Bridge finite element model correction method based on ground-based radar

Abstract

The invention relates to a bridge finite element model correction method based on a ground-based radar, and belongs to the technical field of structure monitoring. The method comprises the following steps: synchronously acquiring deformation data of a bridge by using a ground-based radar; carrying out noise reduction processing on the dynamic deflection by utilizing the combination of a variation mode decomposition algorithm optimized by the improved whale optimization algorithm and a wavelet threshold value; performing modal identification by using a frequency domain decomposition method, and determining main modals of the first four orders of the bridge structure; establishing a bridge initial finite element model, and realizing mapping through a Kriging agent model, namely establishing a correlation between a correction parameter and a target response value; according to the method, fitness functions are respectively constructed by adopting residual values of four-order modal vertical bending frequencies, finally, a Pareto set is obtained through calculation by improving a multi-target whale algorithm, meanwhile, indexes are proposed to measure the quality of solutions in the Pareto set, and an optimal solution is selected to be used for correcting the model. Compared with a traditional bridge finite element model correction mode, the method has the obvious advantages of being non-contact, high in speed, high in precision and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural monitoring, and particularly relates to a method for correcting a finite element model of a bridge based on a ground-based radar. Background Art

[0002] When a bridge enters the traffic operation stage after completion acceptance, with the passage of time, it will inevitably be affected by various degrees of diseases and damages. The reasons may include material aging, environmental corrosion, natural disasters, and the interaction of vehicle loads, etc. In addition, due to the relevant assumptions and simplifications in the finite element simulation process, there are non-negligible errors between the simulation response results of the finite element model established based on the initial design drawings and the results tested by the structural health monitoring system. Therefore, correcting the original finite element model to make the simulated response values calculated by it tend to the true response values of the structure has become an important research field with practical significance.

[0003] Current research on the correction of the finite element model of bridge structures mostly focuses on improving the optimization algorithm or surrogate model, so as to continuously narrow the gap between the finite element model and the actual structure. However, these methods have the following problems: the corrected parameter values cannot simultaneously satisfy the optimal solutions of multiple objective functions, and they also do not conform to the material properties of actual engineering. Therefore, the optimal solution only represents the best mathematical solution and is not suitable as an actual correction solution. Summary of the Invention

[0004] The purpose of the present invention is to overcome the problems existing in the existing methods, and provide a method for correcting a finite element model of a bridge based on a ground-based radar. This method can not only monitor the dynamic deflection of the bridge in a non-contact manner, but also obtain the optimal solution of the correction parameters that meet the actual engineering.

[0005] To achieve the above purpose, the technical solution of the present invention is: a method for correcting a finite element model of a bridge based on a ground-based radar, including:

[0006] Step S1: Synchronously collect the deformation data of the bridge by using a ground-based radar, and position and distinguish the bridge through the signal-to-noise ratio, distance, and angle to obtain the deformation information at the mid-span of the bridge;

[0007] Step S2: Use the variational mode decomposition algorithm VMD optimized by the improved whale optimization algorithm CSWOA and the wavelet threshold WT to perform noise reduction processing on the dynamic deflection;

[0008] Step S3: Use the frequency domain decomposition method FDD to perform modal identification on the signal obtained in Step S2 to determine the first 4 main modes of the bridge structure;

[0009] Step S4: Establish an initial finite element model of the bridge and a Kriging surrogate model;

[0010] Step S5: Use the residual values of the fourth-order modal vertical bending frequencies to construct a fitness function respectively. Calculate the Pareto set through the improved multi-objective whale optimization algorithm CS-MOWOA. At the same time, propose an index to measure the quality of the solutions in the Pareto set, and select an optimal solution to correct the model.

[0011] In an embodiment of the present invention, in step S1, the ground-based radar is a radar device with a sampling rate of up to 200 Hz, which can collect deformations with sub-millimeter accuracy in the one-dimensional line-of-sight direction.

[0012] In an embodiment of the present invention, in step S1, the ground-based radar includes a radar sensor, a frequency modulation device, a data acquisition and control device, a power supply system, and auxiliary equipment.

[0013] In an embodiment of the present invention, in step S2, the method of processing the deformation data by using the variational mode decomposition algorithm VMD optimized by the improved whale optimization algorithm CSWOA and the wavelet threshold WT is as follows: Use the improved CSWOA to optimize the VMD parameters, that is, the decomposition layer number K and the penalty factor α, and perform WT denoising on the high-frequency IMF components after VMD decomposition.

[0014] In an embodiment of the present invention, in step S2, the specific steps of processing the deformation data by using the variational mode decomposition algorithm VMD optimized by the improved whale optimization algorithm CSWOA and the wavelet threshold WT are as follows:

[0015] Step S21: Use the mean of empirical permutation entropy as the fitness function of the improved CSWOA; reflect the complexity change of a time series during the time process, calculate the empirical permutation entropy in a fixed-size sliding time window, and define the empirical permutation entropy of order d and delay τ through a time window (x t ,x t-1 ,…,x t-M-dτ+1 ) as:

[0016]

[0017] where: q j =#{k∈{t,t-1,…,t-M+1}|(x k ,x k-τ ,…,x k-dτ )}, the window size M is defined as the number of ordinal patterns in the window;

[0018] The fitness function represented by the mean of empirical permutation entropy is obtained by the definition, expressed as:

[0019]

[0020] where: IMF kare the intrinsic mode functions after VMD decomposition; min is the minimum value function;

[0021] Step S22: Take the decomposition layer number K and the penalty factor α of VMD as the two-dimensional objective of the improved CSWOA search, and the mean value of empirical permutation entropy as the fitness function of the improved CSWOA to obtain the optimal parameters K best and α best ;

[0022] Step S23: Use the obtained optimal parameters to input into VMD to decompose the signal obtained in Step S1, and obtain K IMF components;

[0023] Step S24: Calculate the kurtosis values of the IMF components according to the kurtosis criterion, classify the signals according to high frequency, medium frequency and low frequency, and the IMF components with kurtosis values much higher than the standard value are regarded as noise signals and eliminated;

[0024] Step S25: Denoise the high-frequency signal and the medium-frequency signal respectively by WT, and merge the denoised high-frequency and medium-frequency signals with the low-frequency signal to obtain the denoised dynamic deflection signal.

[0025] In an embodiment of the present invention, in Step S3, the frequency domain decomposition method FDD is used to perform modal identification on the signal obtained in Step S2 to determine the first 4 main modes of the bridge structure. The specific implementation method is as follows:

[0026] Perform singular value decomposition on the power spectral density matrix of the measured signal at different frequency points, extract the poles of the structure, and then accurately estimate the modal parameters of the system.

[0027] In an embodiment of the present invention, in Step S4, the specific steps of establishing the initial finite element model and the Kriging surrogate model of the bridge are as follows:

[0028] Step S41: Use the finite element software ANSYS to model the bridge, adopt the modal parameter identification method of the Lanczos method in the ANSYS software, and select the required extended modes to extract the first 4 modal frequencies and the corresponding vibration modes;

[0029] Step S42: Select the elastic modulus, density, Poisson's ratio, and deck pavement thickness as candidate correction parameters, and screen the required correction parameters through the sensitivity analysis of the modal frequencies;

[0030] Step S43: Normalize the sample input correction parameters to eliminate the negative impact caused by different dimensions; establish design points by means of Latin hypercube sampling, and input the design points into ANSYS one by one to calculate the corresponding fourth-order vertical bending frequencies;

[0031] Step S44: Achieve the refined construction of the Kriging surrogate model; on the MATLAB platform, construct the Kriging surrogate model in combination with the DACE toolbox. The specific method is as follows: First, input the design sample points and the corresponding sample values into the dacefit function to obtain the prediction matrix dmodel, and then realize the response value prediction by calling the predictor function.

[0032] In an embodiment of the present invention, the initial parameters of dacefit are set as follows:

[0033] (1) The regression model selects the second-order polynomial;

[0034] (2) The correlation model selects the Gaussian correlation function;

[0035] (3) The initial value of the correlation function parameter vector is set to

[0036] (4) The upper and lower limits of the correlation function parameter vector are set to [0.1, 1000].

[0037] In an embodiment of the present invention, in step S5, the fitness function is constructed by using the residual values of the fourth-order modal vertical bending frequencies respectively. Finally, the Pareto set is calculated through the improved multi-objective whale optimization algorithm CS-MOWOA. At the same time, an index is proposed to measure the quality of the solutions in the Pareto set, and an optimal solution is selected to correct the model. The specific steps are as follows:

[0038] Step S51: Select the first 4-order modal frequencies of the bridge as the monitoring data to construct the fitness function. The residual between the measured true frequency value of the bridge and the finite element calculated frequency value is expressed as:

[0039]

[0040] In the formula, f i FE 、f i test respectively represent the i-th frequency values of the finite element calculation and the measurement;

[0041]

[0042] Among them: represents the objective function of n objects, respectively represent different sub-objective functions;

[0043] Step S52: Take the fourth-order frequency of the continuous beam bridge as the corresponding four fitness functions for the corresponding four-objective problem, and perform optimization and solution through CS-MOWOA. The parameters of the algorithm are set as follows: the initial population size N = 50; the maximum number of iterations T = 500; the upper and lower bounds of the search interval are 0.8 and 1.2 respectively. In each iteration of the multi-objective optimization algorithm, the algorithm gradually iterates based on the provided objective functions and finally generates a set of Pareto optimal solutions and their corresponding frontier sets.

[0044] Step S53: In actual bridge monitoring, the first three-order modal frequencies of the structure are considered. Therefore, place the fourth-order frequency in the lowest dominant layer of the objective function, and select an appropriate Pareto solution according to the maximum residual.

[0045] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be run by a processor are stored. When the processor runs the computer program instructions, the method steps as described in any of the above can be implemented.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] 1. The present invention uses ground-based radar to monitor the dynamic deflection of the bridge, which can monitor all-day and all-weather in a non-contact and long-distance manner, quickly obtain high-precision dynamic responses, and avoid the defects of traditional instruments that require contact monitoring.

[0048] 2. The present invention uses an improved whale optimization algorithm to optimize VMD and combines wavelet thresholding for noise reduction, which can effectively remove some noise and improve the data processing efficiency.

[0049] 3. The present invention uses the frequency domain decomposition method (FDD) to identify the mode of the signal. The frequency domain decomposition method is simple to operate and has strong anti-noise ability, and can accurately estimate the modal parameters of the system.

[0050] 4. The Kriging surrogate model constructed by the present invention combines linear regression components and non-parametric components, namely polynomials and random distributions, which improves the prediction efficiency of traditional regression methods;

[0051] 5. The present invention optimizes the objective function through an improved multi-objective whale algorithm (CS-MOWOA) to obtain a Pareto set. The improved multi-objective whale optimization algorithm has higher convergence accuracy and optimization stability. At the same time, an index is proposed to measure the quality of the solutions in the Pareto set, and an optimal solution is selected to correct the model.

[0052] 6. The algorithm of the present invention is simple to implement, has a fast running speed and high accuracy. Description of the Drawings

[0053] Figure 1It is the architecture diagram of a method for correcting the finite element model of a bridge based on a ground-based radar proposed by the present invention.

[0054] Figure 2 It is an example of synchronous monitoring of the ground-based radar of the present invention and a method for converting vibration amplitudes.

[0055] Figure 3 It is the GB-SAR environmental excitation signal.

[0056] Figure 4 It is the identification result of the frequency domain decomposition method.

[0057] Figure 5 It is the finite element model of the bridge.

[0058] Figure 6 It is the boundary condition constraint of the finite element model.

[0059] Figure 7 It is the vibration mode comparison diagram.

[0060] Figure 8 It is the partition diagram of candidate parameters of the finite element model.

[0061] Figure 9 It is the sensitivity analysis diagram of the frequency response to parameters.

[0062] Figure 10 It is the Latin hypercube sampling sample point.

[0063] Figure 11 It is the Kriging response surface and MSE diagram.

[0064] Figure 12 It is the Pareto front diagram.

[0065] Figure 13 It is to select the optimal solution from the Pareto set. Specific implementation manners

[0066] Next, in conjunction with the accompanying drawings, the technical solutions of the embodiments of the present invention will be specifically described. It should be understood that the embodiments described herein are only used to illustrate and explain the present invention and are not used to limit the present invention.

[0067] It should be noted that the following detailed descriptions are all exemplary and are intended to provide further explanations for the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0068] Note that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly dictates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they specify the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0069] The present invention provides a method for correcting a finite element model of a bridge based on a ground-based radar, including:

[0070] Step S1: Synchronously collect the deformation data of the bridge by using a ground-based radar, position and distinguish the bridge through signal-to-noise ratio, distance, and angle, and obtain the deformation information of the mid-span of the bridge;

[0071] Step S2: Denoise the dynamic deflection by using the variational mode decomposition algorithm (VMD) optimized by the improved whale optimization algorithm (CSWOA) and the wavelet threshold (WT);

[0072] Step S3: Perform modal identification on the signal obtained in Step S2 by using the frequency domain decomposition method (FDD) to determine the first 4 main modes of the bridge structure;

[0073] Step S4: Establish an initial finite element model of the bridge and a Kriging surrogate model;

[0074] Step S5: Construct fitness functions respectively by using the residual values of the fourth-order modal vertical bending frequencies, calculate the Pareto set through the improved multi-objective whale algorithm (CS-MOWOA), and at the same time propose an index to measure the quality of the solutions in the Pareto set, and select an optimal solution to correct the model.

[0075] The following is the specific implementation process of the present invention.

[0076] As Figure 1 shown, the present invention provides a method for correcting a finite element model of a bridge based on a ground-based radar, including the following steps:

[0077] Step S1: Synchronously collect the deformation data of the bridge by using a ground-based radar, position and distinguish the bridge through signal-to-noise ratio, distance, and angle, and obtain the deformation information of the bridge;

[0078] Step S2: Denoise the dynamic deflection by using the variational mode decomposition algorithm (VMD) optimized by the improved whale optimization algorithm (CSWOA) and the wavelet threshold (WT);

[0079] Step S3: Perform modal identification on the signal obtained in Step S2 by using the frequency domain decomposition method (FDD) to determine the first 4 main modes of the bridge structure;

[0080] Step S4: Establish the initial finite element model and the Kriging surrogate model of the bridge;

[0081] Step S5: Construct fitness functions respectively using the residual values of the fourth-order modal vertical bending frequencies, and finally calculate the Pareto set through the improved multi-objective whale optimization algorithm (CS-MOWOA). At the same time, propose an index to measure the quality of the solutions in the Pareto set, and select an optimal solution to correct the model.

[0082] In the example of the present invention, the ground-based radar in step S1 is a radar device with a sampling rate of up to 200 Hz, which can collect deformations with sub-millimeter accuracy in the one-dimensional line-of-sight direction. It has the advantages of non-contact and high precision and does not affect traffic.

[0083] In the example of the present invention, in step S1, the ground-based radar device includes a radar sensor, a frequency modulation device, a data acquisition and control device, a power supply system, and auxiliary equipment, which are simple to carry and install.

[0084] In the example of the present invention, in step S1, a corner reflector is installed at the mid-span of the second span to enhance the reflected signal, and the ground-based radar is used to collect the deformation data of the bridge under the ambient excitation test, such as Figure 3 (a). The bridge measurement points are located and distinguished through the signal-to-noise ratio, distance, and angle, and the vibration response information of the mid-span of the second span of the bridge is obtained. Then, the time history of the measurement points is converted, and the conversion method is as shown in Figure 2 (b). The schematic diagram of bridge monitoring is as shown in Figure 2 (a).

[0085] In the example of the present invention, in step S2, the variational mode decomposition algorithm (VMD) optimized by the improved whale optimization algorithm (CSWOA) and the wavelet threshold (WT) are used to process the deformation data at the mid-span of the second span. The specific steps are as follows:

[0086] Step S21: Use the empirical permutation entropy mean as the fitness function of the improved whale optimization algorithm; it reflects the complexity change of a time series in the time process and is usually calculated in a fixed-size sliding time window. Define the empirical permutation entropy of order d and delay τ through a time window (x t , x t-1 , …, x t-M-dτ+1 ) as:

[0087]

[0088] Where: q j = #{k ∈ {t, t - 1, …, t - M + 1}|(x k , x k-τ , …, x k-dτ)}, the window size M is defined as the number of ordinal patterns in the window.

[0089] From the definition, the fitness function of the empirical permutation entropy mean can be obtained, expressed as:

[0090]

[0091] Among them: IMF k are the intrinsic mode functions after VMD decomposition; min is the minimum value function;

[0092] Step S22: Take the decomposition layer number K and the penalty factor α of VMD as the two-dimensional objective searched by the improved whale optimization algorithm, and the empirical permutation entropy mean as the fitness function of the improved whale optimization algorithm to obtain the optimal parameters K best and α best ;

[0093] Step S23: Use the obtained optimal parameters to input into VMD to decompose the signal obtained in Step S1, and obtain K IMF components.

[0094] Step S24: Calculate the kurtosis values of the IMF components according to the kurtosis criterion, classify the signals according to high frequency, medium frequency and low frequency, and the IMF components with kurtosis values much higher than the standard value are regarded as noise signals and removed;

[0095] Step S25: Perform wavelet threshold denoising on the high-frequency signal and the medium-frequency signal respectively, and merge the denoised high-frequency and medium-frequency signals with the low-frequency signal to obtain the denoised dynamic deflection signal comparison as Figure 3 (b) shown.

[0096] In the embodiment of the present invention, in the step S3, the frequency domain decomposition method (FDD) is used to perform modal identification on the signal obtained in step S2 to determine the first 4 main modes of the bridge structure. The specific steps are as follows:

[0097] Step S31: After denoising the signal measured by the radar, perform singular value decomposition on the power spectral density matrix of the measured signal at different frequency points, extract the poles of the structure, and then accurately estimate the modal parameters of the system as Figure 4 shown.

[0098] In the embodiment of the present invention, in the step S4, the specific steps for establishing the initial finite element model of the bridge and the Kriging surrogate model are as follows:

[0099] Step S41: Use the finite element software ANSYS developed by Ansys Technology Company in the United States to model the bridge as Figure 5 , where the main beam part is simulated by Solid65 solid elements; the boundary conditions are constrained as Figure 6As shown; the concrete strength grade of the material is C50, the initial elastic modulus E = 34500 Mpa; the concrete density is 2600 kg / m3, and the Poisson's ratio is 0.2. The Lanczos method is used, and the required extended modes are selected to extract the first 4-order modal frequencies and the corresponding vibration modes. The comparison diagram of the measured vertical bending vibration mode of the bridge and the ANSYS vertical bending vibration mode is as shown in Figure 7 shown, and the frequency comparison is shown in Table 1.

[0100] Table 1 Comparison of true frequency and calculated frequency

[0101]

[0102] Step S42: Select elastic modulus, density, Poisson's ratio, bridge deck paving thickness, etc. as candidate correction parameters. The candidate parameter division diagram is as shown in Figure 8 shown, and the candidate parameter list is shown in Table 2. And the required correction parameters are screened through the sensitivity analysis of the modal frequencies as shown in Figure 9 shown.

[0103] Table 2 Candidate correction parameter list

[0104]

[0105]

[0106] Step S43: Normalize the sample input correction parameters to eliminate the negative impact caused by different dimensions. Combining rich engineering practice experience and the physical properties of the parameters themselves, the change range of 0.8 - 1.2 is taken as the change range of the parameters to be corrected. The Latin hypercube sampling method is used to establish design points as shown in Figure 10 shown, and the design points are successively input into ANSYS to calculate the corresponding fourth-order vertical bending frequencies.

[0107] Step S44: Through the sample data obtained above, a refined Kriging surrogate model is realized. On the MATLAB platform, a Kriging surrogate model is constructed in combination with the DACE toolbox; the specific method is as follows: First, input the design sample points and the corresponding sample values into the dacefit function to obtain the prediction matrix dmodel, and then the response value prediction is realized by calling the predictor function. The Kriging response surface and MSE diagram are as shown in Figure 11 shown. The initial parameter settings of Dacefit are as follows:

[0108] (1) The regression model selects a second-order polynomial;

[0109] (2) The correlation model selects a Gaussian correlation function;

[0110] (3) The initial value of the correlation function parameter vector is set to

[0111] (4) The upper and lower limits of the relevant function parameter vector are set to [0.1, 1000].

[0112] In the example of the present invention, in the step S5, the fitness function is constructed by using the residual values of the fourth-order modal vertical bending frequencies respectively, and finally the Pareto set is calculated by the improved multi-objective whale optimization algorithm (CS-MOWOA). At the same time, an index is proposed to measure the quality of the solutions in the Pareto set, and an optimal solution is selected to correct the model. The specific steps are as follows:

[0113] Step S51: The first 4-order modal frequencies of the bridge are selected as the monitoring data to construct the fitness function. The residual between the measured true frequency value of the bridge and the finite element calculated frequency value is expressed as:

[0114]

[0115] In the formula, f i FE 、f i test respectively represent the i-th frequency values of the finite element calculation and the measurement;

[0116]

[0117] Among them: represents the objective function of n objects, respectively represent different sub-objective functions;

[0118] Step S52: The fourth-order frequencies of the continuous beam bridge are used as the corresponding four fitness functions, corresponding to the four-objective problem, and the optimization is solved by the improved multi-objective whale optimization algorithm (CS-MOWOA). The parameters of the algorithm are set as follows: the initial population size N = 50; the maximum number of iterations T = 500; the upper and lower bounds of the search interval are 0.8 and 1.2 respectively. In each iteration of the multi-objective optimization algorithm, the algorithm is gradually iterated based on the provided objective function and finally generates a set of Pareto optimal solutions and their corresponding front sets as Figure 12 shown. At the same time, in order to eliminate the interference of random errors, improve the robustness of the test results, and ensure the global optimization of the solutions. In this paper, the upper limit of the maximum number of iterations is set to 15 times. If the results do not improve after 5 consecutive rounds of calculations by the algorithm, it can be considered that the global optimal solution has been approached or reached.

[0119] Step S53: In the actual bridge monitoring, more attention is paid to the first three-order modal frequencies of the structure. Therefore, the fourth-order frequency is placed in the lowest dominance layer of the objective function. At the same time, the appropriate Pareto solution is selected according to the maximum residual.

[0120]

[0121] In the formula, represents the residual sum represents the corresponding order frequency

[0122]

[0123] In the formula, R min represents the minimum residual value, x pref represents the optimal solution, N pareto represents the number of Pareto solutions

[0124] Figure 13 Shows the selection of the optimal solution from the Pareto set, and the red star in the figure represents the optimal solution

[0125] The present invention also provides a computer-readable storage medium, on which computer program instructions capable of being run by a processor are stored. When the processor runs the computer program instructions, the method steps as described in any of the above can be implemented

[0126] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes

[0127] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in one Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks

[0128] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured product including an instruction device, and the instruction device implements the functions specified in one Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks

[0129] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one process or multiple processes and / or blocks Figure 1 one process or multiple processes and / or blocks Figure 1 steps of the functions specified in one block or multiple blocks.

[0130] As described above, it is only the preferred embodiment of the present invention, and it is not a limitation to the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for correcting the finite element model of a bridge based on ground-based radar, characterized in that Including: Step S1: Use ground-based radar to synchronously collect the deformation data of the bridge, locate and distinguish the bridge through signal-to-noise ratio, distance, and angle, and obtain the deformation information at the mid-span of the bridge. Step S2: Use the variational mode decomposition algorithm VMD optimized by the improved whale optimization algorithm CSWOA and wavelet threshold WT to denoise the dynamic deflection. Step S3: Use the frequency domain decomposition method FDD to perform modal identification on the signal obtained in Step S2, and determine the first 4 main modes of the bridge structure. Step S4: Establish the initial finite element model and Kriging surrogate model of the bridge. Step S5: Construct fitness functions using the residual values of the fourth-order modal vertical bending frequencies respectively, calculate the Pareto set through the improved multi-objective whale algorithm CS-MOWOA, and at the same time propose an index to measure the quality of the solutions in the Pareto set, and select an optimal solution to correct the model.

2. The method for correcting the finite element model of a bridge based on a ground-based radar according to claim 1, wherein In Step S1, the ground-based radar is a radar device with a maximum sampling rate of 200 Hz, which can collect sub-millimeter-level accurate deformation in the one-dimensional line-of-sight direction.

3. A method for correcting a finite element model of a bridge based on a ground-based radar according to claim 1, characterized in that, In Step S1, the ground-based radar includes a radar sensor, a frequency modulation device, a data acquisition and control device, a power supply system, and auxiliary equipment.

4. A method for correcting a finite element model of a bridge based on a ground-based radar according to claim 1, characterized in that, In Step S2, the method of using the variational mode decomposition algorithm VMD optimized by the improved whale optimization algorithm CSWOA and wavelet threshold WT to process the deformation data is as follows: Use the improved CSWOA to optimize the VMD parameters, that is, the decomposition layer number K and the penalty factor α, and perform WT denoising on the high-frequency IMF components after VMD decomposition.

5. A method for correcting a finite element model of a bridge based on a ground-based radar according to claim 4, characterized in that, In Step S2, the specific steps of using the variational mode decomposition algorithm VMD optimized by the improved whale optimization algorithm CSWOA and wavelet threshold WT to process the deformation data are as follows: Step S21: Use the empirical permutation entropy mean as the fitness function of the improved CSWOA; it reflects the complexity change of a time series over time. Calculate the empirical permutation entropy in a fixed-size sliding time window, and define the empirical permutation entropy of order d and delay τ through a time window (x t , x t-1 , …, x t-M-dτ+1 ) as follows: where: q j = #{k ∈ {t, t - 1, …, t - M + 1}|(x k , x k-τ , …, x k-dτ )}, the window size M is defined as the number of ordinal patterns in the window; The fitness function is obtained from the definition as the mean of the empirical permutation entropy, expressed as: Where: IMF k are the individual intrinsic mode functions after VMD decomposition; min is the minimum value function; Step S22: Take the decomposition level K of VMD and the penalty factor α as the two-dimensional objective for the improved CSWOA search, and take the mean value of the empirical permutation entropy as the fitness function of the improved CSWOA to obtain the optimal parameters K best and α best ; Step S23: Use the obtained optimal parameters to input into VMD to decompose the signal obtained in Step S1, and obtain K IMF components. Step S24: Calculate the kurtosis values of the IMF components according to the kurtosis criterion, classify the signals according to high frequency, medium frequency, and low frequency, and the IMF components with kurtosis values much higher than the standard value are regarded as noise signals and removed. Step S25: Perform WT denoising on the high-frequency and medium-frequency signals respectively, and merge the denoised high-frequency and medium-frequency signals with the low-frequency signals to obtain the denoised dynamic deflection signal.

6. The method for correcting the finite element model of a bridge based on a ground-based radar according to claim 1, wherein, In Step S3, the specific implementation method of using the frequency domain decomposition method FDD to perform modal identification on the signal obtained in Step S2 and determine the first 4 main modes of the bridge structure is as follows: Perform singular value decomposition on the power spectral density matrix of the measured signal at different frequency points, extract the poles of the structure, and then accurately estimate the modal parameters of the system.

7. A method for correcting the finite element model of a bridge based on ground-based radar according to claim 1, characterized in that, In Step S4, the specific steps of establishing the initial finite element model and Kriging surrogate model of the bridge are as follows: Step S41: Use the finite element software ANSYS to model the bridge, adopt the modal parameter identification method of the Lanczos method in the ANSYS software, and select the required extended modes to extract the first 4 modal frequencies and the corresponding vibration modes. Step S42: Select the elastic modulus, density, Poisson's ratio, and bridge deck paving thickness as candidate correction parameters, and screen the required correction parameters through sensitivity analysis of the modal frequency; Step S43: Normalize the sample input correction parameters to eliminate the negative impact caused by different dimensions; establish design points by means of Latin hypercube sampling, and successively input the design points into ANSYS to calculate the corresponding fourth-order vertical bending frequency; Step S44: Realize the refined construction of the Kriging surrogate model; on the MATLAB platform, combine the DACE toolbox to construct the Kriging surrogate model. The specific method is as follows: First, input the design sample points and the corresponding sample values into the dacefit function to obtain the prediction matrix dmodel, and then realize the response value prediction by calling the predictor function.

8. A method for correcting a finite element model of a bridge based on a ground-based radar according to claim 7, characterized in that, The initial parameter settings of dacefit are as follows: (1) The regression model selects a second-order polynomial; (2) The correlation model selects a Gaussian correlation function; (3) The initial value of the correlation function parameter vector is set to (4) The upper and lower limits of the correlation function parameter vector are set to [0.1, 1000].

9. A method for correcting the finite element model of a bridge based on a ground-based radar according to claim 1, characterized in that, In step S5, fitness functions are constructed respectively using the residual values of the fourth-order modal vertical bending frequency. Finally, the Pareto set is obtained by calculating with the improved multi-objective whale optimization algorithm CS-MOWOA. At the same time, an index is proposed to measure the quality of the solutions in the Pareto set, and an optimal solution is selected for model correction. The specific steps are as follows: Step S51: Select the first 4-order modal frequencies of the bridge as monitoring data to construct a fitness function. The residual between the measured true frequency value of the bridge and the finite element calculated frequency value is expressed as: where f i FE and f i test respectively represent the i-th frequency values obtained from finite element calculations and field measurements; Wherein: represents the objective function of n objects, respectively represent different sub-objective functions; Step S52: Use the fourth-order frequencies of the continuous beam bridge as the corresponding four fitness functions, corresponding to a four-objective problem, and perform optimization and solution through CS-MOWOA; the parameter settings for the algorithm are: the initial population size N = 50; the maximum number of iterations T = 500; the upper and lower bounds of the search interval are 0.8 and 1.2 respectively; in each iteration of the multi-objective optimization algorithm, the algorithm is based on the provided objective functions, iterates step by step and finally generates a set of Pareto optimal solution sets and their corresponding front sets; Step S53: In actual bridge monitoring, the first three-order modal frequencies of the structure are considered. Therefore, the fourth-order frequency is placed in the lowest dominant layer of the objective function, and the appropriate Pareto solution is selected according to the maximum residual.

10. A computer-readable storage medium, on which computer program instructions capable of being run by a processor are stored. When the processor runs the computer program instructions, the method steps described in any one of claims 1-9 can be implemented.

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