Vortex-induced vibration response prediction method for double-deck steel truss bridges based on machine learning algorithm

Abstract

The present invention discloses a method for predicting the vortex-induced vibration response of a double-deck steel truss bridge based on a machine learning algorithm. Through wind tunnel tests on double-deck steel truss bridge segment models, the influence of various ancillary facilities and additional aerodynamic measures on the vortex-induced vibration of the double-deck steel truss bridge section is experimentally analyzed. Through numerical simulation, the vortex-induced vibration generation mechanism of the completed bridge segment model is analyzed, and the influence of parameter changes of additional aerodynamic measures on the vortex-induced vibration of the double-deck steel truss bridge section is explored. Based on the machine learning algorithm, a prediction model for the section amplitude under different wind speeds and a prediction model for the vortex-induced vibration characteristic parameters under different additional aerodynamic measures are established to predict the vortex-induced vibration response of the double-deck steel truss bridge. The method of the present invention, combining wind tunnel tests, numerical simulations, and machine learning methods, realizes the prediction of the vortex-induced vibration response of the double-deck steel truss bridge with good stability and high prediction accuracy, thereby providing a reference for bridge design, operation, and maintenance.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge vortex-induced vibration response, and specifically to a vortex-induced vibration response prediction method for a double-deck steel truss bridge based on a machine learning algorithm. Background Art

[0002] A double-deck bridge deck can improve the operating efficiency of the bridge. The road-rail dual-use bridge with steel truss as the main beam brings great convenience to traffic. Compared with the traditional main beam form, the steel truss has more complex aerodynamic performance, and the vortex shedding and attachment of its structural surface in the wind field environment are also more complicated.

[0003] Currently, the primary approaches to addressing vortex-induced vibrations in bridges include wind tunnel testing and numerical simulation. Wind tunnel testing, while relatively mature, is expensive and suffers from poor visualization. Numerical simulation, on the other hand, offers lower costs and high visualization, but suffers from low prediction accuracy. Therefore, it is crucial to develop a method for predicting the vortex-induced vibration response of double-deck steel truss bridges to improve prediction stability, accuracy, and cost. Summary of the Invention

[0004] The purpose of the present invention is to provide a vortex-induced vibration response prediction method for a double-deck steel truss bridge based on machine learning to address the above defects.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] The vortex-induced vibration response prediction method for a double-deck steel truss bridge based on a machine learning algorithm includes the following steps:

[0007] S1. Use ANSYS software to establish a finite element model of a double-deck steel truss bridge and calculate its dynamic characteristics. Based on this, design a segmental model wind tunnel test, conduct force and vibration tests, and thus obtain the vortex-induced vibration characteristics of the double-deck steel truss bridge.

[0008] S2. Add three additional facilities to the double-deck steel truss bridge: upper maintenance railings, maintenance vehicle tracks, and track noise barriers; and three additional aerodynamic measures: air nozzles, deflectors, and central stabilizers. Analyze the vortex-induced vibration response of the bridge through wind tunnel tests to determine the vortex-induced vibration response of the additional facilities and aerodynamic measures to the double-deck steel truss bridge.

[0009] S3. Computational fluid dynamics (CFD) numerical simulations of a double-deck steel truss bridge section were performed using the Fluent platform, and the independence of the number of grids, web member positions, and time steps was verified. The vortex-induced vibration of the double-deck steel truss bridge was analyzed by varying the parameters of the additional aerodynamic measures, and the influence of the multi-parameter additional aerodynamic measures on the vortex-induced vibration of the double-deck steel truss bridge was determined.

[0010] S4. Using three machine learning algorithms, SVR, BPNN, and RF, a cross-sectional amplitude prediction model for a double-deck steel truss bridge at different wind speeds and a vortex-induced vibration characteristic parameter prediction model under different additional aerodynamic measures were established. The prediction model parameters were optimized to achieve the best and most effective prediction of the cross-sectional vortex-induced vibration response of the double-deck steel truss bridge.

[0011] Preferably, the S1 step is as follows:

[0012] S11. Calculation of bridge dynamic characteristics:

[0013] Using ANSYS software, a three-dimensional finite element model of the double-deck steel truss bridge was constructed and dynamic characteristics were calculated to obtain the vibration mode and frequency of the double-deck steel truss bridge structure, providing a basis for the design parameters of the wind tunnel test model.

[0014] S12. Segmental model wind tunnel test design:

[0015] Based on the actual bridge size, wind tunnel test section size, and similarity criteria, the segment model scale ratio and test wind speed ratio of the double-deck steel truss bridge were determined, and a segment model of the double-deck steel truss bridge was constructed. The segment model of the double-deck steel truss bridge was installed in the test wind tunnel via an angle of attack turntable and steel brackets, and the data acquisition equipment used in the test was installed.

[0016] S13. Wind tunnel test analysis of segmental models:

[0017] (1) Force measurement test: The static three-force coefficients of the segment models in the construction state and the completed bridge state were measured. The static three-force coefficients of the segment models in the construction state and the completed bridge state were obtained when the wind speeds were 10 m / s, 15 m / s and 20 m / s and the downwind angle was within the range of -12° to +12°, and the corresponding static three-force coefficients were calculated.

[0018] (2) Vibration test: The changes in the vertical amplitude and torsional angle of the segment model at wind attack angles of 0, ±3°, and ±5° were recorded using a laser displacement sensor, thereby obtaining the vertical bending vortex vibration response and torsional vortex vibration response of the segment model in the construction state and the completed bridge state;

[0019] (3) Time history and spectrum response: The time history spectrum at the maximum reduction amplitude of the vertical bending vortex vibration zone and the maximum torsion angle of the two torsion vortex vibration zones are converted to obtain the dominant frequency and compared with the vertical bending or torsion frequency of the model.

[0020] Preferably, in step S11, the dynamic characteristic calculation includes static calculation and dynamic calculation. The static calculation refers to considering the influence of geometric nonlinearity under constant load, and the dynamic calculation uses the Block Lanczos method to perform dynamic solution in the construction state and the bridge completion state.

[0021] Preferably, in step S12, the data acquisition equipment includes a slope measuring instrument, a wind speed measurement system, a laser displacement sensor and a high-frequency force balance, specifically including: a multifunctional slope measuring instrument for measuring angles; a TFI series 100 Cobra pulsating wind speed measurement system that can accurately measure three-dimensional pulsating wind speed in the flow field, with a measurement accuracy after zero calibration higher than 0.5 m / s and a frequency of up to 2000 Hz; a type II laser displacement sensor that can stably detect various targets; and a high-frequency force balance that can measure pressure and torque in six degrees of freedom.

[0022] Preferably, the S4 step is as follows:

[0023] S41. Machine learning algorithm determination:

[0024] Determine the use of three machine learning algorithms, SVR, BPNN, and RF, to construct a prediction model for the cross-sectional amplitude of a double-deck steel truss bridge at different wind speeds and a prediction model for the vortex-vibration characteristic parameters under different additional aerodynamic measures;

[0025] S42. Model learning sample data processing:

[0026] In step S3, the calculation results of 58 simulated working conditions, including the original cross-section, are integrated to obtain a VIV-R data set for predicting vortex vibration characteristic parameters; numerical calculations are performed for 20 different wind speeds in the reduced wind speed range of 1.5 to 3.0 for each working condition in the VIV-R data set to obtain a VIV-A data set for surface amplitude prediction; the VIV-A data set and the VIV-R data set are normalized using the MATLAB program and the mapminmax function; a k-fold cross-validation method is used to determine the ratio of the training set to the test set, and the average of the k test results is used as the evaluation parameter;

[0027] S43. Prediction of Sectional Amplitude of Double-Deck Steel Truss Bridges:

[0028] (1) Model parameter optimization:

[0029] A prediction model was established based on three machine learning algorithms: SVR, BPPNN, and RF, and the model parameters were optimized using the k-fold cross-validation method.

[0030] (2) Evaluation of prediction results:

[0031] The VIV-A dataset is divided into training set and test set according to 9:1. The evaluation indicators RMSE and R 2 Obtain the best model for predicting the amplitude of a double-deck steel truss bridge under different wind speeds;

[0032] (3) Prediction model optimization:

[0033] The optimal model is optimized using the genetic algorithm (GA) and the particle swarm algorithm (PSO). An optimized model is established and the amplitude prediction results are compared with the optimal model to verify the effectiveness of the optimized model and obtain the best effective model for amplitude prediction, thus completing the entire process of amplitude prediction for the double-deck steel truss bridge section under different wind speeds.

[0034] S44. Prediction of vortex-induced vibration characteristic parameters:

[0035] (1) Model parameter optimization:

[0036] A prediction model was established based on three machine learning algorithms: SVR, BPPNN, and RF. The VIV-R dataset was used to train the established prediction model, and the model parameters were optimized using the k-fold cross-validation method.

[0037] (2) Evaluation of prediction results:

[0038] The VIV-R dataset is divided into training set and test set according to the ratio of 3:1. The evaluation indicators RMSE and R 2 The optimal model for predicting the vortex vibration of double-deck steel truss bridge section is obtained by obtaining the starting wind speed, locking interval length and maximum reduced amplitude.

[0039] (3) Prediction model optimization:

[0040] The optimal model is optimized by genetic algorithm GA and particle swarm algorithm PSO, and an optimized model is established. The amplitude prediction results are compared with the optimal model to verify the effectiveness of the optimized model and obtain the best effective model for amplitude prediction, thus completing the entire process of predicting the vortex-vibration characteristic parameters of the double-deck steel truss bridge section.

[0041] The beneficial effects of the present invention are:

[0042] The present invention proposes a vortex-induced vibration response prediction method for a double-deck steel truss bridge based on a machine learning algorithm. Combined with wind tunnel tests and numerical simulations, the method studies the influence of additional aerodynamic measures on the vortex-induced vibration of a double-deck steel truss bridge. The data such as the vibration starting wind speed, locking range, and maximum amplitude of the double-deck steel truss bridge are obtained and compiled into a learning sample database. The vortex-induced vibration response of the double-deck steel truss bridge is predicted through a machine learning method. The method has low cost, high visualization, good stability, and high prediction accuracy, thereby providing a reference for bridge design, operation, and maintenance. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is the technical roadmap of the present invention.

[0044] Figure 2 The comparison chart of the static three-force coefficients between wind tunnel test and numerical simulation;

[0045] Figure 3This is a comparison chart of vortex vibration response between wind tunnel test and numerical simulation;

[0046] Figure 4 This is the vortex shedding evolution diagram of a double-deck steel truss bridge section during a single vibration cycle;

[0047] Figure 5 The following are the prediction results (amplitude prediction) of three machine learning models;

[0048] Figure 6 Comparison of predicted values ​​and actual values ​​(amplitude prediction) of three machine learning models;

[0049] Figure 7 This is the operation flow chart of the GA-BPNN model;

[0050] Figure 8 It is the operation flow chart of the PSO-BPNN model;

[0051] Figure 9 This is a comparison chart of prediction results before and after BPNN model optimization (amplitude prediction);

[0052] Figure 10 The following are the prediction results (vortex vibration characteristic parameter prediction) of three machine learning models;

[0053] Figure 11 Comparison of predicted values ​​and actual values ​​of three machine learning models (vortex vibration characteristic parameter prediction); DETAILED DESCRIPTION

[0054] The present invention is further described below with reference to the embodiments. It should be noted that these are merely examples and illustrations of the concept of the present invention. Those skilled in the art may make various modifications or additions to the described specific embodiments or replace them in a similar manner. As long as they do not deviate from the concept of the invention or exceed the scope defined by the claims, they should be deemed to fall within the scope of protection of the present invention.

[0055] Example 1:

[0056] like Figure 1-11 As shown in FIG, a vortex-induced vibration response prediction method for a double-deck steel truss bridge based on a machine learning algorithm includes the following steps:

[0057] S1. A finite element model of a double-deck steel truss bridge was established using ANSYS software to calculate its dynamic characteristics. Based on this, a wind tunnel test of the segment model was designed. Force and vibration measurements were performed to obtain the vortex-vibration influence characteristics of the double-deck steel truss bridge.

[0058] S11. Bridge dynamic characteristics analysis:

[0059] A three-dimensional finite element model of the double-deck steel truss bridge was constructed using ANSYS software and dynamic characteristics analysis was performed to obtain the vibration mode and frequency of the double-deck steel truss bridge structure, providing a basis for the design parameters of the wind tunnel test model.

[0060] (1) Overview of double-deck steel truss bridge project:

[0061] Let’s take the Chongqing Huangjuetuo Yangtze River Bridge as an example:

[0062] The Chongqing Huangjuetuo Yangtze River Bridge is a long-span suspension bridge for both road and rail, located on the connecting road of the Chongqing-Changsha Expressway. It has two decks: the upper deck has six lanes in both directions, while the lower deck has a two-way track in the center, flanked by four lanes and pedestrian walkways. According to the Huangjuetuo Yangtze River Bridge's construction drawing design specifications, its design base wind speed is 27.5 m / s averaged at 10 meters above ground level for 10 minutes with a return period of 100 years.

[0063] (2) Constructing a three-dimensional finite element model:

[0064] By calculating the dynamic characteristics of a bridge, we can determine the vibration modes and frequencies of the bridge structure, providing a basis for designing parameters for wind tunnel test models. ANSYS software was used to analyze the dynamic characteristics of the Huangjuetuo Yangtze River Bridge. The 3D finite element model of the Huangjuetuo Yangtze River Bridge includes the side span main cables, main span main cables, suspenders, rigid arms, main towers, main beams, crossbeams, web members, and chords, with dimensions identical to those of the actual bridge.

[0065] (3) Dynamic characteristics analysis:

[0066] The calculation of dynamic characteristics includes static calculation and dynamic calculation. Static calculation refers to considering the influence of geometric nonlinearity under constant load. Dynamic calculation uses the Block Lanczos method to solve the dynamic problems in the construction state and the completed bridge state. The construction state refers to the state when the main beam hoisting progress is 100% and no ancillary facilities are installed.

[0067] The finite element dynamic characteristics calculation results of the construction state and the completed bridge state models obtained provide a reference for the design of the construction state and the completed bridge state segment models in the wind tunnel test.

[0068] S12. Segmental model wind tunnel test design:

[0069] According to the actual bridge size, wind tunnel test section size and similarity criteria, the segment model scale ratio and test wind speed ratio of the double-deck steel truss bridge are determined, and the segment model of the double-deck steel truss bridge is constructed; the segment model of the double-deck steel truss bridge is installed in the test wind tunnel through the attack angle turntable and steel bracket, and the data acquisition equipment used in the test is installed.

[0070] The wind tunnel tests were conducted in the DC teaching wind tunnel laboratory at Chongqing University. The test tunnel utilizes an all-steel welded structure, consisting of wall panels, bulkheads, longitudinal ribs, and a supporting frame. This is a DC air-intake wind tunnel with a test section wind speed range of 0.5 to 35 m / s. The flow field quality meets the general requirements for atmospheric boundary layer wind tunnels, with a turbulence level of less than 0.3%.

[0071] According to the actual bridge size, the size of the wind tunnel test section, and the requirements of the similarity criterion, the segment model scale ratio of the double-deck steel truss bridge was determined to be 1:55, the test wind speed ratio was 1:4.48, and the segment model of the double-deck steel truss bridge was constructed.

[0072] In the test wind tunnel, a segmental model of a double-deck steel truss bridge was designed to vary the wind's angle of attack by adjusting the angle of the angle-of-attack turntable. Eight springs, mounted above and below the steel supports, provided the system with vertical and torsional stiffness, ensuring the segmental model could translate vertically and rotate about its cross-sectional axis, thereby accurately simulating the vibration characteristics of both vertical and torsional degrees of freedom. Laser displacement sensors were placed at both ends of the steel supports to collect the segmental model's time-history vibration response.

[0073] The data acquisition equipment used in the test includes a slope meter, a wind speed measurement system, a laser displacement sensor, and a high-frequency force balance. Specifically, they include: a multifunctional slope meter for measuring angles; a TFI Series 100 Cobra pulsating wind speed measurement system that can accurately measure three-dimensional pulsating wind speed in the flow field, with a zero-calibrated measurement accuracy of better than 0.5m / s and a frequency of up to 2000Hz; a Type II laser displacement sensor that can stably detect various targets; and a high-frequency force balance developed by ATI that can measure pressure and torque in six degrees of freedom. It uses noiseless silicon strain gauge technology, has high hardness, and has overload self-protection functions.

[0074] S13. Wind tunnel test analysis of segmental models:

[0075] (1) Force measurement test.

[0076] To analyze the static characteristics of the main girder of a double-deck steel truss bridge, the static three-dimensional force coefficients were determined for segmental models in both the construction and completed states. The force measurements were performed to determine the static three-dimensional forces on the segmental models in both the construction and completed states at wind speeds of 10 m / s, 15 m / s, and 20 m / s, with a downwind angle of attack ranging from -12° to +12°. The corresponding static three-dimensional force coefficients were then calculated.

[0077] (2) Vibration test.

[0078] The experiment measured the vortex vibration amplitudes of the segment models at wind angles of 0, ±3°, and ±5° for both the constructed and completed bridge models. Laser displacement sensors were used to record the changes in vertical amplitude and torsional angle at wind angles of 0, ±3°, and ±5°, thereby determining the vertical-bending and torsional vortex vibration responses of the segment models at both the constructed and completed bridge models.

[0079] (3) Time course and spectrum response.

[0080] During vibration testing, the completed bridge segment model experienced vertical bending and torsional vortex vibrations at wind angles of +3° and +5°. The time-history spectra at the maximum reduced amplitude in the vertical bending vortex vibration zone and the maximum torsional angle in the two torsional vortex vibration zones were converted to obtain the dominant frequencies and compared with the model's vertical bending or torsional frequencies.

[0081] S2. Three additional facilities, namely, upper maintenance road railings, maintenance vehicle tracks, and track sound barriers, as well as three additional aerodynamic measures, namely, wind nozzles, guide plates, and central stabilizer plates, were added to the double-deck steel truss bridge. The vortex-induced vibration response of the double-deck steel truss bridge at wind attack angles of +3° and +5° was analyzed through wind tunnel tests to obtain the vortex-induced vibration response patterns of the additional facilities and aerodynamic measures.

[0082] Wind tunnel tests revealed that both ancillary facilities and additional aerodynamic measures have an impact on the cross-sectional vortex-induced vibration of double-deck steel truss bridges, but the ancillary facilities generally have a negative impact. When properly positioned, additional aerodynamic measures can effectively suppress the vortex-induced vibration of double-deck steel truss bridges. Specifically, reducing the air permeability of the upper maintenance road railings, moving the maintenance vehicle track inward, or adding a track sound barrier will increase the maximum reduced amplitude and maximum torsion angle of the double-deck steel truss bridge. Adding upper chord nozzles, web member deflectors, lower chord deflectors, and a central stabilizer plate can effectively suppress the vortex-induced vibration of the main girder. Adding web member nozzles has no significant effect on suppressing the vortex-induced vibration of the main girder, while adding upper chord deflectors exacerbates the vortex-induced vibration response. Adding nozzles to both the upper chord and web members has the best suppression effect on vertical bending vortex-induced vibration, while adding deflectors to both the web member and lower chord member has the best suppression effect on torsional vortex-induced vibration. Adding deflectors to both the upper chord and lower chord member exacerbates the vortex-induced vibration response.

[0083] S3. Computational fluid dynamics (CFD) numerical simulations of the double-deck steel truss bridge section were performed using the Fluent platform, and the independence of the number of grids, web position, and time step was verified. The vortex-induced vibration of the double-deck steel truss bridge was analyzed by varying the parameters of the additional aerodynamic measures, and the influence of multi-parameter additional aerodynamic measures on the vortex-induced vibration of the double-deck steel truss bridge was determined.

[0084] S31. CFD numerical simulation method.

[0085] (1) Original cross-section simulation. The Reynolds time-averaged simulation (RANS) method is used to solve the flow field characteristics, and the turbulence model selected is the SST k-ω. The numerical simulation uses an unstructured grid, and two dynamic mesh algorithms, smoothing and reconstruction, are used to realize the movement and update of the grid.

[0086] (2) UDF secondary development. The vortex vibration of the double-deck steel truss bridge section can be regarded as a rigid body motion in a two-dimensional flow field. Therefore, the DEFINE_CG_MOTION macro is used to define the linear velocity and angular velocity of the rigid body at each time step. For the CFD numerical simulation of the vortex vibration of the double-deck steel truss bridge section, only the vertical vibration is considered, that is, the displacement in the y direction. The differential equation of the vertical vibration is:

[0087]

[0088] Where m is the mass of the structure, and are the acceleration and velocity of the vertical vibration of the structure, ω h is the vertical bending natural frequency of the structure, ζ h is the initial damping ratio of the vertical bending of the structure, F t is the force exerted by the fluid on the structure at time t.

[0089] S32. Numerical simulation verification.

[0090] (1) Modeling was performed in ANSYS SpaceClaim according to the model dimensions used in the wind tunnel test. The SST k-ω model, which is well-suited for flows around bluff bodies, was selected as the turbulence model for the CFD numerical simulations. To verify the validity of the numerical simulations, the independence of the number of grid cells, the position of the web members, and the time step was verified.

[0091] (2) To verify the accuracy of CFD numerical simulation, the static three-force coefficients of the original section of the double-deck steel truss bridge in the completed state are compared between the wind tunnel test and the numerical simulation at five wind attack angles of 0, ±3° and ±5° when the wind speed of the actual bridge is 10m / s. Figure 2 As shown. Figure 1 The minimum error between the experimental and simulated values ​​for the static three-force coefficient is 1.23%, and the maximum error is 9.08%. The average errors for the drag coefficient, lift coefficient, and moment coefficient are 2.92%, 3.13%, and 6.15%, respectively, for an overall average error of 4.07%. The simulation results for the static three-force coefficient indicate that the numerical simulation has a small error and high accuracy.

[0092] (3) According to step S2, the vertical bending vortex vibration occurred in the double-deck steel truss bridge section at wind attack angles of +3° and +5°, and the locking interval was within the range of 1.0 to 3.4 reduced wind speeds. Therefore, the numerical simulation was also carried out within this wind speed range, and the corresponding calculated wind speed was 0.64m / s to 2.16m / s. The vertical bending amplitude at different reduced wind speeds was calculated using the UDF program and compared with the results of the wind tunnel test. The wind tunnel test and numerical simulation vortex vibration response comparison is as follows: Figure 3 shown.

[0093] Depend on Figure 3 (a) It can be seen that the maximum reduced amplitude of the numerical simulation at +3° wind angle is 0.298, and the error with the experiment is 12.9%; Figure 3 (b) As can be seen, the maximum reduced amplitude in the numerical simulation at a +5° wind angle of attack is 0.374, with an error of 9.0% compared to the experimental result. This indicates that the vertical bending vortex-induced vibration response results obtained from the numerical simulation and wind tunnel test are similar. The onset wind speed and locking interval length of the numerical simulation are consistent with those of the wind tunnel test, with only a slight difference in the maximum reduced amplitude, and the errors are all within a reasonable range. This demonstrates that the meshing and parameter settings used are reasonable and can basically achieve vortex-induced vibration simulation of double-deck steel truss bridge sections.

[0094] (4) The vortex vibration mechanism of the double-layer steel truss bridge section is explored by analyzing the flow field around the main beam section. Taking the simulation results of the wind speed of 1.35m / s at a wind angle of +3° as an example, the generation, attachment, separation and shedding of the vortex after the incoming flow passes through the double-layer steel truss bridge section are analyzed. The vortex volume evolution in a single vibration cycle is shown as follows: Figure 4 As shown. Figure 4 It can be seen that the vortex shedding conditions are different at the upper deck, the web member position, and the lower deck. The vortex shedding period of the upper deck is close to the structural vibration period, the vortex shedding period at the web member position is smaller than the vibration period, and the vortex shedding period in the windward area of ​​the lower deck is smaller than the vibration period, indicating that the vertical bending vortex vibration of the double-deck steel truss bridge section is dominated by the vortex shedding of the upper deck.

[0095] S33. Additional aerodynamic measures to suppress vibration.

[0096] It can be seen from step S2 that the upper chord nozzle has a good suppressing effect on vortex vibration, but the web nozzle has no obvious suppressing effect on vortex vibration, so only the parameters of the upper chord nozzle are considered to set the nozzle simulation working condition. With the nozzle angle a, the nozzle corner tip position (x / l) and the wind attack angle as variables, several nozzle simulation working conditions are set to carry out the vortex vibration suppression test of the double-layer steel truss bridge. It can be seen from step S2 that installing guide plates at the three positions of the upper chord, web and lower chord will significantly affect the vortex vibration response of the double-layer steel truss bridge section. Since adding a guide plate at the upper chord will aggravate the vortex vibration response, adding a guide plate at the upper chord is not considered. With the guide plate height ratio and position as variables, several guide plate simulation working conditions are set to carry out the vortex vibration suppression test of the double-layer steel truss bridge with guide plates of different parameters.

[0097] By setting up four combinations of additional aerodynamic measures, namely "upper chord air nozzle + central stabilizing plate", "web and lower chord guide plate + central stabilizing plate", "upper chord air nozzle + web and lower chord guide plate", and "upper chord air nozzle + web and lower chord guide plate + central stabilizing plate", and setting up multiple simulation working conditions, the effects of different combinations of additional aerodynamic measures on the vortex-induced vibration suppression of double-deck steel truss bridges were verified.

[0098] S4. Using three machine learning algorithms, SVR, BPNN, and RF, a cross-sectional amplitude prediction model for a double-deck steel truss bridge under different wind speeds and a vortex-induced vibration characteristic parameter prediction model under different additional aerodynamic measures were established. The k-fold cross-validation method was used to optimize the parameters and divide the data sets of the four models. The prediction performance was evaluated by the root mean square error and determination coefficient, and the most adaptable vortex-induced vibration response prediction model for a double-deck steel truss bridge was determined, achieving effective prediction of the cross-sectional vortex-induced vibration response of a double-deck steel truss bridge.

[0099] S41. Determine the machine learning algorithm.

[0100] (1) Support Vector Regression (SVR).

[0101] SVR parameters include kernel function, penalty factor C, and insensitivity function ε. The kernel function maps the input features to a high-dimensional space and converts inseparable sample points into separable sample points. The kernel function is a Gaussian kernel function, and its expression is:

[0102] K(x,x′)=exp(-γ||xx′|| 2 ,

[0103] Where x and x' represent the eigenvectors of the two sample points; γ is the kernel function scale parameter, which controls the influence range of the sample point in the feature space; the penalty factor C is the tolerance of the SVR model to errors. Later in the model training, γ and C will be optimized to obtain better prediction results.

[0104] (2) Back propagation neural network algorithm (BPNN).

[0105] Back Propagation Neural Networks (BPNNs) consist of two parts: forward propagation of data and backward propagation of errors. Their working principle is as follows: the input value propagates forward from the input layer through the hidden layers to the output layer, resulting in the output value. The error between the output value and the expected value is then propagated backward through the hidden layers. During this process, the weights in the model are continuously adjusted to reduce the error between the output value and the expected value. The most classic three-layer BPNN structure consists of an input layer, an output layer, and a hidden layer. Later, the number of hidden layers and hidden layer nodes in the network will be adjusted based on this to find the optimal model parameters.

[0106] (3) Random Forest (RF).

[0107] Random Forest (RF) combines the advantages of decision trees and randomness, boasting strong data mining capabilities and high prediction accuracy. Therefore, it is widely used to solve prediction problems. Using Random Forest to solve regression problems involves two steps: First, constructing a decision tree. Two-thirds of the samples (in-bag data) are randomly sampled with replacement from the training set as the sample set for training the decision tree. The tree is then segmented based on random features until a stopping condition is met. The remaining one-third of the samples (out-of-bag data) are used to evaluate the error, resulting in a single decision tree model. If the model is sampled and trained m times, m decision tree models can be obtained. Second, integrating the regression outputs, averaging the predictions of each decision tree as the final output.

[0108] S42. Model learning sample data processing.

[0109] For the prediction of the cross-sectional amplitude of a double-deck steel truss bridge under different wind speeds, the wind attack angle, reduced wind speed, upper chord wind nozzle angle, upper chord wind nozzle corner tip position, web member deflector height ratio, lower chord deflector height ratio and central stabilizer plate height are used as feature inputs, and the vertical bending reduced amplitude is used as feature output.

[0110] For the prediction of vortex-induced vibration characteristic parameters of double-deck steel truss bridges under different additional aerodynamic measures, the wind attack angle, upper chord wind nozzle angle, upper chord wind nozzle corner tip position, web member guide plate height ratio, lower chord guide plate height ratio and central stabilizer plate height are used as characteristic inputs, and the vortex-induced vibration starting wind speed, locking interval length and maximum reduced amplitude are used as characteristic outputs.

[0111] The dataset used to predict the vortex-induced vibration characteristic parameters of double-deck steel truss bridge sections is defined as the VIV-R dataset. Step S3 summarizes the calculation results of 58 simulation conditions, including: setting the nozzle simulation condition by changing the parameters of the upper chord nozzle; setting the deflector simulation condition by changing the height ratio and position parameters of the deflectors installed at the web and lower chord positions; and setting the simulation condition of a combination of various additional aerodynamic measures. The VIV-R dataset is shown in Table 1.

[0112] Table 1. VIV-R dataset for prediction of vortex-induced vibration characteristic parameters of double-deck steel truss bridge sections

[0113]

[0114] For each working condition in Table 1, numerical calculations were performed at 20 different wind speeds within the range of 1.5 to 3.0 for the reduced wind speed. As a result, a VIV-A dataset containing 1160 samples for the prediction of the cross-section amplitude of double-deck steel truss bridges was obtained.

[0115] The VIV-A dataset and VIV-R dataset were imported into the MATLAB program and normalized (minimum-maximum normalization) using the mapminmax function. The mapping range of the characteristic parameters was set to 0-1.

[0116] The k-fold cross-validation method is used to determine the ratio of the training set to the test set. The k-fold cross-validation method divides the VIV-A or VIV-R dataset into k equal subsets. In each cross-validation, one of the subsets is selected as the test set, and the remaining k-1 subsets are used as the training set. A total of k iterations are performed, and the average of the k test results is used as the evaluation parameter.

[0117] S4.3. Prediction of section amplitude of double-deck steel truss bridge.

[0118] (1) Optimization of model parameters.

[0119] A prediction model was established based on three machine learning algorithms: SVR, BPPNN, and RF. The model parameters were optimized through cross-validation. The cross-validation folds were 4, 6, 8, and 10. The results were evaluated using the root mean square error (RMSE). The closer the RMSE is to 0, the better the model prediction effect. The calculation formula is:

[0120]

[0121] In the formula, k is the cross-validation fold, n is the number of samples, and y i and Y i are the expected output and predicted output respectively.

[0122] Model parameter optimization for amplitude prediction was performed based on the SVR, BPPNN, and RF prediction models. The SVR model parameter optimization result was achieved with a cross-validation fold of 10, a penalty factor and kernel function scale parameter of 10.0, and an RMSE of 0.361. The BPNN model optimization result was achieved with a cross-validation fold of 10, 13 nodes in the first and second hidden layers, and 6 nodes, respectively, and an RMSE of 0.197. The RF model optimization result was achieved with a cross-validation fold of 10, 120 decision nodes, and a minimum leaf size of 1, and an RMSE of 0.396.

[0123] (2) Evaluation of prediction results.

[0124] The optimization results show that under 10-fold cross-validation, the root mean square error of the three machine learning models, SVR, BPNN, and RF, for predicting the cross-sectional amplitude of a double-deck steel truss bridge is very small. To compare the prediction performance of the three models under the same conditions, the VIV-A dataset was divided into training and test sets at a ratio of 9:1. The model parameters were set according to the parameters that achieved the minimum RMSE under 10-fold cross-validation. The amplitude prediction results are shown in Figure 2. Figure 5 As shown in the figure, the amplitude prediction value is compared with the actual value. Figure 6 shown.

[0125] In addition to RMSE, the evaluation indicators used also include the determination coefficient R 2 , R 2 The closer it is to 1, the higher the prediction accuracy of the model is. The calculation formula is:

[0126]

[0127] Where y i is the expected output, is the model prediction output, is the test set mean, and n is the number of samples.

[0128] Depend on Figure 5 The BPNN model has the smallest amplitude prediction error, with an RMSE of 0.197. However, based on the optimization results for the model parameters, the RF model should have better prediction performance than the SVR. However, the SVR model actually performed better in predicting the amplitude of the double-deck steel truss bridge, with an RMSE of 0.361, only slightly higher than the BPNN model. This indicates that the RF model's prediction performance deteriorates on new data, likely due to overfitting caused by setting the minimum number of leaves to 1.

[0129] Depend on Figure 6 It can be seen that the R of SVR, BPNN and RF models 2 They are 0.9407, 0.9723 and 0.9288 respectively. Figure 6 (a) It can be seen that when the amplitude is small, the comparison points between the amplitude prediction value of the SVR model and the actual value are evenly distributed on both sides of the reference line; when the amplitude is large, the comparison points are mainly distributed on the lower side of the reference line, indicating that when the amplitude is large, the prediction result of the SVR model is too small. Figure 6 (b) It can be seen that when the reduced amplitude is less than 0.4, the comparison points between the amplitude prediction value of the BPNN model and the actual value are evenly distributed on both sides of the reference line, indicating that the results of the BPNN model for predicting the amplitude of the double-deck steel truss bridge section are highly reliable. Figure 6 As shown in Figure (c), the comparison points between the RF model's predicted amplitude and the actual value are concentrated on the reference line when the amplitude is low, but deviate to the lower right of the reference line when the amplitude is large. This indicates that when the amplitude is large, the RF model's amplitude prediction is smaller than the actual value. In summary, the BPNN model performs best for amplitude prediction of double-deck steel truss bridges under different wind speeds.

[0130] (3) Prediction model optimization.

[0131] The BPNN model is optimized by introducing Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) to obtain higher prediction accuracy.

[0132] The genetic algorithm and particle swarm optimization algorithm are combined with BPNN to establish GA-BPNN and PSO-BPNN models. The specific operation process of the optimized model is as follows: Figure 7 and Figure 8 shown.

[0133] The amplitude prediction results of GA-BPNN and PSO-BPNN models were compared with the BPNN model to verify the effectiveness of the optimization model. Figure 9 shown.

[0134] Depend on Figure 9 It can be seen that the R of GA-BPNN and PSO-BPNN models is better than that of the original BPNN model. 2 From the perspective of prediction results, the comparison points between the amplitude prediction values ​​and actual values ​​of the GA-BPNN and PSO-BPNN models are closer to the reference line than those of the BPNN model, indicating that their prediction results are better.

[0135] In order to quantify the optimization effect of the model, the RMSE and R2 changes of the BPNN model before and after optimization are obtained, as shown in Table 2.

[0136] Table 2. Evaluation of prediction results before and after BPNN model optimization (amplitude prediction)

[0137]

[0138] As shown in Table 2, the GA-BPNN and PSO-BPNN models have improved the prediction accuracy compared with the original BPNN model. The RMSE of the GA-BPNN and PSO-BPNN models are 0.150 and 0.164, respectively, which are reduced by 23.9% and 16.8% compared with the BPNN model; 2 The BPNN model is 0.9898 and 0.9878 respectively, which are 1.8% and 1.6% higher than those of the BPNN model, indicating that the prediction performance of the optimized models has been improved. Among them, the GA-BPNN model is more suitable for predicting the amplitude of the double-deck steel truss bridge section under different wind speeds.

[0139] S4.4. Prediction of vortex-induced vibration characteristic parameters.

[0140] (1) Optimization of model parameters.

[0141] The VIV-R dataset was used to train the established machine learning model, and the model parameters were optimized and the dataset was divided by cross-validation to achieve the prediction of vortex-vibration characteristic parameters of double-deck steel truss bridges under different additional aerodynamic measures. The output features in the VIV-R dataset include three parameters: the starting wind speed, the locking interval length, and the maximum reduced amplitude. Since the prediction accuracy of the machine learning model for a single characteristic parameter output is higher than that for multiple characteristic parameters output, in order to ensure the validity of the prediction results, only one characteristic parameter is predicted each time the model is established. When the sample size of the dataset is 10 3 When the sample size of the data set is less than 10, the number of cross-validation is generally large. 3 The number of cross-validation is generally small. The VIV-R dataset has 58 groups of sample data. To ensure that each fold has enough samples for training, a 4-fold cross-validation is used for optimization.

[0142] The SVR model parameter optimization results show that when C is 10.0 and γ is 0.4, the prediction of the onset wind speed is the best, with an RMSE of 0.026; when C is 9.8 and γ is 0.3, the prediction of the lock-in interval length is the best, with an RMSE of 0.036; and when C is 9.1 and γ is 0.6, the prediction of the maximum reduced amplitude is the best, with an RMSE of 0.342. The minimum RMSE for the predicted vortex onset wind speed and lock-in interval length is around 0.03, only 1 / 10 of the minimum RMSE for the maximum reduced amplitude, indicating that SVR can more accurately predict the onset wind speed and lock-in interval length under different additional aerodynamic measures.

[0143] The BPNN model parameter optimization results show that the impact of the number of hidden layer nodes on the BPNN model's prediction performance is highly uncertain. When the number of first-layer nodes is 5 and the number of second-layer nodes is 49, the prediction of the onset wind speed is optimal, with an RMSE of 0.041. When the number of first-layer and second-layer nodes is 7, the prediction of the locking interval length is optimal, with an RMSE of 0.041. When the number of first-layer nodes is 7 and the number of second-layer nodes is 22, the prediction of the maximum reduced amplitude is optimal, with an RMSE of 0.596. These results indicate that the BPNN model can effectively predict the onset wind speed, locking interval length, and maximum reduced amplitude of vortex-induced vibrations in double-deck steel truss bridges.

[0144] The RF model parameter optimization results show that when n is 25 and leaf is 1, the RF model is most effective in predicting the initiation wind speed, with an RMSE of 0.038; when n is 50 and leaf is 1, the RF model is most effective in predicting the locking interval length, with an RMSE of 0.036; and when n is 45 and leaf is 1, the RF model is most effective in predicting the maximum reduced amplitude, with an RMSE of 0.669. These results indicate that the root mean square error (RMSE) of the RF model for predicting the characteristic parameters of vortex-induced vibrations in double-deck steel truss bridge sections is within a reasonable range.

[0145] (2) Analysis of prediction results.

[0146] In order to evaluate the prediction effect of three machine learning models, SVR, BPNN and RF, on vortex-induced vibration characteristic parameters, the VIV-R dataset was divided into training set and test set according to a ratio of 3:1, and the model was established with the optimal parameter setting for prediction. Figure 10 As shown in the figure, the comparison between the predicted value and the actual value of the vortex vibration characteristic parameter is as follows: Figure 11 shown.

[0147] Depend on Figure 10 It can be seen that the prediction curves of the three models for the starting wind speed, locking interval length and maximum reduced amplitude are close to the actual expected curves, indicating that their prediction effects are good. Figure 11 As can be seen, the comparison points between the predicted and actual vortex-induced vibration characteristic parameters of the SVR model are all concentrated on the reference line, while the comparison points between the predicted and actual vortex-induced vibration characteristic parameters of the BPNN and RF models are mostly close to the reference line. This indicates that the SVR model has a high degree of confidence in its prediction of vortex-induced vibration characteristic parameters, while the BPNN and RF models have a certain degree of confidence. Therefore, the SVR, BPNN, and RF models can all accurately predict the vortex-induced vibration initiation wind speed, locking interval length, and maximum reduced amplitude for double-deck steel truss bridge sections under different additional aerodynamic measures.

[0148] In order to quantitatively analyze the prediction effects of different models on different characteristic parameters, the RMSE and R of three machine learning models for predicting vortex-induced vibration characteristic parameters of double-deck steel truss bridges are given.2 , as shown in Table 3.

[0149] Table 3. Prediction results of three machine learning models (vortex vibration characteristic parameter prediction)

[0150]

[0151] As shown in Table 3, the RMSE of the SVR model for predicting the vortex vibration initiation wind speed, locking interval length and maximum reduced amplitude of the double-deck steel truss bridge section are the smallest, which are 0.026, 0.036 and 0.342 respectively. 2 The RMSEs of the BPNN model and the RF model for the prediction of the vibration wind speed, the locking interval length and the maximum reduced amplitude are all within a reasonable range, but R 2 However, the results are not high and are lower than those of the SVR model, indicating that the BPNN and RF models do not perform as well as the SVR model on small sample data sets. In summary, when the sample size of the additional aerodynamic measures working condition is small, the SVR model has the best prediction effect on the starting wind speed, locking interval length, and maximum reduced amplitude of the vortex vibration of the double-deck steel truss bridge section.

[0152] (3) Prediction model optimization.

[0153] GA and PSO were used to optimize the SVR model that performed best in predicting the vortex-induced vibration characteristic parameters of a double-deck steel truss bridge section, and the GA-SVR and PSO-SVR models were established. The prediction results of the SVR model were compared with those of the GA-SVR and PSO-SVR models, and the RMSE and R of the SVR model for the three characteristic parameters before and after optimization were given. 2 , as shown in Table 4.

[0154] Table 4. Evaluation of prediction results before and after SVR model optimization (vortex vibration characteristic parameter prediction)

[0155]

[0156] As shown in Table 4, the GA-SVR and PSO-SVR models have improved the prediction accuracy compared with the original SVR model. The RMSE of the GA-SVR model for the prediction of the starting wind speed is reduced by 26.9%, and the R 2 The RMSE of the lock interval length prediction was reduced by 8.3%, and R 2 Improved by 2.7%; RMSE for the maximum discounted amplitude prediction decreased by 19.8%, R 2 The RMSE of the PSO-SVR model for wind speed prediction is reduced by 34.6%, and R 2Improved by 0.2%; RMSE for the prediction of the lock interval length decreased by 20.8%, R 2 Improved by 4.2%; RMSE of the maximum discounted amplitude prediction decreased by 24.9%, R 2 The prediction results show that the prediction performance of the optimized models has been improved. Among them, the PSO-SVR model is more suitable for predicting the vortex-induced vibration characteristic parameters of double-layer steel truss sections.

[0157] The present invention proposes a vortex-induced vibration response prediction method for a double-deck steel truss bridge based on a machine learning algorithm. Combined with wind tunnel tests and numerical simulations, the method studies the influence of additional aerodynamic measures on the vortex-induced vibration of a double-deck steel truss bridge. The data such as the vibration starting wind speed, locking range, and maximum amplitude of the double-deck steel truss bridge are obtained and compiled into a learning sample database. The vortex-induced vibration response of the double-deck steel truss bridge is predicted through a machine learning method. The method has low cost, high visualization, good stability, and high prediction accuracy, thereby providing a reference for bridge design, operation, and maintenance.

[0158] The above is an exemplary description of the invention. Obviously, the specific implementation of the present invention is not limited to the above-mentioned method. As long as such non-substantial improvements are made by adopting the method concept and technical solution of the present invention, or the concept and technical solution of the invention are directly applied to other occasions without improvement, they are all within the scope of protection of the present invention.

Claims

1. A method for predicting vortex-induced vibration response of a double-deck steel truss bridge based on a machine learning algorithm, characterized in that: The following steps are involved: S1. Use ANSYS software to establish a finite element model of a double-deck steel truss bridge and calculate its dynamic characteristics. Based on this, design a segmental model wind tunnel test, conduct force and vibration tests, and thus obtain the vortex-induced vibration characteristics of the double-deck steel truss bridge. S2. Add three additional facilities to the double-deck steel truss bridge: upper maintenance railings, maintenance vehicle tracks, and track noise barriers; and three additional aerodynamic measures: air nozzles, deflectors, and central stabilizers. Analyze the vortex-induced vibration response of the bridge through wind tunnel tests to determine the vortex-induced vibration response of the additional facilities and aerodynamic measures to the double-deck steel truss bridge. S3. Use the Fluent platform to perform fluid dynamics CFD numerical simulations on the cross-section of a double-deck steel truss bridge, and verify the independence of the number of grids, web member positions, and time steps. Analyze the vortex-induced vibration of the double-deck steel truss bridge by varying the parameters of the additional aerodynamic measures, and determine the influence of multi-parameter additional aerodynamic measures on the vortex-induced vibration of the double-deck steel truss bridge. S4. Using three machine learning algorithms, SVR, BPNN, and RF, a prediction model for the cross-sectional amplitude of a double-deck steel truss bridge at different wind speeds and a prediction model for the vortex-induced vibration characteristic parameters under different additional aerodynamic measures were established. The prediction model parameters were optimized to achieve the best and most effective prediction of the cross-sectional vortex-induced vibration response of the double-deck steel truss bridge. The S1 step is detailed as follows: S11. Calculation of bridge dynamic characteristics: Using ANSYS software, a three-dimensional finite element model of the double-deck steel truss bridge was constructed and dynamic characteristics were calculated to obtain the vibration mode and frequency of the double-deck steel truss bridge structure, providing a basis for the design parameters of the wind tunnel test model. S12. Segmental model wind tunnel test design: Based on the actual bridge size, wind tunnel test section size, and similarity criteria, the segment model scale ratio and test wind speed ratio of the double-deck steel truss bridge were determined, and a segment model of the double-deck steel truss bridge was constructed. The segment model of the double-deck steel truss bridge was installed in the test wind tunnel via an angle of attack turntable and steel brackets, and the data acquisition equipment used in the test was installed. S13. Wind tunnel test analysis of segmental models: (1) Force measurement test: The static three-force coefficients of the segment models in the construction state and the completed bridge state were measured. The static three-force coefficients of the segment models in the construction state and the completed bridge state were obtained when the wind speeds were 10 m / s, 15 m / s and 20 m / s and the downwind angle was within the range of -12° to +12°, and the corresponding static three-force coefficients were calculated. (2) Vibration test: The changes in the vertical amplitude and torsional angle of the segment model at wind attack angles of 0, ±3°, and ±5° were recorded using a laser displacement sensor, thereby obtaining the vertical bending vortex vibration response and torsional vortex vibration response of the segment model in the construction state and the completed bridge state; (3) Time history and spectrum response: The time history spectrum at the maximum reduction amplitude of the vertical bending vortex vibration zone and the maximum torsion angle of the two torsion vortex vibration zones are converted to obtain the dominant frequency and compared with the vertical bending or torsion frequency of the model.

2. The vortex-induced vibration response prediction method for a double-deck steel truss bridge based on a machine learning algorithm according to claim 1 is characterized in that: In step S11, the dynamic characteristic calculation includes static calculation and dynamic calculation. The static calculation refers to considering the influence of geometric nonlinearity under constant load, and the dynamic calculation uses the Block Lanczos method to perform dynamic solutions in the construction state and the completed bridge state.

3. The vortex-induced vibration response prediction method of a double-deck steel truss bridge based on a machine learning algorithm according to claim 1 is characterized in that: In step S12, the data acquisition equipment includes a slope measuring instrument, a wind speed measurement system, a laser displacement sensor and a high-frequency force balance, specifically including: a multifunctional slope measuring instrument for measuring angles; a TFI series 100 Cobra pulsating wind speed measurement system that can accurately measure three-dimensional pulsating wind speed in a flow field, with a measurement accuracy after zero calibration exceeding 0.5 m / s and a frequency of up to 2000 Hz; a type II laser displacement sensor that can stably detect various targets; and a high-frequency force balance that can measure pressure and torque in six degrees of freedom.

4. The vortex-induced vibration response prediction method for a double-deck steel truss bridge based on a machine learning algorithm according to claim 1 is characterized in that: The S4 step is detailed as follows: S41. Machine learning algorithm determination: Determine the use of three machine learning algorithms, SVR, BPNN, and RF, to construct a prediction model for the cross-sectional amplitude of a double-deck steel truss bridge at different wind speeds and a prediction model for the vortex-vibration characteristic parameters under different additional aerodynamic measures; S42. Model learning sample data processing: In step S3, the calculation results of 58 simulated working conditions, including the original cross-section, are integrated to obtain a VIV-R data set for predicting vortex vibration characteristic parameters; numerical calculations are performed for 20 different wind speeds in the reduced wind speed range of 1.5 to 3.0 for each working condition in the VIV-R data set to obtain a VIV-A data set for surface amplitude prediction; the VIV-A data set and the VIV-R data set are normalized using the MATLAB program and the mapminmax function; a k-fold cross-validation method is used to determine the ratio of the training set to the test set, and the average of the k test results is used as the evaluation parameter; S43. Prediction of Sectional Amplitude of Double-Deck Steel Truss Bridges: (1) Model parameter optimization: A prediction model was established based on three machine learning algorithms: SVR, BPPNN, and RF, and the model parameters were optimized using the k-fold cross-validation method. (2) Evaluation of prediction results: The VIV-A dataset is divided into training set and test set according to 9:

1. The evaluation indicators RMSE and R 2 Obtain the best model for predicting the amplitude of a double-deck steel truss bridge under different wind speeds; (3) Prediction model optimization: The optimal model is optimized using the genetic algorithm (GA) and the particle swarm algorithm (PSO). An optimized model is established and the amplitude prediction results are compared with the optimal model to verify the effectiveness of the optimized model and obtain the best effective model for amplitude prediction, thus completing the entire process of amplitude prediction for the double-deck steel truss bridge section under different wind speeds. S44. Prediction of vortex-induced vibration characteristic parameters: (1) Model parameter optimization: A prediction model was established based on three machine learning algorithms: SVR, BPPNN, and RF. The VIV-R dataset was used to train the established prediction model, and the model parameters were optimized using the k-fold cross-validation method. (2) Evaluation of prediction results: The VIV-R dataset is divided into training set and test set according to the ratio of 3:

1. The evaluation indicators RMSE and R 2 The optimal model for predicting the vortex vibration of double-deck steel truss bridge section is obtained by obtaining the starting wind speed, locking interval length and maximum reduced amplitude. (3) Prediction model optimization: The optimal model is optimized by genetic algorithm GA and particle swarm algorithm PSO, and an optimized model is established. The amplitude prediction results are compared with the optimal model to verify the effectiveness of the optimized model and obtain the best effective model for amplitude prediction, thus completing the entire process of predicting the vortex-vibration characteristic parameters of the double-deck steel truss bridge section.

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