning system based on the fusion of surrogate model and finite element, characterized in that, Including: The first main control module is used to simulate the real load of the bridge with the finite element model of structural multi-scale to calculate the bridge structure response, and construct a data set based on the real load and the structure response; The second main control module is used to construct a finite element surrogate model and train the finite element surrogate model with the data set to extract the relationship between the weight matrix analysis of the neural network and the output items; The third main control module is used to directly correct the finite element model with the structural damage information monitored on site for damage correction, and calculate the model correction parameter α for the preliminary adjustment of the structure; The fourth main control module is used to analyze the signals of the excitation monitoring points and the response monitoring points monitored on site with the trained finite element surrogate model to obtain the model correction parameter β based on data analysis; The fifth main control module is used to obtain the corrected multi-scale finite element model according to the model correction parameters of damage correction and data analysis; The fifth main control module is used to perform the following steps: If the model correction parameter α and the model correction parameter β have the same correction target but different correction times, the model correction parameter α is directly used as a physical constraint to train the neural network; If the model completes health monitoring at this time and the model correction parameter α directly obtained through monitoring can explain the state of the structure, the model correction parameter α represents the refined component adjustment parameter γ; If the model correction parameter α will cause an adjustment of the overall model, or if a new physical constraint is generated when monitoring the bridge structure at this time, the refined component adjustment parameter γ is constructed using the model correction parameter β and the model correction parameter α, and the finite element model is updated using the refined component adjustment parameter γ to obtain the corrected multi-scale finite element model; The sixth main control module is used to generate a data set for training and updating the finite element surrogate model using the corrected multi-scale finite element model.

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