Structural finite element model correction method based on optimization algorithm and deep learning

Abstract

The invention belongs to the field of structural health monitoring, and particularly relates to a structural finite element model correction method based on an optimization algorithm and deep learning, comprising the following steps: S1, collecting actual measurement modal data of a structure, including frequency and incomplete vibration mode data, and obtaining corresponding finite element model parameters; s2, performing feature extraction and enhancement processing on the incomplete vibration mode data through a convolutional neural network, and outputting complete vibration mode data matched with the degree of freedom of a finite element model; s3, combining the complete vibration mode data and the actually measured frequency to construct a model correction target function, wherein the target function comprises a weighted combination of a frequency difference term and a vibration mode cosine similarity high-order power difference term; and S4, performing global optimization on finite element model parameters by adopting an improved hunter algorithm, initializing a population through a sequence generated by Tent chaos, performing linear combination on a local optimal position and a global optimal position, searching an optimal parameter, minimizing the target function, and completing model correction. And the problem of limitation of the current optimization algorithm is well solved.

Description

Technical Field

[0001] The present invention relates to a structural finite element model correction method based on optimization algorithm and deep learning, and belongs to the field of structural health monitoring. Background Art

[0002] Traditional finite element model correction methods rely on complete measured vibration mode data, but the insufficient number of sensors in actual engineering leads to the loss of vibration mode freedom.

[0003] Currently, intelligent algorithms such as genetic algorithms and predator algorithms are prone to falling into local optimality and do not fully utilize deep learning's ability to process incomplete data, which leads to limitations in optimization algorithms. In addition, when traditional optimization algorithms optimize parameters with more than 30 dimensions, the convergence failure rate is as high as 60%, and the computational time increases exponentially with the increase in dimensions. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the present invention provides a structural finite element model correction method based on optimization algorithm and deep learning, which effectively solves the problems that current intelligent algorithms such as genetic algorithms and predator algorithms are prone to falling into local optimality, and do not fully utilize the processing capabilities of deep learning for incomplete data, which leads to limitations of optimization algorithms. In addition, when traditional optimization algorithms optimize parameters with more than 30 dimensions, the convergence failure rate is as high as 60%, and the computational time increases exponentially with the increase in dimensions.

[0005] One embodiment of the present invention provides a structural finite element model correction method based on optimization algorithm and deep learning, comprising the following steps:

[0006] S1. Collect measured modal data of the structure, including frequency and incomplete vibration shape data, and establish the corresponding finite element model;

[0007] S2. performing feature extraction and enhancement processing on the incomplete mode shape data through a convolutional neural network, and outputting complete mode shape data that matches the degrees of freedom of the finite element model;

[0008] S3. Constructing a model correction objective function based on the complete vibration mode data and the measured frequency, wherein the objective function includes a weighted combination of a frequency difference term and a vibration mode cosine similarity high-order power difference term;

[0009] S4. Use the improved predator algorithm to globally optimize the finite element model parameters, initialize the population through the sequence generated by Tent chaos, linearly combine the local optimal position with the global optimal position, find the optimal parameters, minimize the objective function, and complete the model correction.

[0010] In one embodiment, in step S1, the measured modal data is collected based on a single-layer aluminum alloy simply supported beam model, the geometric parameters of the simply supported beam are length 3.00m, width 0.15m, thickness 0.01m, divided into 12 segments, each segment is 0.25m long; sensors are arranged at the end points of each segment, and the vibration response data of the first four modes are collected through hammer excitation and accelerometers.

[0011] In one embodiment, in step S2, the training process of the convolutional neural network includes:

[0012] The input data are incomplete vibration modes under limited measurement points, and the output data are complete vibration modes generated by the initial finite element model;

[0013] The convolutional neural network structure includes an input layer, three convolutional layers, three pooling layers, two fully connected layers, and an output layer. The convolutional layers and fully connected layers use the ReLU activation function, the output layer uses the linear activation function, and the loss function is the mean square error.

[0014] The network's initial learning rate was 0.001; the decay factor was 0.5 every 20 epochs; and the batch size was 128. The 30,000 data sets were divided into training, validation, and test sets in a ratio of 8:1:1. The Adam optimization algorithm was used for parameter updates during training, and training was iterated 200 times.

[0015] In one embodiment, in step S3, the objective function expression is:

[0016]

[0017] in, and are the i-th order test frequency and calculation frequency, C SIi is the high-order power of the cosine similarity of the i-th order vibration mode, c1 and c2 are the weighting coefficients of frequency and vibration mode, and m=4 is the modal order.

[0018] In one embodiment, in step S4, the optimization strategy of the improved predator algorithm includes:

[0019] Initializing the population through the sequence generated by Tent chaos can enhance population diversity and improve the early convergence speed of the algorithm. The expression is:

[0020]

[0021] Where y j is the jth particle, Cauchy(0,1) is the standard Cauchy distribution, and its random variable output function is tan[(r5-0.5)π];

[0022] In addition, in the standard HPO algorithm, the predator only updates its current position based on the average position and the prey position, and the algorithm is prone to fall into local optimality. Therefore, the global optimal position T pos(k) The position update formula is introduced to linearly combine the prey position and average position with the global optimal position, which makes the predator's search space wider and improves the global search ability of the algorithm.

[0023] Furthermore, in the standard HPO algorithm, the prey only updates its current position based on the global optimal position, limiting the algorithm's search range. Linearly combining the local optimal position with the global optimal position increases the prey's search range, improving the algorithm's development capabilities and making it more likely to find the global optimal solution in the early stages of evolution. The new position update formula is as follows:

[0024]

[0025] Where x j,k (t) is the current position of the predator, x j,k (t+1) is the next iteration position of the predator, k = 1, 2…d, C represents the balance parameter between exploration and exploitation, and its value decreases from 1 to 0.02 during the iteration process, P pos is the position of the prey, μ is the average of all positions, Z is the adaptive parameter, r5 is a random number in [0, 1], β = 0.1 is the adjustment parameter, if r5 < β, the search agent is regarded as a predator, if r5 ≥ β, the search agent is regarded as a prey.

[0026] In one embodiment, the method is applicable to damage identification and safety assessment of bridge structures, and the finite element model parameters include material elastic modulus, density, cross-sectional geometric parameters, and boundary constraints.

[0027] In one embodiment, the training data set of the convolutional neural network is generated by a finite element model, including incomplete vibration modes and corresponding complete vibration modes under different damage conditions, and the data enhancement method includes noise addition and vibration mode interpolation.

[0028] In one embodiment, the performance of the improved predator algorithm is tested and verified by three test functions, the algorithm parameters are set to a population size of 100, a maximum number of iterations of 200, and the results are averaged after 10 runs.

[0029] In one embodiment, the unit stiffness is used as the correction parameter. When the model is corrected, the algorithm termination condition is that the maximum number of iterations reaches 10,000 or the objective function value is ≤1e-5. The accuracy is evaluated by calculating the MAC value of the frequency error and vibration mode before and after correction. For each correction, the algorithm is run 10 times and the average value is taken to obtain the unit stiffness correction value of the numerical model. The unit stiffness correction value is further used to obtain the corrected structural model, and the first four frequencies and vibration modes of the corrected model are calculated.

[0030] The above technical solution provides a structural finite element model correction method based on optimization algorithm and deep learning, which has the following beneficial effects:

[0031] 1. By using a one-dimensional convolutional neural network (CNN) to enhance the incomplete vibration modes at six measurement points, the vibration modes’ degrees of freedom were increased from 6 to 12, with a reconstruction error of less than 3%. In single-layer simply supported beam experiments, the vibration mode MAC (modal assurance criterion) value was increased from 0.76 to 0.95. Furthermore, the number of sensors was reduced, lowering hardware costs, making this system suitable for economical monitoring of large-span structures such as bridges.

[0032] 2. The improved predator-predator algorithm (IHPO) uses a chaotic mapping to initialize the population and a dynamic inertia weight strategy. In 30-dimensional parameter optimization, it converges faster than the standard HPO and achieves a global optimal solution rate of 92%. For the cross-sea cable-stayed bridge model, the single correction time is shorter than that of traditional optimization algorithms.

[0033] 3. When Gaussian noise with a signal-to-noise ratio of 20dB is added to the input data, the vibration mode reconstruction error is smaller than that of the traditional polynomial interpolation method.

[0034] 4. Combining one-dimensional CNN mode enhancement with an improved predator algorithm solves the problem of "incomplete data + low optimization efficiency"; BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0036] Figure 1 This is the core flow chart of the present invention;

[0037] Figure 2 This is a finite element model diagram of a simply supported beam test of the present invention;

[0038] Figure 3 This is a diagram of a simply supported beam test model of the present invention;

[0039] Figure 4 This is a structural diagram of the convolutional neural network of the present invention;

[0040] Figure 5 The test function image and iteration curve graph of the improved predator algorithm in the present invention;

[0041] Figure 6 This is a diagram showing the arrangement of accelerometers for a continuous rigid frame bridge according to the present invention;

[0042] Figure 7 This is a graph of experimental data for the invention. DETAILED DESCRIPTION

[0043] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0044] In the description of the present invention, it should be understood that descriptions involving orientations, such as up, down, front, back, left, right, etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, they cannot be understood as limitations on the present invention.

[0045] In the description of the present invention, "several" means one or more, "many" means more than two, "greater than," "less than," and "exceed" are understood to exclude the number itself, while "above," "below," and "within" are understood to include the number itself. The use of "first" and "second" in the description is solely for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance, implicitly specifying the number of the indicated technical features, or implicitly specifying the order of the indicated technical features.

[0046] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0047] Combine Figures 1 to 2 As shown, one embodiment of the present invention provides a structural finite element model correction method based on optimization algorithm and deep learning, comprising the following steps:

[0048] S1. Collect measured modal data of the structure, including frequency and incomplete vibration shape data, and establish the corresponding finite element model;

[0049] S2. performing feature extraction and enhancement processing on the incomplete mode shape data through a convolutional neural network, and outputting complete mode shape data that matches the degrees of freedom of the finite element model;

[0050] S3. Constructing a model correction objective function based on the complete vibration mode data and the measured frequency, wherein the objective function includes a weighted combination of a frequency difference term and a vibration mode cosine similarity high-order power difference term;

[0051] S4. Globally optimize the finite element model parameters using an improved predator algorithm, initialize the population through a sequence generated by Tent chaos, linearly combine the local optimal position with the global optimal position, find the optimal parameters, minimize the objective function, and complete the model correction;

[0052] In step S1, the measured modal data is collected based on a single-layer aluminum alloy simply supported beam model. The geometric parameters of the simply supported beam are 3.00m in length, 0.15m in width, and 0.01m in thickness. The beam is divided into 12 segments, each 0.25m in length. Sensors are placed at the end points of each segment, and vibration response data of the first four modes are collected through hammer excitation and accelerometers.

[0053] In step S2, the training process of the convolutional neural network includes:

[0054] The input data are incomplete vibration modes under limited measurement points, and the output data are complete vibration modes generated by the initial finite element model;

[0055] The convolutional neural network structure includes an input layer, three convolutional layers, three pooling layers, two fully connected layers, and an output layer. The convolutional layers and fully connected layers use the ReLU activation function, the output layer uses the linear activation function, and the loss function is the mean square error.

[0056] The network's initial learning rate was 0.001; the decay factor was 0.5 every 20 rounds; and the batch size was 128. The 30,000 data sets were divided into training, validation, and test sets in a ratio of 8:1:1. The Adam optimization algorithm was used for parameter updates during training, and training was iterated 200 times.

[0057] In step S3, the objective function expression is:

[0058]

[0059] in, and are the i-th order test frequency and calculation frequency, C SIi is the high-order power of the cosine similarity of the i-th order vibration mode, c1 and c2 are the weighting coefficients of frequency and vibration mode, and m=4 is the modal order.

[0060] In step S4, the optimization strategy of the improved predator algorithm includes:

[0061] Initializing the population through the sequence generated by Tent chaos can enhance population diversity and improve the early convergence speed of the algorithm. The expression is:

[0062]

[0063] Where y j is the jth particle, Cauchy(0,1) is the standard Cauchy distribution, and its random variable output function is tan[(r5-0.5)π];

[0064] In addition, in the standard HPO algorithm, the predator only updates its current position based on the average position and the prey position, and the algorithm is prone to fall into local optimality. Therefore, the global optimal position T pos(k) The position update formula is introduced to linearly combine the prey position and average position with the global optimal position, which makes the predator's search space wider and improves the global search ability of the algorithm.

[0065] Furthermore, in the standard HPO algorithm, the prey only updates its current position based on the global optimal position, limiting the algorithm's search range. Linearly combining the local optimal position with the global optimal position increases the prey's search range, improving the algorithm's development capabilities and making it more likely to find the global optimal solution in the early stages of evolution. The new position update formula is as follows:

[0066]

[0067] Where x j,k (t) is the current position of the predator, x j,k (t+1) is the next iteration position of the predator, k = 1, 2…d, C represents the balance parameter between exploration and exploitation, and its value decreases from 1 to 0.02 during the iteration process, P pos is the position of the prey, μ is the average of all positions, Z is the adaptive parameter, r5 is a random number in [0, 1], β = 0.1 is the adjustment parameter, if r5 < β, the search agent is considered as a predator, if r5 ≥ β, the search agent is considered as a prey;

[0068] The method is applicable to damage identification and safety assessment of bridge structures, wherein the finite element model parameters include material elastic modulus, density, cross-sectional geometric parameters and boundary constraints;

[0069] The training data set of the convolutional neural network is generated by a finite element model, including incomplete vibration modes and corresponding complete vibration modes under different damage conditions. The data enhancement method includes noise addition and vibration mode interpolation.

[0070] The performance of the improved predator algorithm was tested and verified using three test functions. The algorithm parameters were set to a population size of 100 and a maximum number of iterations of 200. The results were averaged after 10 runs.

[0071] In the model correction, the unit stiffness is used as the correction parameter. During the model correction, the algorithm termination condition is that the maximum number of iterations reaches 10,000 or the objective function value is ≤1e-5. The accuracy is evaluated by calculating the MAC value of the frequency error and vibration mode before and after correction. During each correction, the algorithm is run 10 times and the average value is taken to obtain the unit stiffness correction value of the numerical model. The unit stiffness correction value is further used to obtain the corrected structural model, and the first four frequencies and vibration modes after the model correction are calculated.

[0072] In this example, in the single-layer simply supported beam verification scenario:

[0073] 1. Specimen parameters

[0074] The simply supported beam test model is as follows Figure 2 As shown;

[0075] Material: Single-layer aluminum alloy beam, elastic modulus 69GPa, density 2900kg / m 3 ;

[0076] Geometric dimensions: 3.00m(L)×0.15m(W)×0.01m(H).

[0077] 2. Simply supported beam finite element model parameters

[0078] The initial finite element model of the simply supported beam structure is established using MATLAB. Figure 3 The model size, unit division and boundary conditions are consistent with the test structure. The material elastic modulus is 6.9×10 10 Pa, density is 2900 kg / m 3 , the cross-sectional area is 1.5×10 -3 m 2 , section moment of inertia 1.25×10 -8 m 4 Through eigenvalue analysis, the first four modal frequencies and vibration shapes of the structure are calculated.

[0079] 3. Data Collection

[0080] Power signal acquisition equipment: DASP dynamic acquisition analyzer and its supporting software developed by Beijing Oriental Vibration and Noise Technology Research Institute, and the sensor is BK single-axis acceleration sensor.

[0081] The beam was divided into 12 segments with a length of 0.25 m. Hammer excitation was applied to the midpoint of segment 7. The vertical acceleration of the endpoints of each segment was collected using an accelerometer, and the first four modal frequencies and vibration shapes of the structure were identified.

[0082] 4. CNN vibration mode enhancement results

[0083] Convolutional neural network structure Figure 4 As shown in Figure 2, the CNN model parameters are set as follows: the weight matrix of Conv1D(16, kernel=3) is 0.12, -0.05, 0.08 (first layer filter example), the convolution kernel size is 3×3, the number of convolution kernels in each convolution layer is 64, 64, and 128 respectively, the number of nodes in each fully connected layer is 256 and 128 respectively, the batch size is 64, the learning rate is 0.01, and the number of training times is 200;

[0084] Under varying degrees of noise contamination, good modal enhancement results were achieved when the number of measurement points accounted for only 54%, 38%, and 31% of the total number of nodes. When the noise level was 10%, the MSE values for all three measurement point conditions were less than 0.23, and the R values were all greater than 0.98. Therefore, the deep learning-based modal enhancement method has good effectiveness and robustness, achieving good results even when the number of sensors accounts for only 31% of the total number of nodes.

[0085] 5. Improved Predator-Hunter Algorithm (IHPO) Optimization Performance Evaluation

[0086] In order to evaluate the optimization performance of the standard predator-predator algorithm (HPO) and the improved predator-predator algorithm (IHPO), three test functions (function images as shown in Figure 5 The algorithm's population size and iteration number are 100 and 200 respectively, and the average value is taken after 10 runs.

[0087] When the maximum number of iterations is reached, the optimal value, worst value, average value, and standard deviation of the objective function of the IHPO algorithm are all less than 1×10 -300 , for the test function f3, it is less than 1×10 -150 ; When the HPO algorithm reaches the maximum number of iterations, all the results for the three test functions are greater than 1×10 -80 Therefore, the convergence accuracy of the IHPO algorithm is significantly higher than that of the HPO algorithm. For the test functions f1, f2, and f3, the IHPO algorithm only needs to iterate the objective function 43, 51, and 74 times, respectively, to converge to 1×10 -30 The HPO algorithm requires 110, 129, and 192 iterations, respectively, to achieve the same convergence results. Therefore, the IHPO algorithm converges significantly faster than the HPO algorithm. In summary, the IHPO algorithm has stronger global optimization capabilities, higher convergence efficiency and accuracy, and greater potential for model correction.

[0088] 4. Correction results of the simply supported beam finite element model based on optimization algorithm and deep learning

[0089] The unit stiffness is used as the correction parameter. When the model is corrected, the algorithm termination condition is that the maximum number of iterations reaches 10,000 or the objective function value is ≤1×10 -5 The algorithm is run 10 times for each correction and the average value is taken to obtain the element stiffness correction value of the numerical model. The element stiffness correction value is further used to obtain the corrected structural model, and the first four frequencies and vibration modes of the corrected model are calculated.

[0090] The average time consumed for model correction after mode shape enhancement is 45% less than that when the mode shape is not enhanced. After the modal shape is enhanced based on deep learning, the errors between the calculated frequencies of each order of the structural model and the measured frequencies are greatly reduced, and the errors are controlled within 0.5%. The MAC values are all greater than 0.99, and the mode shape is well matched.

[0091] In the application scenario of continuous rigid frame bridge engineering:

[0092] 1. Bridge parameters

[0093] The main bridge adopts a 64m+120m+64m concrete continuous rigid frame bridge. The main piers of the lower structure are reinforced concrete double-legged thin-walled piers. The pier body is consolidated with the upper structure box girder, and the transition piers are thin-walled piers.

[0094] Sensor layout: The DH5907 wireless bridge modal test and analysis system is used to collect structural vibration signals. Its ambient temperature operating range is 0℃~60℃, which is suitable for environmental monitoring. In the modal test, the layout of the accelerometer is as follows: Figure 6 As shown in the figure, the acceleration signal is collected to identify the first to third order natural frequencies and vibration modes of the bridge.

[0095] 2. Continuous rigid frame bridge finite element model parameters

[0096] The initial finite element model was established based on MATLAB. The superstructure and piers were discretized into 2-node 3D beam elements. The Poisson's ratio of the material was 0.2, and the mass density of the superstructure and piers was 2500 kg / m 3 and 2450kg / m 3 The superstructure and piers were discretized into 74 and 44 elements, respectively, for a total of 118 elements in the main bridge. For the boundary condition simulation, the superstructure was assumed to be fixed to the top of the piers; the vertical and lateral translational degrees of freedom, as well as the vertical and longitudinal rotational degrees of freedom, were constrained at both ends of the superstructure.

[0097] 3. Results of the modified finite element model of a concrete continuous rigid frame bridge based on optimization algorithms and deep learning

[0098] Modal enhancement results: The MAC value of the first three modes increased from 0.85 to 0.935;

[0099] Model correction results: The maximum relative error of the first three vertical bending frequencies was reduced from 15.11% to 2.79%; the MAC values of the first three vibration modes were all above 0.98.

[0100] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformation made by using the paper document and the contents of the drawings of the present invention under the inventive concept of the present invention, or direct / indirect application in other related technical fields, is included in the patent protection scope of the present invention.

Claims

1. A structural finite element model correction method based on optimization algorithm and deep learning, characterized in that: The following steps are involved: S1. Collect measured modal data of the structure, including frequency and incomplete vibration shape data, and establish the corresponding finite element model; S2. performing feature extraction and enhancement processing on the incomplete mode shape data through a convolutional neural network, and outputting complete mode shape data that matches the degrees of freedom of the finite element model; S3. Constructing a model correction objective function based on the complete vibration mode data and the measured frequency, wherein the objective function includes a weighted combination of a frequency difference term and a vibration mode cosine similarity high-order power difference term; S4. Use the improved predator algorithm to globally optimize the finite element model parameters, initialize the population through the sequence generated by Tent chaos, linearly combine the local optimal position with the global optimal position, find the optimal parameters, minimize the objective function, and complete the model correction.

2. The structural finite element model correction method based on optimization algorithm and deep learning according to claim 1 is characterized in that: In step S1, the measured modal data is collected based on a single-layer aluminum alloy simply supported beam model. The geometric parameters of the simply supported beam are length 3.00m, width 0.15m, thickness 0.01m, and it is divided into 12 segments, each with a length of 0.25m. The sensors are arranged at the end points of each segment, and the first four modal frequencies and vibration modes are collected through hammer excitation and accelerometers.

3. The structural finite element model correction method based on optimization algorithm and deep learning according to claim 1 is characterized in that: In step S1, the initial finite element model of the simply supported beam structure is established using MATLAB software. The size, unit division and boundary conditions of the model are consistent with the test structure. The first four modal frequencies and vibration shapes of the structure are calculated through eigenvalue analysis.

4. The structural finite element model correction method based on optimization algorithm and deep learning according to claim 1, characterized in that: In step S2, the training process of the convolutional neural network includes: The input data are incomplete vibration modes under limited measurement points, and the output data are complete vibration modes generated by the initial finite element model; The convolutional neural network structure includes an input layer, three convolutional layers, three pooling layers, two fully connected layers, and an output layer. The convolutional layers and fully connected layers use the ReLU activation function, the output layer uses the linear activation function, and the loss function is the mean square error. The network's initial learning rate was 0.001; the decay factor was 0.5 every 20 epochs; and the batch size was 128. The 30,000 data sets were divided into training, validation, and test sets in an 8:1:1 ratio. The "Adam" optimization algorithm was used for parameter updates during training, and training was iterated 200 times.

5. The structural finite element model correction method based on optimization algorithm and deep learning according to claim 3 is characterized in that: In step S3, the objective function expression is: in, and are the i-th order test frequency and calculation frequency, C SIi is the high-order power of the cosine similarity of the i-th order vibration mode, c1 and c2 are the weighting coefficients of frequency and vibration mode, and m=4 is the modal order.

6. According to the structural finite element model correction method based on optimization algorithm and deep learning according to claim 1, in step S4, the optimization strategy of the improved predator algorithm includes: Initializing the population through the sequence generated by Tent chaos can enhance population diversity and improve the early convergence speed of the algorithm. The expression is: Where y j is the jth particle, Cauchy(0,1) is the standard Cauchy distribution, and its random variable output function is tan[(r5-0.5)π]; In addition, in the standard HPO algorithm, the predator only updates its current position based on the average position and the prey position, and the algorithm is prone to fall into local optimality. Therefore, the global optimal position T pos(k) The position update formula is introduced to linearly combine the prey position and average position with the global optimal position, which makes the predator's search space wider and improves the global search ability of the algorithm. Furthermore, in the standard HPO algorithm, the prey only updates its current position based on the global optimal position, limiting the algorithm's search range. Linearly combining the local optimal position with the global optimal position increases the prey's search range, improving the algorithm's development capabilities and making it more likely to find the global optimal solution in the early stages of evolution. The new position update formula is as follows: Where x j,k (t) is the current position of the predator, x j,k (t+1) is the next iteration position of the predator, k = 1, 2…d, C represents the balance parameter between exploration and exploitation, and its value decreases from 1 to 0.02 during the iteration process, P pos is the position of the prey, μ is the average of all positions, Z is the adaptive parameter, r5 is a random number in [0, 1], β = 0.1 is the adjustment parameter, if r5 < β, the search agent is regarded as a predator, if r5 ≥ β, the search agent is regarded as a prey.

7. The structural finite element model correction method based on optimization algorithm and deep learning according to claim 5, characterized in that: The method is applicable to damage identification and safety assessment of bridge structures, and the finite element model parameters include material elastic modulus, density, cross-sectional geometric parameters and boundary constraints.

8. The structural finite element model correction method based on optimization algorithm and deep learning according to claim 5, characterized in that: The training data set of the convolutional neural network is generated through a finite element model, including incomplete vibration modes and corresponding complete vibration modes under different damage conditions. The data enhancement method includes noise addition and vibration mode interpolation.

9. The structural finite element model correction method based on optimization algorithm and deep learning according to claim 5, characterized in that: The performance of the improved predator algorithm was tested and verified using three test functions. The algorithm parameters were set to a population size of 100 and a maximum number of iterations of 200. The algorithm was run 10 times and the average results were taken.

10. The structural finite element model correction method based on optimization algorithm and deep learning according to claim 5, characterized in that: Taking the unit stiffness as the correction parameter, when the model is corrected, the algorithm termination condition is that the maximum number of iterations reaches 10,000 or the objective function value is ≤1e-5. The accuracy is evaluated by calculating the MAC value of the frequency error and vibration mode before and after correction. The algorithm is run 10 times for each correction and the average value is taken to obtain the unit stiffness correction value of the numerical model. The corrected structural model is further obtained from the unit stiffness correction value, and the first four frequencies and vibration modes of the corrected model are calculated.

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