Intelligent identification method, medium and electronic equipment for flutter derivatives in two-dimensional cross-sections of bridges

Abstract

This invention relates to the field of bridge aerodynamic parameter identification technology, providing a method, medium, and electronic device for intelligent identification of flutter derivatives of two-dimensional bridge cross-sections. The method includes: acquiring two-dimensional bridge cross-section information data; constructing a finite element model of the two-dimensional bridge cross-section; acquiring the free vibration time series of the two-dimensional bridge cross-section at a certain wind speed before the flutter critical wind speed; building a bi-branch hybrid network, and constructing a neural network-based two-dimensional bridge cross-section flutter derivative identification model by adding Scanlan flutter derivative physical theory constraints to the loss function; and identifying the flutter derivatives of the free vibration time series of the two-dimensional bridge cross-section at that wind speed. This invention, through network structure design and physical constraints of the loss function, ensures that the identification results conform to the Scanlan flutter theory framework, solving the problem of the physical interpretability of neural network output, and providing an achievable data-physics fusion paradigm for the identification of aerodynamic parameters of two-dimensional bridge cross-sections.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge aerodynamic characteristic parameter identification, in particular to a bridge two-dimensional section flutter derivative intelligent identification method, medium and electronic equipment. BACKGROUND

[0002] Flutter is an aerodynamic elastic instability phenomenon of a bridge flexible structure under the action of wind load, which may cause large vibration and even damage of the structure. The flutter derivative of a bridge section is a set of important parameters used to describe the aerodynamic self-excitation force on the section in the wind field, reflecting the aerodynamic characteristics of the bridge section. Neither the flutter instability mechanism research nor the flutter critical condition research can be carried out without the identification of the flutter derivative. Therefore, how to accurately identify the flutter derivative of the bridge section has been a hot and frontier field of research in bridge wind engineering.

[0003] Traditional flutter derivative identification methods are mainly based on wind tunnel test data, and are realized by forced vibration method, free vibration decay method, etc. However, there are problems such as high test cost, long cycle, and large environmental interference. At the same time, when dealing with noisy vibration signals, traditional data-driven methods (such as basic neural network, support vector machine, least squares method, etc.) are prone to overfitting and lack of physical meaning, resulting in insufficient identification accuracy and difficulty in meeting the actual engineering requirements.

[0004] In the prior art, some studies attempt to incorporate physical constraints into data-driven models, but mostly use a single loss function or simple network structure, without fully considering the strong coupling between the envelope characteristics of the vibration signal and the aerodynamic equation, resulting in weak model generalization ability and poor noise robustness. In addition, most methods lack effective vibration displacement reconstruction verification links, and cannot intuitively evaluate the reliability of the flutter derivative identification results, limiting their application in engineering practice.

[0005] Therefore, it is necessary to design a bridge two-dimensional section flutter derivative intelligent identification method based on physical information neural network to solve the problems in the prior art. SUMMARY

[0006] The present application aims to provide a bridge two-dimensional section flutter derivative intelligent identification method, medium and electronic equipment to solve the problem that the flutter derivative identification result accuracy in the prior art cannot meet the requirements, and the specific technical solutions are as follows:

[0007] A bridge two-dimensional section flutter derivative intelligent identification method, comprising the following steps:

[0008] S1, obtaining bridge two-dimensional section information data; constructing a bridge two-dimensional section finite element model based on the bridge two-dimensional section information data;

[0009] S2, obtaining free vibration time series of the bridge two-dimensional section at a wind speed before the critical flutter wind speed based on the bridge two-dimensional section finite element model;

[0010] S3, constructing a data set based on the free vibration time series obtained in S2, and generating training data for model training;

[0011] S4, building a double-branch hybrid neural network by adding a Scanlan flutter derivative physical theory constraint in the loss function; training the neural network based on the training data obtained in S3 to obtain a neural network-based two-dimensional bridge section flutter derivative identification model;

[0012] S5, identifying the flutter derivative of the free vibration time series of the bridge two-dimensional section at the wind speed by the neural network-based two-dimensional bridge section flutter derivative identification model obtained in S4 to obtain the corresponding flutter derivative of the two-dimensional bridge section at the wind speed label.

[0013] Preferably, in S1:

[0014] The bridge two-dimensional section information data includes the equivalent mass, the equivalent mass moment, the vertical bending modal damping, the torsional modal damping, the vertical bending modal linear stiffness and the torsional modal linear stiffness of the unit length of the bridge two-dimensional section;

[0015] The bridge two-dimensional section finite element model is constructed based on the bridge two-dimensional section information data using fluid mechanics simulation software, specifically including:

[0016] ①, setting the model parameters, calculation domain range and boundary condition division of the bridge two-dimensional section finite element model, the model parameters including the aerodynamic shape of the bridge two-dimensional section, the distance of the bridge two-dimensional section from the fluid inlet and the fluid outlet; the calculation domain range includes the vertical height and horizontal length of the calculation domain; the boundary conditions include the left boundary condition, the right boundary condition, the upper boundary condition, the lower boundary condition and the bridge section surface condition;

[0017] ②, meshing the calculation domain of the bridge two-dimensional section finite element model, dividing the calculation domain into rigid grid area, dynamic grid area and static grid area, wherein the dynamic grid area and the static grid area are both structured grid, the dynamic grid area and the static grid area are connected by unstructured grid, and the rigid grid area is divided into boundary layer grid and quadrilateral unstructured grid;

[0018] ③, combining the bridge two-dimensional section information data, and writing a UDF file based on the Newmark-β method with unconditional convergence.

[0019] Preferably, the two-dimensional cross-sectional finite element model of the bridge is the SST k-ω turbulence model, and the pressure-velocity problem is solved using the SIMPLEC algorithm, with the difference scheme using second-order accuracy.

[0020] Preferably, S2 specifically involves: using fluid dynamics calculation software and the UDF file written in S1, performing transient solution of the two-dimensional cross-section motion state of the bridge based on the NS equation, obtaining the free vibration time history data of the two-dimensional cross-section of the bridge at a certain wind speed before the flutter critical wind speed, the free vibration time history data including time, vertical displacement and torsional angle; and generating a free vibration time series.

[0021] Preferably, S3 specifically involves: matching the free vibration time history data obtained in S2 with its wind speed label, removing abnormal attenuation segments, and constructing a dataset of sample-label pairs, which is the training data used for model training. The variables in the dataset under the wind speed sample are time, vertical displacement, and torsional angle.

[0022] Preferably, S4 specifically includes the following steps:

[0023] S4.1. Use Hilbert transform to preprocess the sample-label dataset obtained in S3 to form the envelope features of vertical displacement time history and torsional displacement time history.

[0024] S4.2 Construct a hybrid neural network model with a dual-branch structure, which includes a main network branch, an envelope network branch, and a fusion layer;

[0025] S4.3 The main network branch takes time, vertical displacement, and torsional displacement as inputs to directly learn the nonlinear mapping relationship between bridge cross-section motion parameters and flutter derivatives; the envelope network branch processes the envelope features of vibration signals and captures key information related to amplitude evolution; the feature fusion layer integrates the high-dimensional features extracted by the main network branch and the envelope network branch, and finally outputs the flutter derivative to be identified.

[0026] S4.4 Design a multi-objective optimization loss function that integrates physical information. This function combines the displacement loss and self-excited force loss according to weights to ensure that the output of the neural network model satisfies the physical meaning of the Scanlan flutter theory framework.

[0027] S4.5 The neural network model uses the AdamW optimizer to update parameters and combines the ReduceLROnPlateau learning rate scheduler to monitor the loss function. When the loss no longer decreases, the learning rate will be automatically reduced to achieve fine-tuning.

[0028] S4.6. Set the number of training rounds and batch size. In each training cycle, traverse the time history data of vertical displacement and torsional angle of the cross section free vibration under the wind speed label, calculate the total loss, perform backpropagation and gradient clipping, update the network weights, and obtain the two-dimensional bridge cross section flutter derivative recognition model based on neural network after training.

[0029] Preferably, in S4.3: the main network branch systematically extracts the transient dynamic features of the vibration signal through a cascaded structure consisting of a linear transformation layer, a two-dimensional convolutional layer, an adaptive average pooling layer and a SiLU activation function, and achieves dimensionality adaptation of the feature tensor by means of reshaping operation. Its core function is to learn the complex nonlinear mapping relationship between motion parameters and flutter derivatives.

[0030] The envelope network branch uses Hilbert transform to preprocess the input signal, extracts envelope information using the absolute value of the signal as the input feature, and captures the gradual trend and amplitude evolution characteristics of nonlinear aerodynamic forces through similar hierarchical structures.

[0031] The fusion layer performs deep fusion of the high-dimensional features extracted from the main network branch and the envelope network branch through a weighted aggregation mechanism.

[0032] Preferably, in S4.3, the eight flutter derivatives to be identified are output.

[0033] The present invention also provides a readable storage medium storing computer program instructions, which, when executed by a processor, implement the intelligent identification method for flutter derivatives of two-dimensional bridge cross sections as described above.

[0034] The present invention also provides an electronic device, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, wherein the computer program instructions are executed by the processor to provide a bridge two-dimensional cross-section flutter derivative intelligent identification method as described above.

[0035] The application of the technical solution of the present invention has the following beneficial effects:

[0036] The intelligent identification method for flutter derivatives of two-dimensional bridge cross-sections provided by this invention specifically includes: acquiring two-dimensional bridge cross-section information data; constructing a finite element model of the two-dimensional bridge cross-section; acquiring free vibration time history data of the two-dimensional bridge cross-section at a certain wind speed before the flutter critical wind speed to generate a free vibration time series; constructing a dataset based on the free vibration time series to generate training data for model training; building a dual-branch hybrid network, and constructing a neural network-based two-dimensional bridge cross-section flutter derivative identification model by adding Scanlan flutter derivative physical theory constraints to the loss function; and identifying the flutter derivatives of the free vibration time series of the two-dimensional bridge cross-section at that wind speed. This invention, through network structure design and physical constraints of the loss function, ensures that the identification results conform to the Scanlan flutter theory framework, solves the problem of physical interpretability of neural network output, and provides an achievable data-physical fusion paradigm for the identification of aerodynamic parameters of two-dimensional bridge cross-sections.

[0037] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0038] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0039] Figure 1 This is a flowchart illustrating the intelligent identification method for flutter derivatives of two-dimensional bridge sections in an embodiment of the present invention.

[0040] Figure 2 This is a schematic diagram of the computational domain and boundary conditions of the two-dimensional cross-section of the bridge in an embodiment of the present invention;

[0041] Figure 3 This invention presents a comparison of frequency domain features and residual analysis of the reconstructed vertical displacement time history of a two-dimensional bridge cross-section at a wind speed of 13.0 m / s using PINN-FD and LS identification results. Specifically: (a) is the vertical displacement-original signal squeezed wavelet transform; (b) is the vertical displacement-LS reconstruction squeezed wavelet transform; (c) is the vertical displacement-PINN-FD reconstruction squeezed wavelet transform; (d) is the vertical displacement-LS reconstruction squeezed wavelet transform error; and (e) is the vertical displacement-PINN-FD reconstruction squeezed wavelet transform error.

[0042] Figure 4This invention presents a comparison of frequency domain features and residual analysis of the reconstructed torsional displacement time history of a two-dimensional bridge cross-section at a wind speed of 13.0 m / s using PINN-FD and LS identification results. Specifically: (a) is the torsional displacement-original signal compression wavelet transform; (b) is the torsional displacement-LS reconstruction compression wavelet transform; (c) is the torsional displacement-PINN-FD reconstruction compression wavelet transform; (d) is the torsional displacement-LS reconstruction compression wavelet transform error; and (e) is the torsional displacement-PINN-FD reconstruction compression wavelet transform error. Detailed Implementation

[0043] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings; however, the present invention can be implemented in many different ways.

[0044] Example:

[0045] See Figure 1 This embodiment provides an intelligent identification method for the flutter derivative of a two-dimensional cross-section of a bridge. The principle is as follows: ① Input feature construction (including time t, vertical displacement h, and torsional displacement) ); ② Two-way branch processing, wherein: the first path includes: neural network forward propagation, the main network branch learns the nonlinear mapping relationship between motion parameters and flutter derivatives; the second path includes: Hilbert transform; neural network forward propagation; envelope network branch processes signal envelope features and extracts features related to signal amplitude; ③ weighted summation of the fusion layer, outputting the 8 identified flutter derivatives; ④ physical loss calculation; ⑤ determine whether it meets the requirements, if yes, output the 8 identified flutter derivatives, otherwise backpropagate, AdamW optimizer updates parameters, gradient clipping; ⑥ iterative training uses ReduceLROnPlateau to adjust the learning rate, outputting the 8 identified flutter derivatives.

[0046] The intelligent identification method for flutter derivatives in two-dimensional bridge cross-sections includes the following steps:

[0047] S1. Obtain two-dimensional cross-sectional information data of the bridge; construct a two-dimensional cross-sectional finite element model of the bridge based on the two-dimensional cross-sectional information data.

[0048] Bridge two-dimensional cross-sectional information data includes the equivalent mass per unit length of the bridge's two-dimensional cross-section. Equivalent mass moment per unit length Vertical bending mode damping Torsional mode damping Vertical bending mode linear stiffness and torsional modal linear stiffness .

[0049] Constructing a two-dimensional finite element model of a bridge based on two-dimensional cross-sectional information data includes the following steps:

[0050] ① Set the model parameters, computational domain range, and boundary conditions of the two-dimensional cross-section finite element model of the bridge. The model parameters include the aerodynamic shape of the two-dimensional cross-section of the bridge and the distances from the two-dimensional cross-section of the bridge to the fluid inlet and fluid outlet. The computational domain range includes the vertical height and horizontal length of the computational domain. The boundary conditions include the left boundary conditions, right boundary conditions, upper boundary conditions, lower boundary conditions, and surface conditions of the bridge cross-section.

[0051] ② The computational domain of the two-dimensional cross-section finite element model of the bridge is meshed, and the computational domain is divided into a rigid mesh region, a dynamic mesh region, and a static mesh region. Structured meshes are used in both the dynamic and static mesh regions, and unstructured meshes are used at the junction of the dynamic and static mesh regions. In the rigid mesh region, except for the surface layer of the conductor section which uses a boundary layer mesh, the rest of the region uses quadrilateral unstructured meshes.

[0052] ③ Combining the two-dimensional cross-sectional information data of the bridge, based on the unconditionally convergent Newmark-β method, and in conjunction with the built-in solution function Compute_Force_And_Moment of the fluid dynamics simulation software, a UDF file is written to calculate and solve the instantaneous vertical displacement and torsional angle of the two-dimensional cross-section of the bridge in the flow field.

[0053] In this embodiment, the two-dimensional cross-sectional finite element model of the bridge is the SST k-ω turbulence model, and the SIMPLEC algorithm is used to solve the pressure-velocity problem. The difference scheme adopts second-order accuracy.

[0054] S2. Based on the finite element model of the bridge's two-dimensional cross-section, obtain the free vibration time history data (including vertical and torsional) of the bridge's two-dimensional cross-section at a certain wind speed before the flutter critical wind speed, and generate a free vibration time series, specifically including:

[0055] Using fluid dynamics calculation software and the UDF file written in S1, the transient solution of the two-dimensional cross-section motion state of the bridge is performed based on the NS equation, and the free vibration time history data of the two-dimensional cross-section of the bridge at a certain wind speed before the flutter critical wind speed is obtained. The free vibration time history data includes time, vertical displacement and torsional angle; and a free vibration time series is generated.

[0056] In this preferred embodiment, steady-state flow around the bridge cross-section is first calculated. After the flow field is fully calculated and stabilized or the calculation residuals and various smooth parameters are stable and converged, a suitable calculation step size is selected for transient calculation. The motion of the two-dimensional cross-section of the bridge is realized using the dynamic mesh technology built into the fluid dynamics calculation software. The mesh reconstruction method uses the Soomthing and Remeshing functions. After the mesh is updated, the next time step is entered for calculation. The calculation continues until the response of the two-dimensional cross-section of the bridge has stabilized. Then, the calculation of this wind speed is stopped, and the numerical calculation of the next wind speed is performed to obtain the free vibration time history data of the two-dimensional cross-section under different wind speeds.

[0057] S3. Construct a dataset based on the free vibration time series obtained in S2 to generate training data for model training. Preferably, in this embodiment, the correspondence between the free vibration time history data obtained in S2 and the corresponding wind speed labels is established to clarify the wind speed condition to which the vibration data belongs. Abnormal attenuation segments in the time history data that do not conform to physical laws over time are identified and removed to ensure data reliability. Finally, the composition of the wind speed sample variables is determined, i.e., a dataset of sample-label pairs is constructed with time as the independent variable in the time series dimension and vertical displacement and torsional angle as the observed variables of the dynamic response. This dataset is the training data for model training. The variables in the dataset for this wind speed sample are time, vertical displacement, and torsional angle.

[0058] S4. Construct a dual-branch hybrid neural network by adding Scanlan flutter derivative physical theory constraints to the loss function; train the model using the training data obtained in S3 to obtain a two-dimensional bridge cross-section flutter derivative recognition model based on the neural network. Specifically, the following steps are included:

[0059] S4.1. Use Hilbert transform to preprocess the sample-label dataset obtained in S3 to form the envelope features of vertical displacement time history and torsional displacement time history.

[0060] S4.2 Construct a hybrid neural network model with a dual-branch structure. This neural network is a dual-path architecture, which includes a main network branch, an envelope network branch, and a fusion layer.

[0061] S4.3 The main network branch takes time, vertical displacement, and torsional displacement as inputs (i.e., the input layer synchronously receives three sets of time history data—time series, vertical displacement, and torsional angle—as the common input source for both branches) and directly learns the nonlinear mapping relationship between the bridge cross-section motion parameters and flutter derivatives; the envelope network branch processes the envelope features of the vibration signal and captures key information related to amplitude evolution; the feature fusion layer integrates the high-dimensional features extracted by the main network branch and the envelope network branch, and finally outputs the eight flutter derivatives to be identified.

[0062] S4.4 Design a multi-objective optimization loss function that integrates physical information. This function combines the displacement loss and self-excited force loss according to weights to ensure that the output of the neural network model satisfies the physical meaning of the Scanlan flutter theory framework.

[0063] S4.5 The neural network model uses the AdamW optimizer to update parameters and combines the ReduceLROnPlateau learning rate scheduler to monitor the loss function. When the loss no longer decreases, the learning rate will be automatically reduced to achieve fine-tuning.

[0064] S4.6. Set the number of training rounds and batch size. In each training cycle, traverse the time history data of vertical displacement and torsional angle of the cross section free vibration under the wind speed label, calculate the total loss, perform backpropagation and gradient clipping, update the network weights, and obtain the two-dimensional bridge cross section flutter derivative recognition model based on neural network after training.

[0065] In this embodiment, the main network branch systematically extracts the transient dynamic features of the vibration signal through a cascaded structure consisting of a linear transformation layer, a two-dimensional convolutional layer, an adaptive average pooling layer, and a SiLU activation function. It also achieves dimensionality adaptation of the feature tensor through a reshaping operation. Its core function is to learn the complex nonlinear mapping relationship between motion parameters and flutter derivatives. The envelope network branch preprocesses the input signal using Hilbert transform, extracting envelope information using the absolute value of the signal as input features. It specifically captures the gradual change trend and amplitude evolution characteristics of nonlinear aerodynamic forces through a similar hierarchical structure. The output features of both branches enter the fusion layer, which deeply fuses the high-dimensional features extracted by the main network branch and the envelope network branch through a weighted aggregation mechanism. This dual-path collaborative design effectively enhances the model's ability to represent aerodynamic nonlinearity.

[0066] In this embodiment, the specific expression of the multi-objective optimization loss function in S4.4 is as follows:

[0067] ;

[0068] in: Optimize the loss function for multiple objectives; For displacement loss; Loss of self-excitation force; This is the weighting coefficient for displacement loss; This is the weighting coefficient for the self-excitation force loss.

[0069] This multi-objective optimization function will guide the neural network to find a set of flutter derivative solutions that not only satisfy instantaneous mechanical equilibrium but also produce the correct system response.

[0070] Displacement loss is expressed as the mean square error between the predicted displacement and the actual displacement, as shown in the following expression:

[0071] ;

[0072] in: for The predicted vertical displacement of the two-dimensional cross-section of the bridge at time t; for The predicted value of the torsion angle of the two-dimensional cross-section of the bridge at time t; This represents a time series with m points. ; express The true value of the vertical displacement of the two-dimensional cross-section of the bridge at time t; express The true value of the torsional angle of the two-dimensional cross-section of the bridge at time t.

[0073] This loss function measures the difference between the output of the positive physics model based on the current predicted parameters and the actual observations, directly guiding the optimization of neural network parameters in the direction that can correctly reproduce the dynamic response.

[0074] The self-excitation force loss is expressed as the mean square error between the predicted force and the actual force, as shown in the following expression:

[0075] ;

[0076] in: express Predicted value of aerodynamic self-excited force in the two-dimensional cross-section of the bridge at time t; express Predicted value of the aerodynamic self-excited moment of the two-dimensional cross-section of the bridge at time t; express The true value of the aerodynamic self-excited force in the two-dimensional cross-section of the bridge at time t; express The true value of the aerodynamic self-excited torque of the two-dimensional cross-section of the bridge at time t.

[0077] This loss function measures the instantaneous difference between the predicted aerodynamic force and the self-excited force calculated from the measurement data, providing a powerful and direct physical gradient for optimizing neural network parameters.

[0078] In the classic Scanlan model of flutter self-excited forces in bridge wind engineering, for streamlined and bluff sections, the aerodynamic self-excited forces and aerodynamic self-excited moments can be expressed as linear functions of eight dimensionless flutter derivatives, as follows:

[0079] ;

[0080] ;

[0081] in: This represents aerodynamic self-excited force. This represents the aerodynamic self-excited torque. and It's about time. The expression; air density; For incoming air velocity; For the converted frequency, it is a dimensionless parameter, and , The width of the bridge cross section. It is the angular frequency of vibration; The time history is for vertical displacement; For torsional displacement time history; For the vertical velocity time history, from Differentiation yields the result; To reverse the velocity time history, by Differentiation yields the result; , , , , , , and These are all flutter derivatives, which are also the output parameters of the neural network.

[0082] If we establish a vibration ordinary differential equation for a two-dimensional bridge cross-section, the equation can be expressed as:

[0083] ;

[0084] ;

[0085] in: It is the time history of vertical acceleration; It is the torsional acceleration time history.

[0086] By combining the various expressions, the vibration differential equation of the two-dimensional cross-section of the bridge can be expressed as a linear function of eight flutter derivatives. In other words, the eight flutter derivatives of the two-dimensional cross-section of the bridge can be obtained from the motion state of the two-dimensional cross-section of the bridge, as follows:

[0087] ;

[0088] ;

[0089] In this embodiment, the eight flutter derivatives predicted by the current iteration of the neural network are utilized. , , , , , , and Based on the classic Scanlan model of flutter self-excited force in bridge wind engineering, the aerodynamic self-excited force and aerodynamic self-excited moment acting on the two-dimensional cross-section of the bridge are calculated. Then, the calculated aerodynamic self-excited force and aerodynamic self-excited moment are substituted into the vibration differential equation of the structure, and the predicted vertical displacement of the two-dimensional cross-section is reconstructed. ) and predicted twist angle ( ), as shown in the following formula:

[0090] ;

[0091] ;

[0092] Preferably, based on the structural motion equation, the force required for the structure to maintain its current motion state is calculated, which should theoretically be equal to the self-excited force; then, the self-excited force is calculated using the flutter derivative currently predicted by the neural network and the observed motion state; the predicted aerodynamic force is compared point by point with the actual force obtained by back-calculation, and its mean square error is calculated.

[0093] Preferably, AdamW is a widely used stochastic optimization algorithm whose core lies in decoupling the weight decay from the gradient update process, thereby obtaining better generalization performance. In each iteration, it updates the network parameters through the following steps: calculating the gradient of the loss function on the current parameters and mini-batch data, updating the exponential moving average of the first moment of the gradient, updating the exponential moving average of the second moment of the gradient, bias correction, applying decoupled weight decay and updating the weights, that is, applying the weight decay term as an independent term to the parameter update.

[0094] Preferably, the ReduceLROnPlateau learning rate scheduler is a learning rate adjustment strategy that can dynamically monitor the training loss of the neural network, adaptively respond to the actual training state of the model, and automatically reduce the learning rate during the training plateau period of the neural network, thereby effectively promoting the model to converge to the optimal solution, making the model training and optimization process more intelligent and efficient.

[0095] S5. Using the two-dimensional bridge cross-section flutter derivative identification model based on neural network obtained in S4, the flutter derivative of the free vibration time series of the two-dimensional bridge cross-section under the wind speed is identified, and the flutter derivative of the two-dimensional bridge cross-section under the wind speed label is obtained (that is, the eight flutter derivatives of the two-dimensional bridge cross-section under the wind speed label are identified).

[0096] This embodiment proposes an intelligent identification method for flutter derivatives in two-dimensional bridge cross-sections, specifically a method based on a physical information neural network. This method addresses the core challenge of balancing "data-driven flexibility" and "the rationality of physical constraints" in flutter derivative identification, overcoming the limitations of traditional methods. Traditional least squares methods heavily rely on linear assumptions, limiting their reliability under strong nonlinear aerodynamic forces; while purely data-driven neural networks possess strong fitting capabilities, their "black box" nature easily leads to results with unclear physical meaning. This invention achieves complementary advantages through a deep fusion mechanism. Specifically, it includes: constructing a dual-branch hybrid neural network architecture. This design addresses the dual-timescale characteristics of "rapidly varying vibrations" and "slowly varying aerodynamic forces" in aeroelastic systems, enabling the displacement branch to accurately fit the instantaneous dynamic response, while the envelope branch specifically captures the gradual trend of nonlinear aerodynamic forces; and deeply embedding Scanlan flutter theory and structural motion equations into the loss function as core optimization constraints, guiding the network to prioritize searching for solutions from a vast number of possible solutions that both conform to the data and strictly satisfy physical laws, thus realizing a paradigm shift from "identification first, verification later" to "ensuring physical consistency in real time during identification." The scheme disclosed in this invention, through a division of labor design oriented towards physical mechanisms and a deeply embedded constraint mechanism, constructs a new paradigm of data and physics collaboration, ensuring that the identification results satisfy both instantaneous mechanical equilibrium and have good physical consistency.

[0097] This embodiment also includes a readable storage medium storing computer program instructions, which, when executed by a processor, implement the intelligent identification method for flutter derivatives of two-dimensional bridge cross sections as described above.

[0098] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in the electronic device.

[0099] This embodiment also includes an electronic device, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, wherein the computer program instructions are executed by the processor to provide a bridge two-dimensional cross-section flutter derivative intelligent identification method as described above.

[0100] The electronic device can be a mobile phone, desktop computer, laptop, handheld computer, cloud server, or other computing device. The electronic device may include, but is not limited to, processors and memory. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0101] Based on a two-dimensional cross-section of an actual bridge, fluid dynamics calculation software was used to study its performance under wind speed conditions. The free vibration time history was calculated. To better evaluate this method, the least squares method was used to identify the flutter derivative of the cross section at this wind speed. The displacement time history was reconstructed using the flutter derivatives obtained by both methods and compared with the original time history. The evaluation index was the coefficient of determination (R²). 2 ), mean square error (MSE), and residuals after time history compression wavelet transform.

[0102] The two-dimensional cross-sectional shape, computational domain, and boundary conditions of the bridge are as follows: Figure 2 As shown, the left side of the computational domain is the velocity inlet boundary, the right side is the pressure outlet boundary, the top and bottom sides of the computational domain are symmetrical boundaries, and the bridge cross-section is a fixed wall boundary. The air density is known. characteristic width of two-dimensional cross-section of bridge equivalent mass per unit length =3.959 kg / m, equivalent mass moment per unit length Vertical bending mode linear stiffness Torsional modal linear stiffness Vertical bending mode damping Torsional modal damping .

[0103] After identification, the two-dimensional cross-section of the bridge was found to be at the incoming wind speed. Table 1 shows the comparison results of the flutter derivatives identified using the present invention, namely, Physics-Informed Neural Networks for FlutterDerivative Identification (PINN-FD), and the Least Squares (LS) method. Analysis shows that the flutter derivatives identified by the PINN-FD method have good consistency with the results of the traditional LS method.

[0104] Table 1. Comparison of flutter derivatives identified by the method of the present invention (PINN-FD) and the least squares method (LS).

[0105]

[0106] Table 2 shows a comparison of the goodness of fit between the reconstructed displacements and the original displacements using the two methods. Based on the coefficient of determination (R²) and mean square error (MSE) indices, the displacement time history reconstructed by the PINN-FD method shows a significantly better fit with the original data than that of the LS method, indicating that this method has higher accuracy in displacement reconstruction.

[0107] Table 2. Comparison of the goodness of fit between the reconstructed displacement and the original displacement using the method of the present invention (PINN-FD) and the least squares method (LS).

[0108]

[0109] To further verify the reliability of the identification results, squeeze wavelet transform analysis was performed on the reconstructed displacement in the frequency domain. Figure 3 The frequency domain characteristics of the vertical displacement time history are compared and residual analysis is shown, where: (a) is the vertical displacement-original signal squeezed wavelet transform; (b) is the vertical displacement-LS reconstruction squeezed wavelet transform; (c) is the vertical displacement-PINN-FD reconstruction squeezed wavelet transform; (d) is the vertical displacement-LS reconstruction squeezed wavelet transform error; and (e) is the vertical displacement-PINN-FD reconstruction squeezed wavelet transform error. Figure 4 The results for the torsional displacement time history are presented, where: (a) is the torsional displacement-original signal squeezed wavelet transform; (b) is the torsional displacement-LS reconstruction squeezed wavelet transform; (c) is the torsional displacement-PINN-FD reconstruction squeezed wavelet transform; (d) is the torsional displacement-LS reconstruction squeezed wavelet transform error; and (e) is the torsional displacement-PINN-FD reconstruction squeezed wavelet transform error. The squeezed wavelet transform results show that the displacement time history reconstructed based on the PINN-FD method is closer to the original signal in the frequency domain characteristics, and its frequency domain residual is significantly smaller than that of the LS method.

[0110] Comprehensive analysis shows that, compared with the traditional least squares method, the flutter derivative intelligent identification method (PINN-FD) based on physical information neural networks proposed in this invention can more accurately identify flutter derivative characteristics. The displacement time history reconstructed by this method shows a better match with the original data in both the time and frequency domains, verifying the effectiveness and superiority of this method in bridge aerodynamic parameter identification.

[0111] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A bridge two-dimensional section flutter derivative intelligent identification method, characterized in that, The method comprises the following steps: S1, obtaining bridge two-dimensional section information data; constructing a bridge two-dimensional section finite element model based on the bridge two-dimensional section information data; S2, obtaining free vibration time series data of the bridge two-dimensional section at a certain wind speed before the critical flutter wind speed based on the bridge two-dimensional section finite element model, and generating the free vibration time series; S3, constructing a data set based on the free vibration time series obtained in S2, and generating training data for model training; S4, building a double-branch hybrid neural network, adding a Scanlan flutter derivative physical theory constraint in the loss function; training combined with the training data obtained in S3 for model training to obtain a neural network-based two-dimensional bridge section flutter derivative identification model; S5, identifying the flutter derivative of the free vibration time series of the bridge two-dimensional section at the wind speed by using the neural network-based two-dimensional bridge section flutter derivative identification model obtained in S4 to obtain the corresponding flutter derivative of the two-dimensional bridge section at the wind speed label; S4 specifically comprises the following steps: S4.1, using Hilbert transform to pre-process the data set of the sample-label pair obtained in S3, and forming envelope features of the vertical displacement time history and the torsional displacement time history; S4.2, constructing a hybrid neural network model with a double-branch structure, which comprises a main network branch, an envelope line network branch and a fusion layer; S4.3, the main network branch takes time, vertical displacement and torsional displacement as input, directly learns the nonlinear mapping relationship between bridge section motion parameters and flutter derivative; the envelope line network branch processes the envelope features of the vibration signal, captures the key information related to amplitude evolution; the feature fusion layer integrates the high-dimensional features extracted by the main network branch and the envelope line network branch, and finally outputs the flutter derivative to be identified; S4.4, designing a multi-objective optimization loss function that fuses physical information, which combines displacement loss and self-excitation force loss by weight to ensure that the output of the neural network model meets the physical meaning of the Scanlan flutter theory framework; S4.5, the neural network model uses AdamW optimizer to update parameters, and combines ReduceLROnPlateau learning rate scheduler to monitor the loss function, when the loss no longer decreases, the learning rate will automatically decrease to realize fine tuning; S4.6, set the training rounds and batch size, in each training period, traverse the section free vibration vertical displacement time history data and torsional angle time history data under the wind speed label, calculate the total loss, perform back propagation and gradient clipping, update the network weight, and obtain the neural network-based two-dimensional bridge section flutter derivative identification model after training.

2. The bridge two-dimensional section flutter derivative intelligent identification method according to claim 1, characterized in that, In S1: The bridge two-dimensional section information data comprises the equivalent mass per unit length, the equivalent mass moment per unit length, the vertical bending modal damping, the torsional modal damping, the vertical bending modal linear stiffness and the torsional modal linear stiffness of the bridge two-dimensional section; The bridge two-dimensional section finite element model is constructed based on the bridge two-dimensional section information data by using fluid mechanics simulation software, specifically comprising: ①, setting the model parameters, calculation domain range and boundary condition division of the bridge two-dimensional section finite element model, the model parameters include the aerodynamic shape of the bridge two-dimensional section, the distance of the bridge two-dimensional section from the fluid inlet and the fluid outlet; the calculation domain range includes the vertical height and horizontal length of the calculation domain; the boundary conditions include the left boundary condition, the right boundary condition, the upper boundary condition, the lower boundary condition and the bridge section surface condition; ②, the calculation domain of the bridge two-dimensional section finite element model is meshed, and the calculation domain is divided into rigid grid area, dynamic grid area and static grid area, wherein the dynamic grid area and the static grid area are both structured grid, the dynamic grid area and the static grid area are connected by unstructured grid, and the rigid grid area is connected by unstructured grid, except that the boundary layer grid is used for the surface layer of the conductor section, the rest of the area is all quadrilateral unstructured grid; ③, combined with the bridge two-dimensional section information data, based on the Newmark-β method with unconditional convergence, a UDF file is written.

3. The bridge two-dimensional section flutter derivative intelligent identification method according to claim 2, characterized in that, The bridge two-dimensional section finite element model is an SST k-ω turbulence model, and the SIMPLEC algorithm is used to solve the pressure-velocity problem, and the difference format adopts second-order accuracy.

4. The bridge two-dimensional section flutter derivative intelligent identification method according to claim 3, characterized in that, S2 is specifically: using fluid mechanics calculation software and the UDF file written in S1, based on N-S equation, the transient solution of the bridge two-dimensional section motion state is obtained, the free vibration time history data of the bridge two-dimensional section under a certain wind speed before the flutter critical wind speed is obtained, and the free vibration time history data includes time, vertical displacement and torsion angle; generate free vibration time sequence.

5. The bridge two-dimensional section flutter derivative intelligent identification method according to claim 4, characterized in that, S3 is specifically: corresponding to the wind speed label of the free vibration time history data obtained by S2, the abnormal attenuation section is removed, and a data set of sample-label pairs is constructed, that is, the training data for model training, the variables of the data set under the wind speed sample are time, vertical displacement and torsion angle.

6. The bridge two-dimensional section flutter derivative intelligent identification method according to claim 1, characterized in that, In S4.3: the main network branch is composed of a cascade structure of linear transformation layer, two-dimensional convolution layer, adaptive average pooling layer and SiLU activation function, which systematically extracts the transient dynamic characteristics of the vibration signal, and realizes the dimension adaptation of the feature tensor through reshaping operation, and its core function is to learn the complex nonlinear mapping relationship between the motion parameters and the flutter derivative; The envelope network branch adopts Hilbert transform for preprocessing of the input signal, extracts envelope line information with signal absolute value as input feature, and specially captures the slowly varying trend and amplitude evolution characteristics of nonlinear aerodynamic force through similar hierarchical structure; The fusion layer deeply fuses the high-dimensional features extracted by the main network branch and the envelope line network branch through a weighted aggregation mechanism.

7. The bridge two-dimensional section flutter derivative intelligent identification method according to claim 6, characterized in that, S4.3 outputs 8 flutter derivatives to be identified.

8. A readable storage medium, characterized by, It stores computer program instructions, which, when executed by a processor, implement a bridge two-dimensional section flutter derivative intelligent identification method according to any one of claims 1 to 7.

9. An electronic device, comprising: It comprises: At least one processor, at least one memory and computer program instructions stored in the memory, when the computer program instructions are executed by the processor, a bridge two-dimensional section flutter derivative intelligent identification method according to any one of claims 1 to 7.

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