Bridge structure nonlinear random wind vibration response prediction method and system based on hybrid time-frequency algorithm

Abstract

This invention relates to a method and system for predicting the nonlinear stochastic wind vibration response of bridge structures based on a hybrid time-frequency algorithm. The method includes constructing a nonlinear aerodynamic model, obtaining key parameters using wind tunnel test data, calculating the torsional mode branch frequency, simulating a pulsating wind field, calculating the reduced frequency based on the torsional mode branch frequency, calculating the AAF and buffeting force based on the simulated pulsating wind field, and solving for the nonlinear stochastic wind vibration response of the bridge structure under wind action. This invention overcomes the problem that current systems cannot simultaneously consider nonlinear aerodynamic forces and turbulent excitation, making it difficult to accurately predict the nonlinear stochastic wind vibration of bridges. Compared with existing methods, this invention has significant advantages in convergence, computational cost, and accuracy, providing effective technical support for bridge wind-resistant design.

Description

Technical Field

[0001] This invention belongs to the field of wind-induced response prediction technology for bridge structures, and relates to a method and system for predicting nonlinear stochastic wind vibration response of bridge structures based on a hybrid time-frequency algorithm, and more particularly to a method and system for predicting bending-torsional coupled nonlinear stochastic wind vibration response of bridge structures based on a hybrid time-frequency algorithm. Background Technology

[0002] Wind-induced buffeting and flutter directly affect the safety and durability of bridge structures and are key considerations in the wind-resistant design of long-span bridges. Bridge wind-resistant design theory has matured significantly, greatly deepening the understanding of wind-induced vibrations in long-span bridges and effectively promoting the rapid development of modern bridge construction. However, a review of the development of bridge wind-resistant theory reveals two remaining shortcomings:

[0003] First, there is a problem of focusing only on turbulence effects while neglecting aerodynamic nonlinearity. Self-excited aerodynamic forces are usually characterized as linear functions of state variables. Flutter response is solved using the classical eigenvalue method, which only considers the correction effect of turbulence on the flutter derivative to a certain extent; buffeting response relies on classical random vibration theory for solution and considers the correction effect of aerodynamic forces on the modal characteristics of the system. In essence, such systems still obey the basic characteristics of the superposition principle, so the system under the coupled action of self-excited force and buffeting force can be deconstructed or linearly reconstructed for each component individually.

[0004] Second, there is a problem of considering only aerodynamic nonlinearity while neglecting turbulence effects. Self-excited aerodynamic forces are often nonlinear functions of state variables, and bridge flutter is usually characterized by supercritical or subcritical Hopf bifurcation, with the post-critical response exhibiting limit cycle oscillations with multiple deterministic periodic solutions. To address this, various equivalent linearization models, time-domain nonlinear models, and black-box models characterizing nonlinear aerodynamic forces have been constructed, and several time-frequency domain algorithms for predicting nonlinear flutter have been proposed. However, these algorithms struggle to account for the turbulent characteristics of natural wind, which may lead to significant deterioration in wind-induced flutter response predictions in areas with complex terrain.

[0005] The above algorithms either neglect aerodynamic nonlinearity or turbulent excitation, often resulting in wind-induced vibration assessment errors exceeding engineering tolerances. Research shows that the coupling effect of turbulent excitation and nonlinear aerodynamic forces renders bridge systems non-autonomous and nonlinear. Their wind-induced vibration response is no longer the classic harmonic flutter or Gaussian buffeting, but rather exhibits hardened nonlinear random vibrations with significant nonlinear characteristics, accompanied by fuzzy aerodynamic stability and instability boundaries. The underlying mechanism is complex and difficult to solve. Although many scholars both domestically and internationally have conducted research on nonlinear random wind-induced vibration algorithms for single-degree-of-freedom systems and attempted to propose practical methods for evaluating response extremum distributions and peak factors, current progress is still insufficient to meet the computational requirements for nonlinear random wind-induced vibration of bridge structures with multiple degrees of freedom.

[0006] Therefore, it is necessary to develop relevant algorithms for effectively predicting the nonlinear random wind-induced vibration of long-span bridges under strong turbulent winds through theoretical analysis, so as to provide theoretical support for the reasonable wind-resistant design of bridge structures under complex terrain conditions. Summary of the Invention

[0007] In view of this, in order to overcome the problem that the current system cannot take into account both nonlinear aerodynamic forces and turbulent excitations, making it difficult to achieve accurate prediction of nonlinear random wind vibration of bridges, this invention provides a method and system for predicting the nonlinear random wind vibration response of bridge structures based on a hybrid time-frequency algorithm.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A method for predicting the nonlinear stochastic wind-induced vibration response of bridge structures based on a hybrid time-frequency algorithm is characterized by the following steps:

[0010] S1. Based on the cross-sectional characteristics, structural characteristics, aerodynamic characteristics and wind field characteristics of the bridge section, a nonlinear aerodynamic model of the bridge structure with bending and torsion coupling is constructed. This model is represented by a nonlinear function of the absolute value of displacement.

[0011] S2. Based on segmental model wind tunnel tests, obtain the classical flutter derivative in the nonlinear aerodynamic model of step S1. and dimensionless aerodynamic parameters And test the cross-section at different angles of attack. The static coefficient below;

[0012] S3. Calculate the average wind speed according to the specified requirements. ;

[0013] S4. Select the initial iteration frequency Calculate the corresponding reduced wind speed and reduction frequency According to the reduced wind speed Correspondingly select aerodynamic parameter values ~ , , Calculate the torsional modal branch frequency ;

[0014] Torsional mode The branching frequency under uniform flow field conditions is solved by the following equation:

[0015]

[0016] In the formula, To the torsional natural circular frequency; This is a dimensionless mass moment of inertia parameter; The moment of inertia per meter of mass; and The amplitude ratio and phase difference of the bending-torsional coupled motion are respectively, and can be solved using the following formula:

[0017]

[0018]

[0019] In the formula, The vertical natural circular frequency; The power amplification factor is expressed as follows:

[0020]

[0021] In the formula, Frequency ratio;

[0022] S5. Define preset fluctuating wind field parameters and use the classical spectral method to simulate the fluctuating longitudinal wind speed at each average wind speed at the bridge site. and vertical wind speed And compare it with existing wind spectra;

[0023] S6. Torsional modal branch frequencies calculated based on step S4 To calculate the reduction frequency ; Calculate the aerodynamic admittance function (AAF) and buffeting force based on the simulated fluctuating wind field wind spectrum in step S5; initialize the state variables. Update time step Calculate the Jacobian matrix. and ; Calculate state variables ;

[0024] S7. Solve the time history of the nonlinear random wind vibration response of the bridge structure system under all wind speed steps to achieve accurate prediction of the nonlinear random wind vibration of the bridge.

[0025] A system for predicting the bending-torsional coupled nonlinear stochastic wind-induced vibration response of bridge structures includes:

[0026] The nonlinear aerodynamic model building module utilizes the cross-sectional, structural, aerodynamic, and wind field characteristics of the bridge section to construct a mathematical model describing the nonlinear aerodynamic forces of the bridge structure involving bending and torsion coupling.

[0027] The wind tunnel test data processing module obtains the classical flutter derivative in the model based on wind tunnel test data. and dimensionless aerodynamic parameters And test the static coefficients under different angles of attack;

[0028] Torsional modal branch frequency calculation module, select initial iteration frequency Calculate the corresponding reduced wind speed and reduction frequency According to the reduced wind speed Correspondingly select aerodynamic parameter values ~ , , Calculate the torsional modal branch frequency ;

[0029] The pulsating wind field simulation module defines the parameters of the pulsating wind field and uses the classical spectral solution method to simulate the wind field;

[0030] The nonlinear random wind vibration response solution module, based on the torsional mode branch frequency... To calculate the reduction frequency Based on the simulated wind field, the AAF and buffeting force are calculated, and the nonlinear stochastic wind vibration response of the bridge structure under wind action is solved.

[0031] The beneficial effects of this invention are as follows:

[0032] 1. The present invention proposes a combination of Newton-Raphson and Newmark- The hybrid time-domain response numerical solution method exhibits good convergence and stability. This means that when solving the time history of nonlinear stochastic wind-induced vibration response, this method can reach a stable solution faster and is insensitive to changes in initial conditions and parameters, thus enhancing convergence and stability.

[0033] 2. Compared with the classic fourth-order Runge-Kutta method (RK4), the method of this invention can obtain satisfactory prediction results in a shorter time under the same numerical samples and computational configuration. This indicates that the method of this invention has a significant improvement in computational efficiency and is particularly suitable for needs involving the computation of a large number of numerical samples.

[0034] 3. This invention effectively solves the problem of bending-torsional coupled nonlinear random wind-induced vibration, providing a new technical means for the wind-resistant design of long-span bridges under strong turbulent wind, and helping to promote the development of bridge design theory and the progress of engineering practice.

[0035] 4. This invention, by constructing a nonlinear aerodynamic model of a bridge structure with bending-torsional coupling and combining it with wind tunnel test data, can more accurately simulate and predict the nonlinear stochastic wind vibration response of bridges under wind action. This method overcomes the problem of neglecting aerodynamic nonlinearity or turbulent excitation in existing technologies, thereby improving the accuracy of prediction results.

[0036] 5. Starting from the fact that buffeting forces lack aerodynamic stiffness, this invention utilizes the modal frequency iteration results under uniform flow fields to replace the modal frequencies under turbulent flow fields, significantly reducing computational costs. This method avoids costly modal frequency calculations under complex wind field conditions, thereby improving computational efficiency and reducing computational costs.

[0037] 6. The method of the present invention is not only applicable to single wind speed conditions, but also to the nonlinear random wind vibration response time history of bridge structure systems under different wind speeds, thus providing an effective technical means for the wind-resistant design of bridge structures under complex terrain conditions and improving its applicability.

[0038] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0039] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0040] Figure 1 This is a flowchart of the method for predicting the nonlinear stochastic wind vibration response of bridge structures using bending-torsional coupling, according to the present invention.

[0041] Figure 2 This is a diagram of the free vibration wind tunnel test system for step S2 of the present invention;

[0042] Figure 3 The result of parameter identification for the coupled nonlinear aerodynamic model in step S2 of this invention is shown below. Figure 3 (a) is the flutter derivative. , The relationship with normalized wind speed Figure 3 (b) is the flutter derivative. , The relationship with normalized wind speed;

[0043] Figure 4 This is a parameter diagram of the nonlinear aerodynamic model corresponding to the main girder of the bridge in an embodiment of the present invention;

[0044] Figure 5 This is a sample time history diagram of the simulated pulsating wind speed in step S5 of the present invention;

[0045] Figure 6 This is a time history diagram of the chattering force time history sample in step S6 of the present invention;

[0046] Figure 7This is a graph showing the nonlinear random wind vibration prediction results for a specified sample obtained by the method of this invention and the RK4 method, wherein... Figure 7 (a) is a convergence verification graph. Figure 7 (b) is a verification diagram for correctness. Detailed Implementation

[0047] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0048] like Figure 1 The method for predicting the nonlinear stochastic wind vibration response of bridge structures based on a hybrid time-frequency algorithm, as shown, includes the following steps:

[0049] S1. Based on the cross-sectional, structural, aerodynamic, and wind field characteristics of the bridge section, a bending-torsional coupled nonlinear aerodynamic model of the bridge structure is constructed. This model is represented by a nonlinear function of the absolute value of displacement; the specific calculation formula is as follows:

[0050]

[0051]

[0052] Unsteady torque and unsteady forces Unsteady moments and unsteady forces generated by the interaction between airflow and structure were calculated to analyze and predict the dynamic response of the structure under wind load.

[0053] In the formula, air density; Average wind speed; Half the width of the main beam; and These are vertical displacement and torsional displacement, respectively. This is the classical flutter derivative; ; For the dimensionless aerodynamic parameters in the model, when ,or When =0, the aerodynamic parameter takes the value of 1;

[0054] S2. Based on segmental model wind tunnel tests, identify the classical flutter derivative in the nonlinear aerodynamic model of step S1. and dimensionless aerodynamic parameters And test the cross-section at different angles of attack. The static coefficient below, and the free vibration test system involved, such as Figure 2 As shown. ~ For example, the identified aerodynamic parameters are as follows: Figure 3 As shown;

[0055] S3. Calculate the average wind speed according to the specified requirements. ;

[0056] S4. Select the initial iteration frequency Calculate the corresponding reduced wind speed and reduction frequency According to the reduced wind speed Correspondingly select aerodynamic parameter values ~ , , Calculate the torsional modal branch frequency ;

[0057] Specifically, S41, select the initial iteration frequency. Calculate the corresponding reduced wind speed ;

[0058] S42. Calculate the torsional modal branch frequencies. ;

[0059] Since buffeting forces have virtually no aerodynamic stiffness effect (i.e., they do not correct the system's modal frequencies), therefore torsional modes... The branching frequency can be solved under uniform flow field conditions using the following formula:

[0060]

[0061] In the formula, To the torsional natural circular frequency; This is a dimensionless mass moment of inertia parameter; The moment of inertia per meter of mass; and These are the amplitude ratio and phase difference of the bending-torsional coupled motion, respectively, which can be solved using the following formula:

[0062]

[0063]

[0064] In the formula, Frequency ratio; The vertical natural circular frequency; The power amplification factor is expressed as follows:

[0065]

[0066] Torsional mode The principle of branch frequency calculation is as follows:

[0067] For a bending-torsional coupled bridge structure, the motion information on its torsional modal branch can be uniformly expressed as:

[0068]

[0069] In the formula, for Movement in a certain direction; This represents the initial amplitude of the system. For time; for Phase of directional motion; For units of complex numbers.

[0070] The mathematical relationship between vertical motion and torsional motion can be expressed as:

[0071]

[0072] Therefore, the amplitude ratio can be used and phase difference This decouples the bending-torsional coupled motion into two independent single-degree-of-freedom motions. Taking torsion as an example, its equation of motion can be expressed as:

[0073]

[0074] in

[0075]

[0076]

[0077] From this, we can obtain

[0078]

[0079] Applying Euler's formula By assuming that the real and imaginary parts on both sides of the equation of motion are equal, the torsional modal branch frequencies mentioned above can be obtained. The calculation formula;

[0080] S43. Iterate the torsional modal branch frequency based on the tolerance. ;

[0081] Check if the residual is less than the tolerance. If it is, end the iteration; otherwise, return to step S41 and repeat steps S41-S42. The iteration convergence evaluation factor is defined as follows:

[0082]

[0083] When the residual between the χ and χ-1 iteration steps is less than the predetermined tolerance (i.e., The iteration terminates when the modal frequencies are considered to have converged. It should be noted that the tolerance ε should be close to zero.

[0084] S5. Define preset fluctuating wind field parameters and use the classical spectral method to simulate the fluctuating longitudinal wind speed at each average wind speed at the bridge site. and vertical wind speed And compared with existing wind spectra. Figure 4 The image shows the sample time history of the simulated fluctuating wind speed. Preset fluctuating wind field parameters include the spectral model, turbulence intensity, integral scale, sampling frequency, number of samples, and sample duration.

[0085] S6. Torsional modal branch frequencies calculated based on step S4 To calculate the reduction frequency ; Calculate the aerodynamic admittance function (AAF) and buffeting force based on the simulated fluctuating wind field wind spectrum in step S5; initialize the state variables. Update time step Calculate the Jacobian matrix. and ; Calculate state variables ;

[0086] Specifically, it includes the following steps:

[0087] S61. Based on the buffeting force spectrum model, and using the static coefficient of the tested section combined with the aerodynamic admittance function (AAF), calculate the buffeting force time history sample. Figure 5 Time history plot of the buffeting force time history sample;

[0088] The buffeting force model is specifically expressed as follows:

[0089]

[0090]

[0091] In the formula, , and All are static coefficients of bridge cross sections; and This represents the derivative of the static coefficient with respect to the angle of attack; , , , and All are aerodynamic admittance functions. and These represent the longitudinal and vertical pulsating wind speeds, respectively.

[0092] S62. Based on the time history of the buffeting force at the current average wind speed step, conduct research on the first specific sample. Solving for the response at each time step; the specific solution approach is as follows:

[0093] For a given time step According to Newmark- Law, No. and The response at each time step follows the following mathematical relationship:

[0094]

[0095]

[0096] in, and The parameters to be selected are typically 0.5 and 0.25, respectively, to ensure unconditional convergence. Furthermore, the system in the... The equations of motion at each time step can be described as follows:

[0097]

[0098] Clearly, the above three formulas can be uniformly described as:

[0099]

[0100] in, The state vector of the system at time t is as follows:

[0101]

[0102] Therefore, according to the Newton-Raphson iterative method, the response between two consecutive time steps must obey the following relationship.

[0103]

[0104] Therefore, we can obtain .

[0105] In the formula, for The first-order partial derivative matrix (also called the Jacobian matrix) is represented by the following specific elements:

[0106]

[0107] in,

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] S7. Repeat step S62 to solve the nonlinear random wind vibration response time history for all time steps under a specific sample.

[0116] S8. Repeat steps S62 and S7 to solve the nonlinear random wind vibration response time history for all samples under the current wind speed step;

[0117] S9. Repeat steps S3 to S8 to solve the time history of the nonlinear random wind vibration response of the bridge structure system under all wind speed steps; terminate the calculation of the nonlinear random wind vibration response.

[0118] Example

[0119] Using the Yangsigang Yangtze River Bridge in central China as a case study, its main span is 1700 meters, and its main girder is a double-layer truss beam. The main girder of this bridge is 28 meters wide and 10 meters high. The equivalent mass per unit length corresponding to the first-order symmetrical vertical vibration mode is calculated. =41609kg / m, natural frequency =0.1244Hz. Equivalent mass moment per unit length corresponding to the first-order symmetrical torsional mode. = natural frequency =0.3047Hz. Its static coefficient and its derivative at a wind angle of attack of 0° were experimentally tested: as well as The parameters of the nonlinear aerodynamic model corresponding to the main beam are as follows: Figure 4 As shown.

[0120] The classical spectral method was used to simulate the time history samples of fluctuating wind speeds, with 100 samples collected for the average wind speed of each target. The Kaimal spectrum was used for the longitudinal fluctuating wind speed spectrum, and the Panofsky-McCormick spectrum was used for the vertical fluctuating wind speed spectrum. Simulation parameters were: sampling frequency 8 Hz (time step 0.125 s); 40,960 data points per sample, total duration 5120 s; and the height of the main beam above the ground. =45 m; Surface roughness =0.05 m.

[0121] Taking an average wind speed of 36 m / s as an example, Figure 5Three typical longitudinal fluctuating wind speed time history samples are presented. Based on the simulated wind speed fluctuations, the buffeting force time history is calculated, as follows: Figure 6 As shown. The aerodynamic admittance function uses the Liepmann approximation of the Sears function, and its squared modulus is expressed as follows:

[0122]

[0123] Calculation of operating conditions

[0124] The aeroelastic response calculation considered two schemes: one including flutter force and one excluding it. For a specific bridge cross-section, the flutter solution curves may exhibit drastically different topologies under different wind speed paths. In the numerical calculation, two initial perturbations were applied to the system at each wind speed, namely... =0.3°, =0.3m and =5.0°, =0.3m, to simulate the updraft and downdraft processes. Different structural damping levels were considered in the calculations: =0.001, 0.003 and 0.005.

[0125] Algorithm convergence, computational efficiency, and correctness

[0126] Based on the classic fourth-order Runge-Kutta method (RK4), this paper explores the advantages of this invention in predicting nonlinear random wind-induced vibrations. The time step for fluctuating wind speed is set to 0.125 s. The calculation of nonlinear random vibrations requires further subdivision of this time step to test the convergence sensitivity of the RK4 method and this invention in terms of time step. Table 1 summarizes the specific number of subdivisions.

[0127] Table 1. Performance comparison of the present invention in calculating nonlinear random wind-induced vibrations

[0128]

[0129] Figure 7 This is a graph showing the nonlinear random wind vibration prediction results for a specified sample obtained by the method of this invention and the RK4 method, wherein... Figure 7 (a) is a convergence verification graph. Figure 7 (b) shows the correctness verification diagram. Table 1 summarizes the corresponding computational cost, convergence, and consistency with the actual response. Note that the RK4 method's calculation results tend to stabilize after the number of subdivisions exceeds 500. At this point, the calculation results can be considered reliable and can be used as a benchmark to verify the correctness of other calculation scenarios.

[0130] like Figure 7 As shown in (a), the predicted response time history remains almost unchanged as the number of subdivisions increases from 1 to 30, demonstrating good convergence. In contrast, as Figure 7 As shown in (b), when the number of subdivisions is insufficient, the RK4 method exhibits poor convergence (<200) or fails to converge (<400), highlighting its high sensitivity to time step size. Secondly, the evolution of the prediction results in this invention is highly consistent with the reference benchmark and does not excessively depend on the time step size, demonstrating its high accuracy. Finally, under the same numerical sample and computational configuration, this invention can obtain satisfactory prediction results in just 5 seconds (as shown in Table 1). In contrast, the RK4 method requires at least 300 subdivisions to obtain satisfactory results, with a time cost approximately 35 times that of this invention. This is clearly unacceptable for situations involving a large number of numerical samples. Overall, this invention demonstrates significant advantages in high accuracy, high convergence, and high efficiency.

[0131] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting the nonlinear stochastic wind-induced vibration response of bridge structures based on a hybrid time-frequency algorithm, characterized in that, Includes the following steps: S1. Based on the cross-sectional characteristics, structural characteristics, aerodynamic characteristics and wind field characteristics of the bridge section, a nonlinear aerodynamic model of the bridge structure with bending and torsion coupling is constructed. This model is represented by a nonlinear function of the absolute value of displacement. S2. Based on segmental model wind tunnel tests, obtain the classical flutter derivative in the nonlinear aerodynamic model of step S1. and dimensionless aerodynamic parameters And test the cross-section at different angles of attack. The static coefficient below; S3. Calculate the average wind speed according to the specified requirements. ; S4. Select the initial iteration frequency Calculate the corresponding reduced wind speed and reduction frequency According to the reduced wind speed Correspondingly select aerodynamic parameter values ~ , Calculate the torsional modal branch frequency ; Torsional modal branching frequency Under uniform flow field conditions, the following equation can be used to solve for the problem: In the formula, To the torsional natural circular frequency; This is a dimensionless mass moment of inertia parameter; The moment of inertia per meter of mass; and The amplitude ratio and phase difference of the bending-torsional coupled motion are respectively, and can be solved using the following formula: In the formula, The vertical natural circular frequency; The power amplification factor is expressed as follows: In the formula, Frequency ratio; S5. Define preset fluctuating wind field parameters and use the classical spectral method to simulate the fluctuating longitudinal wind speed at each average wind speed at the bridge site. and vertical wind speed And compare it with existing wind spectra; S6. Torsional modal branch frequencies calculated based on step S4 To calculate the reduction frequency ; Calculate the aerodynamic admittance function (AAF) and buffeting force based on the simulated fluctuating wind field wind spectrum in step S5; initialize the state variables. Update time step Calculate the Jacobian matrix. and ; Calculate state variables ; S7. Solve the time history of the nonlinear random wind vibration response of the bridge structure system under all wind speed steps to achieve accurate prediction of the nonlinear random wind vibration of the bridge.

2. The nonlinear stochastic wind-induced vibration response prediction method as described in claim 1, characterized in that, The specific calculation formula for the nonlinear aerodynamic model of the bridge structure in step S1 is as follows: In the formula, air density; Average wind speed; Half the width of the main beam; and These are vertical displacement and torsional displacement, respectively. This is the classical flutter derivative; ; For the dimensionless aerodynamic parameters in the model, when ,or When =0, the aerodynamic parameter is set to 1.

3. The nonlinear stochastic wind-induced vibration response prediction method as described in claim 2, characterized in that, Torsional mode in step S4 The principle of branch frequency calculation is as follows: For a flexural-torsional coupled bridge structure, the motion information on its torsional modal branch is described as follows: In the formula, for Movement in direction; This represents the initial amplitude of the system. For time; for Phase of directional motion; For unit complex numbers; The mathematical relationship between vertical motion and torsional motion is expressed as follows: Therefore, using the amplitude ratio and phase difference Decouple the bending-torsional coupled motion from two independent single-degree-of-freedom motions; the equation of motion for torsion is expressed as: in Therefore, we can conclude that: Applying Euler's formula By assuming that the real and imaginary parts on both sides of the equation of motion are equal, the torsional modal branch frequencies mentioned above can be obtained. The calculation formula.

4. The nonlinear stochastic wind-induced vibration response prediction method as described in claim 3, characterized in that, Step S4 Iterates the torsional mode branch frequency based on the tolerance. That is: check if the residual is less than the tolerance; if so, end the iteration; otherwise, return to continue calculating the torsional modal branch frequency. Residual comparisons are performed, where the iterative convergence evaluation factor is defined as follows: When the residual between the χ and χ-1 iteration steps is less than the predetermined tolerance, i.e. The iteration is terminated when the modal frequencies are considered to have converged.

5. The nonlinear stochastic wind-induced vibration response prediction method as described in claim 1, characterized in that, The preset parameters for the pulsating wind field in step S5 include the spectral model, turbulence intensity, integral scale, sampling frequency, number of samples, and sample duration.

6. The nonlinear stochastic wind-induced vibration response prediction method as described in claim 4, characterized in that, Step S6 specifically includes the following steps: S61. Based on the buffeting force spectrum model, and using the static coefficient of the tested section combined with the aerodynamic admittance function (AAF), calculate the buffeting force time history sample. The buffeting force model is specifically expressed as follows: In the formula, , and All are static coefficients of bridge cross sections; and This represents the derivative of the static coefficient with respect to the angle of attack; , , , and All are aerodynamic admittance functions. and These represent the longitudinal and vertical pulsating wind speeds, respectively. S62. Based on the time history of the buffeting force of the current average wind speed step, conduct research on the first specific sample. Solving for the response at each time step; the specific solution approach is as follows: For a given time step According to Newmark- Law, No. and The response at each time step follows the following mathematical relationship: in, and The parameters to be selected are 0.5 and 0.25, respectively, to ensure unconditional convergence; in addition, the system in the... The equations of motion at each time step are described as follows: Clearly, the three formulas mentioned above in step S62 can be uniformly described as follows: in, The state vector of the system at time t is as follows: Therefore, according to the Newton-Raphson iterative method, the response between two consecutive time steps must conform to the following relationship: Therefore, we can obtain ; In the formula, for The first-order partial derivative matrix is ​​given by: where the elements are specifically expressed as: in, 。 7. The nonlinear stochastic wind-induced vibration response prediction method as described in claim 1, characterized in that, Step S7 sequentially includes solving the nonlinear random wind vibration response time history for all time steps under a specific sample, the nonlinear random wind vibration response time history for all samples under the current wind speed step, and solving the nonlinear random wind vibration response time history of the bridge structure system under all wind speed steps.

8. A system for predicting the bending-torsional coupled nonlinear stochastic wind-induced vibration response of bridge structures, based on the method for predicting the nonlinear stochastic wind-induced vibration response of bridge structures based on a hybrid time-frequency algorithm as described in any one of claims 1 to 7, characterized in that, include: The nonlinear aerodynamic model building module utilizes the cross-sectional, structural, aerodynamic, and wind field characteristics of the bridge section to construct a mathematical model describing the nonlinear aerodynamic forces of the bridge structure involving bending and torsion coupling. The wind tunnel test data processing module obtains the classical flutter derivative in the model based on wind tunnel test data. and dimensionless aerodynamic parameters And test the static coefficients under different angles of attack; Torsional modal branch frequency calculation module, select initial iteration frequency Calculate the corresponding reduced wind speed and reduction frequency According to the reduced wind speed Correspondingly select aerodynamic parameter values ~ , , Calculate the torsional modal branch frequency ; The pulsating wind field simulation module defines the parameters of the pulsating wind field and uses the classical spectral solution method to simulate the wind field; The nonlinear random wind vibration response solution module, based on the torsional mode branch frequency... To calculate the reduction frequency The aerodynamic admittance function (AAF) and buffeting force are calculated based on the simulated wind field, and the nonlinear stochastic wind vibration response of the bridge structure under wind action is solved.

9. The nonlinear stochastic wind vibration response prediction system as described in claim 8, characterized in that, The nonlinear stochastic wind vibration response solution module adopts Newton-Raphson and Newmark- We use a hybrid time-domain numerical solution method to solve the problem, ensuring convergence and computational efficiency.

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