Vortex-induced vibration response prediction method of double-layer steel truss bridge based on machine learning algorithm

Abstract

The invention discloses a vortex-induced vibration response prediction method for a double-layer steel truss bridge based on a machine learning algorithm, and the method comprises the steps: carrying out the wind tunnel test of a section model of the double-layer steel truss bridge, and carrying out the test analysis of the influence rule of various subsidiary facilities and additional pneumatic measures on the vortex-induced vibration of the section of the double-layer steel truss bridge; the vortex vibration generation mechanism of the bridge forming state segment model is analyzed through numerical simulation, and the influence rule of additional pneumatic measure parameter change on the vortex vibration of the section of the double-layer steel truss bridge is explored; based on a machine learning algorithm, a section amplitude prediction model under different wind speeds and a vortex vibration characteristic parameter prediction model under different additional pneumatic measures are established to predict the vortex vibration response of the double-layer steel truss bridge. According to the method, wind tunnel test, numerical simulation and machine learning methods are combined, the vortex-induced vibration response of the double-layer steel truss bridge is predicted, the stability is good, the prediction accuracy is high, and therefore reference is provided for bridge design, operation and maintenance.

Description

Technical Field

[0001] The present invention relates to the technical field of vortex-induced vibration response of bridges, 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. A road-rail dual-purpose bridge with a steel truss as the main beam has brought 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 a wind field environment are also more complicated.

[0003] At present, the main means to solve the vortex-induced vibration problem of bridges include wind tunnel tests and numerical simulations. Wind tunnel tests are relatively mature in technology, but they are expensive and have poor visualization; while numerical simulations are low in cost and highly visualized, but the prediction accuracy is not high. Therefore, it is very necessary to develop a vortex-induced vibration response prediction method for double-deck steel truss bridges to improve prediction stability, prediction accuracy and reduce prediction costs. 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 solve 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 of 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, calculate its dynamic characteristics, and use this as a basis to design a segment model wind tunnel test, and conduct force and vibration tests respectively to obtain the vortex-vibration influence characteristics of the double-deck steel truss bridge;

[0008] S2. Add three additional facilities, namely upper maintenance railings, maintenance vehicle tracks and track sound barriers, as well as three additional aerodynamic measures, namely wind nozzles, guide plates and central stabilizer plates, to the double-deck steel truss bridge. Analyze its vortex-induced vibration response through wind tunnel tests to obtain the vortex-induced vibration response law of the additional facilities and additional aerodynamic measures to the double-deck steel truss bridge.

[0009] S3. Computational fluid dynamics (CFD) numerical simulation of the double-deck steel truss bridge section was carried out using the Fluent platform, and the independence of the number of grids, web position and time step was verified; the vortex vibration value of the double-deck steel truss bridge was analyzed by changing the parameters of the additional aerodynamic measures, and the influence of the multi-parameter additional aerodynamic measures on the vortex vibration of the double-deck steel truss bridge was determined;

[0010] S4. Through three machine learning algorithms, SVR, BPNN and RF, a cross-sectional amplitude prediction model of a double-deck steel truss bridge under different wind speeds and a vortex-oscillation characteristic parameter prediction model under different additional aerodynamic measures were established. The prediction model parameters were optimized to achieve the best and effective prediction of the cross-sectional vortex-oscillation 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] 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 angle of attack turntable and steel bracket, and the data acquisition equipment used in the test is installed;

[0016] S13. Wind tunnel test analysis of segment model:

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

[0018] (2) Vibration test: The changes in the vertical amplitude and torsion angle of the segment model at wind attack angles of 0, ±3°, and ±5° were recorded using a laser displacement sensor to obtain 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 reduced 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 measuring system, a laser displacement sensor and a high-frequency force measuring 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, and its measurement accuracy after zero calibration is higher than 0.5m / s, and the frequency is as high as 2000Hz; a type II laser displacement sensor that can stably detect various targets; and a high-frequency force measuring 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 determines:

[0024] Determine the use of three machine learning algorithms, SVR, BPNN and RF, to build 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 section are integrated to obtain the VIV-R data set for predicting vortex vibration characteristic parameters; numerical calculations are performed for 20 different wind speeds in the range of reduced wind speed of 1.5 to 3.0 for each working condition in the VIV-R data set to obtain the VIV-A data set for surface amplitude prediction; the VIV-A data set and the VIV-R data set are normalized by the MATLAB program and the mapminmax function; the k-fold cross validation method is used to determine the ratio of the training set and the test set, and the average value of the k test results is used as the evaluation parameter;

[0027] S43, double-deck steel truss bridge section amplitude prediction:

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

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

[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 through 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 the 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 best model is optimized by genetic algorithm GA and particle swarm algorithm PSO, and the optimization model is established. The amplitude prediction results are compared with the best model to verify the effectiveness of the optimization model and obtain the best effective model for amplitude prediction, thus completing the whole 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-oscillation 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 influence of additional aerodynamic measures on the vortex-oscillation of the double-deck steel truss bridge is studied, and data such as the starting wind speed, locking interval, and maximum amplitude of the double-deck steel truss bridge are obtained and organized into a learning sample database. Then, the vortex-oscillation 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 It is the technical roadmap of the present invention.

[0044] Figure 2 This is a comparison chart of the static three-force coefficients of 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 in 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 It is the operation flow chart of GA-BPNN model;

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

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

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

[0053] Fig.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 in conjunction with 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 protection scope of the present invention.

[0055] Embodiment 1:

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

[0057] S1. The finite element model of the double-deck steel truss bridge was established using ANSYS software, and its dynamic characteristics were calculated. Based on this, the segment model wind tunnel test was designed, and force and vibration tests were carried out respectively 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 the dynamic characteristics were analyzed 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] Take the Chongqing Huangjuetuo Yangtze River Bridge as an example:

[0062] Chongqing Huangjuetuo Yangtze River Bridge is a large-span suspension bridge for both road and rail. It is located at the connecting road of Chongqing-Changsha Expressway. It has two decks, with six lanes in both directions on the upper deck and two-way tracks in the middle of the lower deck, and four lanes in both directions and pedestrian paths on both sides. According to the design instructions of the construction drawing of Huangjuetuo Yangtze River Bridge, the basic wind speed is designed as follows: with a return period of 100 years, the average maximum wind speed at 10 meters above the ground for 10 minutes is 27.5m / s.

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

[0064] By calculating the dynamic characteristics of the bridge, the vibration mode and frequency of the bridge structure can be obtained, providing a basis for the design parameters of the wind tunnel test model. For the Huangjuetuo Yangtze River Bridge, ANSYS software is used to analyze its dynamic characteristics. The three-dimensional finite element model of the Huangjuetuo Yangtze River Bridge covers the side span main cable, main span main cable, suspender, rigid arm, main tower, main beam, cross beam, web member and chord, and the size is exactly the same as the actual bridge size.

[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, and dynamic calculation uses the Block Lanczos method to solve the dynamics of 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] Based on the finite element dynamic characteristics calculation results of the construction state and the completed bridge state models, a reference is provided 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 body through the attack angle turntable and steel bracket, and the data acquisition equipment used in the test is installed.

[0070] This wind tunnel test was conducted in the DC teaching wind tunnel laboratory of Chongqing University. The test wind tunnel body adopts an all-steel welded structure, which is welded by the cave wall panel, partition frame, longitudinal rib plate and support frame. The wind tunnel is a DC air-inhaling wind tunnel. The wind speed range of the test section is 0.5-35m / s. The flow field quality meets the general requirements of the atmospheric boundary layer wind tunnel, and the turbulence is 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 is determined to be 1:55, the test wind speed ratio is 1:4.48, and the segment model of the double-deck steel truss bridge is constructed.

[0072] The segment model of the double-deck steel truss bridge achieves wind attack angle change in the test wind tunnel by adjusting the angle of attack turntable; eight spring suspensions are arranged above and below the steel support to provide vertical bending stiffness and torsional stiffness for the system, ensuring that the segment model can move vertically and rotate around the cross-section axis, thereby accurately simulating the vibration characteristics of the two degrees of freedom of vertical bending and torsion. Laser displacement sensors are arranged at both ends of the steel support to collect the vibration time history response of the segment model.

[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: 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 measurement accuracy of more than 0.5m / s after zero calibration 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 noise-free silicon strain technology and has high hardness and overload self-protection functions.

[0074] S13. Wind tunnel test analysis of segment model:

[0075] (1) Force measurement test

[0076] In order to analyze the static characteristics of the main beam of a double-deck steel truss bridge, the static three-force coefficients of the segment models in the construction state and the completed bridge state were measured. The static three-force of the segment models in the construction state and the completed bridge state under the test wind speed of 10m / s, 15m / s and 20m / s and the downwind attack angle in the range of -12° to +12° were obtained from the force measurement test, and the corresponding static three-force coefficients were calculated.

[0077] (2) Vibration test.

[0078] The experiment measured the vortex vibration amplitude of the segment model in the construction state and the completed bridge state at five wind attack angles of 0, ±3° and ±5°. The changes in the vertical amplitude and torsion angle of the segment model at wind attack angles of 0, ±3° and ±5° were recorded by laser displacement sensors, 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.

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

[0080] In the vibration test, the segment model of the completed bridge state experienced vertical bending and torsional vortex vibration at wind attack angles of +3° and +5°. The time-history spectrum at the maximum reduced amplitude of the vertical bending vortex vibration zone and the maximum torsion angle of the two torsional vortex vibration zones was converted to obtain the dominant frequency, which was compared with the vertical bending or torsional frequency of the model.

[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, are added to the double-deck steel truss bridge. The vortex-oscillation response of the double-deck steel truss bridge at wind attack angles of +3° and +5° is analyzed through wind tunnel tests, and the vortex-oscillation response law of the additional facilities and additional aerodynamic measures to the double-deck steel truss bridge is obtained.

[0082] Through the wind tunnel test, it is known that both the auxiliary facilities and additional aerodynamic measures have an impact on the cross-section vortex vibration of the double-deck steel truss bridge, but the auxiliary facilities are mostly adverse. When the additional aerodynamic measures are installed in the correct position, they can effectively suppress the vortex vibration of the double-deck steel truss bridge. Specifically, reducing the air permeability of the upper maintenance road railing, moving the maintenance vehicle track position inward, or adding a track sound barrier will increase the maximum reduction amplitude and maximum torsion angle of the double-deck steel truss bridge; adding the upper chord wind nozzle, the web guide plate, the lower chord guide plate and the central stabilizer plate can effectively suppress the main beam vortex vibration; adding the web wind nozzle has no obvious inhibitory effect on the main beam vortex vibration, and adding the upper chord guide plate will aggravate the main beam vortex vibration response. Adding wind nozzles at the upper chord and the web at the same time has the best suppression effect on the vertical bending vortex vibration, adding guide plates at the web and the lower chord at the same time has the best suppression effect on the torsional vortex vibration, and adding guide plates at the upper chord and the lower chord at the same time will aggravate the vortex vibration response.

[0083] S3. Computational fluid dynamics (CFD) numerical simulation of the double-deck steel truss bridge section was carried out using the Fluent platform, and the independence of the number of grids, web position and time step was verified. The vortex-oscillation value of the double-deck steel truss bridge was analyzed by changing the parameters of the additional aerodynamic measures, and the influence of multi-parameter additional aerodynamic measures on the vortex-oscillation 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 method (RANS) is used to solve the flow field characteristics, and the turbulence model selected is SST k-ω. The numerical simulation uses unstructured grids, and two dynamic grid 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-layer 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-layer 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 software according to the model size of the wind tunnel test. In the CFD numerical simulation, the SST k-ω model, which is well adapted to the flow around the blunt body section, was selected as the turbulence model. In order to verify the effectiveness of the numerical simulation calculation, the number of grids, the position of the web and the time step were verified to be independent.

[0091] (2) To verify the accuracy of CFD numerical simulation, the static three-force coefficients of the original section of the completed double-deck steel truss bridge were compared between the wind tunnel test and numerical simulation at five wind attack angles of 0, ±3° and ±5° when the wind speed of the actual bridge was 10 m / s. Figure 2 As shown. Figure 1 It can be seen that the minimum error between the test value and the simulation value of the static three-force coefficient is 1.23%, the maximum error is 9.08%, the average errors of the drag coefficient, lift coefficient and moment coefficient are 2.92%, 3.13% and 6.15% respectively, and the overall average error is 4.07%. From the simulation results of the static three-force coefficient, 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 amplitudes at different reduced wind speeds were 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 shown in Figure 2. Figure 3 shown.

[0093] Depend on Figure 3 (a) It can be seen that the maximum reduced amplitude of the numerical simulation under +3° wind attack angle is 0.298, and the error with the test is 12.9%; Figure 3 (b) It can be seen that the maximum reduced amplitude of the numerical simulation under a wind attack angle of +5° is 0.374, and the error with the test is 9.0%. It can be seen that the vertical bending vortex-oscillation response results obtained by numerical simulation and wind tunnel test are similar, and the starting wind speed and locking interval length of the numerical simulation are consistent with the wind tunnel test, with only a slight difference in the maximum reduced amplitude, and the errors are all within a reasonable range. This shows that the adopted grid division and parameter setting are reasonable, and the vortex-oscillation simulation of the double-layer steel truss bridge section can be basically realized.

[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 attack 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 of the upper deck, the web member position and the lower deck are different. 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 pneumatic 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. Therefore, only the parameters of the upper chord nozzle are considered to set the nozzle simulation working condition. With the nozzle angle a, the tip position of the nozzle corner (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, the web and the lower chord will significantly affect the vortex vibration response of the cross section of the double-layer steel truss bridge. 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 vibration suppression test of the vortex vibration 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", a variety of simulation working conditions were set up to verify the vibration suppression law of the vortex-vibration of the double-deck steel truss bridge by different combinations of additional aerodynamic measures.

[0098] S4. Through the three machine learning algorithms of SVR, BPNN and RF, a cross-sectional amplitude prediction model of a double-deck steel truss bridge under different wind speeds and a vortex-oscillation 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. The most adaptable vortex-oscillation response prediction model of a double-deck steel truss bridge was determined, and the effective prediction of the cross-sectional vortex-oscillation response of a double-deck steel truss bridge was achieved.

[0099] S41. Determine the machine learning algorithm.

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

[0101] SVR parameters include kernel function, penalty factor C, and insensitive function ε. The kernel function maps the input features to a high-dimensional space and transforms 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] In the formula, x and x' represent the feature vectors of 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. In the later stage of 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 (BPNN) consists of two parts: data forward propagation and error back propagation. Its working principle is: the input value propagates forward from the input layer through the hidden layer to the output layer, and the output value is obtained; then, the error between the output value and the expected value is back propagated through the hidden layer. 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 includes an input layer, an output layer, and a hidden layer. The number of hidden layers and the number of hidden layer nodes of the network will be adjusted on this basis in the later stage to find the optimal model parameters.

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

[0107] Random Forest (RF) combines the advantages of decision trees and randomness, has strong data mining capabilities and high prediction accuracy, and is therefore widely used to solve prediction problems. Using random forests to deal with regression problems is divided into two parts: the first is to build a decision tree, randomly extract 2 / 3 of the samples (in-bag data) from the training set with replacement as the sample set to train the decision tree, and split based on random features until the stopping condition is met. The remaining 1 / 3 of the samples (out-of-bag data) are used to evaluate the error, thereby obtaining a single decision tree model. A total of m times of extraction and training can obtain m decision tree models. The second is to integrate the regression output and take the average of the prediction results 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 guide plate height ratio, lower chord guide plate 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-oscillation 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 starting wind speed of vortex-oscillation, locking interval length and maximum reduced amplitude are used as characteristic outputs.

[0111] The data set used for the prediction of vortex vibration characteristic parameters of the double-deck steel truss bridge section is defined as the VIV-R data set. The calculation results of 58 simulation conditions, including: changing the parameters of the upper chord nozzle to set the nozzle simulation condition, changing the height ratio and position parameters of the guide plate installed at the web and lower chord positions to set the guide plate simulation condition, and setting a combination of multiple additional aerodynamic measures to simulate the working condition, are sorted out in step S3 to obtain the VIV-R data set, as shown in Table 1.

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

[0113]

[0114] For each working condition in Table 1, 20 different wind speeds were numerically calculated in the range of reduced wind speed of 1.5 to 3.0, so a VIV-A data set containing 1160 samples for the prediction of the section amplitude of double-deck steel truss bridges can be obtained.

[0115] The VIV-A data set and the VIV-R data set were imported into the MATLAB program and normalized using the mapminmax function (minimum-maximum normalization). 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 and the test set. The k-fold cross-validation method is to divide the VIV-A or VIV-R data set into k subsets of equal number, select one of the subsets as the test set in each cross-validation, and use the remaining k-1 subsets as the training set. A total of k iterations are performed, and the average value 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 by 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 prediction effect of the model. 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] Based on the three prediction models of SVR, BPPNN and RF, the model parameters for amplitude prediction were optimized respectively. The optimization results of the SVR model parameters are: when the cross-validation fold is 10, the penalty factor and the kernel function scale parameter are both 10.0, the RMSE is 0.361. The optimization results of the BPNN model are: when the cross-validation fold is 10, the number of nodes in the first and second hidden layers are 13 and 6 respectively, the RMSE is 0.197. The optimization results of the RF model are: when the cross-validation fold is 10, the number of decisions is 120 and the minimum number of leaves is 1, the RMSE is 0.396.

[0123] (2) Evaluation of prediction results.

[0124] From the optimization results, we can see that under 10-fold cross validation, the root mean square error of the prediction of the cross-sectional amplitude of the double-deck steel truss bridge by the three machine learning models SVR, BPNN and RF is very small. In order to compare the prediction effects of the three models under the same conditions, the VIV-A data set is divided into a training set and a test set at a ratio of 9:1, and the model parameters are set according to the parameters that achieve the minimum RMSE under 10-fold cross validation. The amplitude prediction results are shown in Figure 2. Figure 5 As shown in Figure 2, the amplitude prediction value is compared with the actual value. Figure 6 shown.

[0125] In addition to RMSE, the evaluation index used also includes 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] In the formula, 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 It can be seen that the BPNN model has the smallest prediction error for the amplitude, with an RMSE of 0.197; however, according to the optimization results of the model parameters, the prediction effect of the RF model should be better than that of the SVR, but the actual result is that the SVR has a better prediction effect on the amplitude of the double-deck steel truss bridge, with an RMSE of 0.361, which is only larger than the BPNN model. This shows that the prediction performance of the established RF model on new data has deteriorated, which may be due to the minimum number of leaves being set to 1, resulting in model overfitting.

[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 and the actual value of the SVR model 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 using the BPNN model to predict the amplitude of the double-deck steel truss bridge section are more reliable. Figure 6 (c) It can be seen that the comparison points between the amplitude prediction value of the RF model and the actual value are concentrated on the reference line when the amplitude is low, and deviate from the reference line to the lower right when the amplitude is large, indicating that when the amplitude is large, the amplitude prediction result of the RF model is smaller than the actual value. In summary, the BPNN model has the best amplitude prediction effect for 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 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 are compared with the BPNN model to verify the effectiveness of the optimization model. Fig. 9 shown.

[0134] Depend on Fig. 9 It can be seen that the R of GA-BPNN and PSO-BPNN models is higher than that of the original BPNN model. 2 From the prediction effect, the comparison points between the amplitude prediction value and the actual value of the GA-BPNN and PSO-BPNN models are closer to the reference line than the BPNN model, indicating that their prediction effect is 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 prediction accuracy of GA-BPNN and PSO-BPNN models is improved compared with the original BPNN model. The RMSE of GA-BPNN and PSO-BPNN models are 0.150 and 0.164, respectively, which are 23.9% and 16.8% lower than that of BPNN model. 2 They are 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 cross section of a double-deck steel truss bridge under different wind speeds.

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

[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 through cross-validation to achieve the prediction of vortex-induced 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 parameter outputs, 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 results of the SVR model parameter optimization are as follows: when C is 10.0 and γ is 0.4, the prediction effect of the starting wind speed is the best, with an RMSE of 0.026; when C is 9.8 and γ is 0.3, the prediction effect of the locking interval length is the best, with an RMSE of 0.036; when C is 9.1 and γ is 0.6, the prediction effect of the maximum reduced amplitude is the best, with an RMSE of 0.342. The minimum RMSE of the predicted vortex starting wind speed and the locking interval length are both around 0.03, which is only 1 / 10 of the minimum RMSE of the predicted maximum reduced amplitude, indicating that SVR can more accurately predict the starting wind speed and locking interval length under different additional aerodynamic measures.

[0143] The results of BPNN model parameter optimization are as follows: there is great uncertainty in the impact of the number of hidden layer nodes on the prediction effect of the BPNN model. When the number of nodes in the first layer is 5 and the number of nodes in the second layer is 49, the prediction effect of the vibration wind speed is the best, and the RMSE is 0.041; when the number of nodes in the first layer and the second layer is 7, the prediction effect of the locking interval length is the best, and the RMSE is 0.041; when the number of nodes in the first layer is 7 and the number of nodes in the second layer is 22, the prediction effect of the maximum reduced amplitude is the best, and the RMSE is 0.596. It can be seen that the BPNN model can better predict the vibration wind speed, locking interval length and maximum reduced amplitude of the vortex vibration of the double-deck steel truss bridge.

[0144] The results of RF model parameter optimization are as follows: when n is 25 and leaf is 1, the RF model has the best effect in predicting the vibration wind speed, with an RMSE of 0.038; when n is 50 and leaf is 1, the RF model has the best effect in predicting the locking interval length, with an RMSE of 0.036; when n is 45 and leaf is 1, the RF model has the best effect in predicting the maximum reduced amplitude, with an RMSE of 0.669. It can be seen that the root mean square error of the RF model in predicting the vortex-vibration characteristic parameters of the double-deck steel truss bridge section 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 data set was divided into training set and test set according to a ratio of 3:1, and the model was established with the optimal parameter settings for prediction. Fig.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: Fig.11 shown.

[0147] Depend on Fig.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. Fig.11 It can be seen that the comparison points between the predicted values ​​and actual values ​​of the vortex-vibration characteristic parameters of the SVR model are concentrated on the reference line, while the comparison points between the predicted values ​​and actual values ​​of the vortex-vibration characteristic parameters of the BPNN and RF models are mostly close to the reference line. It can be seen that the SVR model has a high degree of credibility in predicting the vortex-vibration characteristic parameters, and the BPNN and RF models have a certain degree of credibility. Therefore, the SVR, BPNN and RF models can accurately predict the vortex-vibration initiation wind speed, locking interval length and maximum reduced amplitude of the double-deck steel truss bridge section 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 SVR model has the best prediction effect on the characteristic parameters of vortex vibration of double-deck steel truss bridge sections. The RMSE 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, it is not high, lower than the SVR model, indicating that the performance of the BPNN and RF models is not as good as the SVR model on a small sample data set. In summary, when the sample size of the additional aerodynamic measures 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-vibration characteristic parameters of the 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 prediction of 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 prediction of the lock interval length was reduced by 8.3%, and R 2 The RMSE of the maximum discounted amplitude prediction was reduced by 19.8%, R 2 The RMSE of the PSO-SVR model for wind speed prediction is reduced by 34.6%, R 2The RMSE of the prediction of the lock interval length was reduced by 20.8%, and R 2 The RMSE of the maximum discounted amplitude prediction was reduced by 24.9%, and 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-vibration characteristic parameters of double-layer steel truss sections.

[0157] The present invention proposes a vortex-oscillation 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 influence of additional aerodynamic measures on the vortex-oscillation of the double-deck steel truss bridge is studied, and data such as the starting wind speed, locking interval, and maximum amplitude of the double-deck steel truss bridge are obtained and organized into a learning sample database. Then, the vortex-oscillation 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 protection scope 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, calculate its dynamic characteristics, and use this as a basis to design a segment model wind tunnel test, and conduct force and vibration tests respectively to obtain the vortex-vibration influence characteristics of the double-deck steel truss bridge; S2. Add three additional facilities, namely upper maintenance railings, maintenance vehicle tracks and track sound barriers, as well as three additional aerodynamic measures, namely wind nozzles, guide plates and central stabilizer plates, to the double-deck steel truss bridge. Analyze its vortex-induced vibration response through wind tunnel tests to obtain the vortex-induced vibration response law of the additional facilities and additional aerodynamic measures to the double-deck steel truss bridge. S3. Computational fluid dynamics (CFD) numerical simulation of the double-deck steel truss bridge section was carried out using the Fluent platform, and the independence of the number of grids, web position and time step was verified; the vortex vibration value of the double-deck steel truss bridge was analyzed by changing the parameters of the additional aerodynamic measures, and the influence of the multi-parameter additional aerodynamic measures on the vortex vibration of the double-deck steel truss bridge was determined; S4. Through three machine learning algorithms, SVR, BPNN and RF, a cross-sectional amplitude prediction model of a double-deck steel truss bridge under different wind speeds and a vortex-oscillation characteristic parameter prediction model under different additional aerodynamic measures were established. The prediction model parameters were optimized to achieve the best and effective prediction of the cross-sectional vortex-oscillation response of the double-deck steel truss bridge.

2. 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: 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: 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 angle of attack turntable and steel bracket, and the data acquisition equipment used in the test is installed; S13. Wind tunnel test analysis of segment model: (1) Force measurement test: The static three-force coefficients of the segment models in the construction state and the completed bridge state are measured to obtain the static three-force coefficients of the segment models in the construction state and the completed bridge state when the wind speed is 10 m / s, 15 m / s and 20 m / s and the downwind angle is in the range of -12° to +12°, and the corresponding static three-force coefficients are calculated; (2) Vibration test: The changes in the vertical amplitude and torsion angle of the segment model at wind attack angles of 0, ±3°, and ±5° were recorded using a laser displacement sensor to obtain 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 reduced 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.

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 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.

4. 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 measuring 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, and its measurement accuracy after zero calibration is higher than 0.5m / s, and the frequency is as high as 2000Hz; 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.

5. 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: The S4 step is as follows: S41. Machine learning algorithm determines: Determine the use of three machine learning algorithms, SVR, BPNN and RF, to build 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 section are integrated to obtain the VIV-R data set for predicting vortex vibration characteristic parameters; numerical calculations are performed for 20 different wind speeds in the range of reduced wind speed of 1.5 to 3.0 for each working condition in the VIV-R data set to obtain the VIV-A data set for surface amplitude prediction; the VIV-A data set and the VIV-R data set are normalized by the MATLAB program and the mapminmax function; the k-fold cross validation method is used to determine the ratio of the training set and the test set, and the average value of the k test results is used as the evaluation parameter; S43, double-deck steel truss bridge section amplitude prediction: (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 the ratio of 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 best model is optimized by genetic algorithm GA and particle swarm algorithm PSO, and the optimized model is established. The amplitude prediction results are compared with the best model to verify the effectiveness of the optimized model and obtain the best effective model for amplitude prediction, thus completing the whole process of amplitude prediction of double-deck steel truss bridge section under different wind speeds. S44. Prediction of characteristic parameters of vortex-induced vibration: (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 through 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 the 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 best model is optimized by genetic algorithm GA and particle swarm algorithm PSO, and the optimization model is established. The amplitude prediction results are compared with the best model to verify the effectiveness of the optimization model and obtain the best effective model for amplitude prediction, thus completing the whole process of predicting the vortex-vibration characteristic parameters of the double-deck steel truss bridge section.

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