A curve track-bridge coupling system support stiffness identification method based on vehicle scanning method

Abstract

The application discloses a curve track-bridge coupling system support stiffness identification method based on a vehicle scanning method, belongs to the field of engineering structure monitoring, and establishes a curve double-beam system mechanical model with a mobile elastic mass, deduces a control equation, and solves the control equation by using a modal superposition method and Laplace transformation, extracts a coupling system frequency from a contact point or a vehicle response, and especially efficiently identifies track modulus by using a fourth frequency component of a first-order modal. The application has the advantages of strong operation maneuverability, high cost benefit ratio and outstanding implementation efficiency, and is suitable for health monitoring of a curve track-bridge coupling system.

Description

Technical Field

[0001] This invention relates to the field of engineering structure monitoring technology, and more specifically to a method for identifying the support stiffness of a curved track-bridge coupled system based on vehicle scanning. Background Technology

[0002] Currently, dynamic detection methods are mainly divided into two categories: direct measurement methods and indirect measurement methods. Direct measurement methods evaluate the dynamic characteristics of a structure by analyzing vibration data acquired by sensors permanently installed on the structure. However, this method has some drawbacks, including high installation costs, excessive data volume, and sensor lifespan being much shorter than the structure's lifespan. It is mainly used in long-span bridges and has limited application in medium- and short-span bridges.

[0003] Traditional static load testing methods require interruption of operation and cannot simulate dynamic effects; dynamic testing methods based on finite element models rely on a large number of accurate parameters and are time-consuming to calculate; methods based on vibration sensors have high requirements for sensor placement and are easily affected by environmental noise.

[0004] Therefore, how to provide a method for identifying the support stiffness of a curved track-bridge coupling system based on vehicle scanning is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a method for identifying the support stiffness of a curved track-bridge coupled system based on vehicle scanning, aiming to solve the above problems and achieve identification that is uninterrupted in operation, accurately simulates dynamics, reduces parameter dependence, is highly resistant to interference, and is real-time and efficient.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for identifying the support stiffness of a curved track-bridge coupled system based on vehicle scanning includes:

[0008] Step 1: Establish a mechanical model of a curved double-beam system with a moving elastic mass;

[0009] Step 2: Derive the control equations based on the mechanical model, including the vertical and torsional vibration control equations for curved rails and bridges, as well as the vibration equations for vehicles;

[0010] Step 3: The displacements of the track and bridge are represented by the modal superposition method, and the vertical responses of the track and bridge are obtained by solving the Laplace transform.

[0011] Step 4: Based on the vertical response of the track and bridge, obtain the vertical displacement and acceleration of the contact point, and obtain the vehicle displacement and acceleration, clarifying the relationship between the key parameters of the contact point response or vehicle response and the support stiffness;

[0012] Step 5: Extract the frequency of the coupled system from the contact point response or vehicle response based on the correlation results, and identify the track modulus through the fourth frequency component of the first-order mode.

[0013] Furthermore, in the mechanical model of the curved double beam system, the double beam is modeled as a warp-free Bernoulli-Euler beam, and based on linear deformation, the discrete fastener-sleeper system is equivalent to a uniformly distributed spring-damper unit.

[0014] Furthermore, the expressions for the vertical and torsional vibration control equations of curved rails and bridges are as follows:

[0015] ;

[0016]

[0017]

[0018]

[0019]

[0020] In the formula and These represent the vertical and torsional displacements of the rail and the bridge, respectively. The subscript 'r' represents the rail, and the subscript 'b' represents the bridge. R is the radius of curvature. Θ For the track support stiffness, E and G represent the elastic modulus and shear modulus, respectively; y express y The moment of inertia of the shaft, J represents the torsional moment of inertia, and ρ represents the mass per unit length of the track or bridge.

[0021] Furthermore, the expression for the vehicle's vibration equation is:

[0022] ;

[0023] in Indicates vertical displacement. The natural frequency of the vehicle, , For the spring stiffness, and For the quality of the vehicle.

[0024] Furthermore, the displacements of the track and bridge are represented using the modal superposition method, and the vertical responses of the track and bridge are obtained by solving the Laplace transform, including:

[0025] The vertical and torsional displacements of the track and bridge are expressed using the modal superposition method as follows:

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] In the formula, and These represent the vertical and torsional displacements of the rail and the bridge, respectively. The subscript 'r' represents the rail, and the subscript 'b' represents the bridge. and Vertical displacement and The generalized coordinates of the corresponding nth mode, and and These are respectively torsional displacements and The generalized coordinates of the nth mode. ;

[0031] The vertical responses of the track and bridge are obtained by solving the Laplace transform, and the expressions are as follows:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] In the formula, and represents the nth-order modal coordinates of the vertical and torsional responses of the track and bridge, respectively; s is a complex variable. , , , , , , These represent the coupled and uncoupled frequencies of the track and bridge, respectively. For vehicle quality, It is the acceleration due to gravity. This refers to the vehicle's driving frequency.

[0037] Furthermore, the key parameters of the support stiffness include: track and bridge frequency, and track stiffness.

[0038] Furthermore, the identification of the orbital modulus through the fourth frequency component of the first-order mode includes obtaining the orbital modulus by reversing the closed-loop solution.

[0039] As can be seen from the above technical solution, compared with the prior art, this invention discloses a method for identifying the support stiffness of a curved track-bridge coupled system based on vehicle scanning. By establishing a mechanical model of a curved double-beam system with a moving elastic mass, deriving the control equations, and solving them using the modal superposition method and Laplace transform, the coupling system frequencies are extracted from the contact point or vehicle response. In particular, the fourth frequency component of the first-order mode is used to efficiently identify the track modulus. This method has the advantages of high operational mobility, high cost-effectiveness, and outstanding implementation efficiency. It can achieve uninterrupted operation, accurate dynamic simulation, reduced parameter dependence, strong anti-interference, and real-time efficient identification, and is suitable for health monitoring of curved track-bridge coupled systems. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0041] Figure 1 A schematic diagram of a curved double-beam system with a moving elastic mass used in a vehicle-rail-bridge system;

[0042] Figure 2 This is a schematic diagram of a vehicle-rail-bridge (VTB) unit structure.

[0043] Figure 3(a) shows the trajectory convergence under different mode numbers;

[0044] Figure 3(b) shows a schematic diagram of bridge convergence under different modal numbers;

[0045] Figure 3(c) shows the vehicle convergence under different modal numbers;

[0046] Figure 4(a) is a schematic diagram of the vertical displacement response at mid-span of the curved bridge;

[0047] Figure 4(b) is a schematic diagram of the vertical acceleration response at mid-span of the curved bridge;

[0048] Figure 5(a) is a schematic diagram of the vertical displacement response at mid-span of the curved track;

[0049] Figure 5(b) is a schematic diagram of the vertical acceleration response at mid-span of the curved track;

[0050] Figure 6(a) is a schematic diagram of the vehicle's vertical acceleration response;

[0051] Figure 6(b) shows the vertical acceleration spectrum of the vehicle;

[0052] Figure 7(a) is a schematic diagram of the vertical acceleration response at the contact point;

[0053] Figure 7(b) shows the vertical acceleration spectrum at the contact point;

[0054] Figure 8(a) shows the vehicle acceleration spectrum.

[0055] Figure 8(b) shows the acceleration spectrum at the contact point;

[0056] Figure 9 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] Example 1:

[0059] See Figure 9 This invention discloses a method for identifying the support stiffness of a curved track-bridge coupling system based on vehicle scanning, comprising:

[0060] Step 1: Establish a mechanical model of a curved double-beam system with a moving elastic mass;

[0061] Step 2: Derive the control equations based on the mechanical model, including the vertical and torsional vibration control equations for curved rails and bridges, as well as the vibration equations for vehicles;

[0062] Step 3: The displacements of the track and bridge are represented by the modal superposition method, and the vertical responses of the track and bridge are obtained by solving the Laplace transform.

[0063] Step 4: Based on the vertical response of the track and bridge, obtain the vertical displacement and acceleration of the contact point, and obtain the vehicle displacement and acceleration, clarifying the relationship between the key parameters of the contact point response or vehicle response and the support stiffness;

[0064] Step 5: Extract the frequency of the coupled system from the contact point response or vehicle response based on the correlation results, and identify the track modulus through the fourth frequency component of the first-order mode.

[0065] Specifically, such as Figure 1 As shown, the rail-bridge system is simulated as a horizontal curved double-beam model, where the upper beam and lower beam simulate the rail and bridge respectively, and both have a uniform length. L and radius of curvature RThe double beams are modeled as warp-free Bernoulli-Euler beams, considering only linear deformation. The discrete fastener-sleeper system is equivalent to a uniformly distributed spring-damper element with spring stiffness of... Θ Damping coefficient is C At a constant speed v The inspection vehicle moves on the rails, determined by stiffness. k v Concentrated mass of spring support M v Alternatively, it is assumed that the vehicle maintains vertical and radial contact with the bridge throughout its motion. Typically, since the vehicle's mass is assumed to be much smaller than the mass of the track and bridge, mass inertia can be ignored.

[0066] Specifically, to derive the closed-form solution, a right-handed coordinate system is established, where x The axis is tangent to the centroidal axis of the beam, and y shaft and z The axes correspond to the horizontal and vertical axes of the beam's cross-section, respectively. Furthermore, and These represent the vertical and torsional displacements of the rails and the bridge, respectively; subscripts r Indicates rail, subscript b It refers to a bridge.

[0067] Specifically, according to Figure 1 Based on the assumptions and mechanical model, the governing equations for the vertical and torsional vibrations (out-of-plane) of curved rails and bridges under vehicle loading can be expressed as follows:

[0068]

[0069] Interacting loads are expressed as follows:

[0070]

[0071] Where the subscript r represents the rail, the subscript b represents the bridge, and R is the radius of curvature; m This refers to the mass per unit length of tracks and bridges. E G and G represent the elastic modulus and shear modulus, respectively; y express y Moment of inertia of the axis, J ρ represents the torsional moment of inertia, and ρ represents the mass per unit length of the track and bridge. Indicates the coordinates of the contact point. g Represents gravitational acceleration. This indicates the track support stiffness, that is, the basic stiffness of the rails. This represents the Dirac function.

[0072] Meanwhile, the vehicle's equation can be expressed as

[0073]

[0074] in Indicates vertical displacement. The natural frequency of the vehicle can be used. calculate, For the spring stiffness, and For the quality of the vehicle.

[0075] For simply supported boundary problems, the vertical and torsional displacements of the track and bridge can be represented by the modal superposition method:

[0076]

[0077] in, and Vertical displacement and The corresponding number n The generalized coordinates of the first mode, and and These are respectively torsional displacements and The n Generalized coordinates of the first mode.

[0078] Substituting equations (3a) to (3d) into equations (1a) to (1d), and multiplying both sides of the equation by... and to x In 0 to L Integrating over the interval, we obtain the following modal motion equations for the thin-walled beam:

[0079]

[0080] Regarding vehicle speed v Speed ​​parameters,

[0081]

[0082] The dot (·) indicates time. t Differentiation; parameters , , , , , , and Listed in equations (A1) to (A8).

[0083] By order , , and The homogeneous parts of equations (3a) to (3d) can be expressed as (i is the imaginary unit):

[0084]

[0085] Represented in matrix form as follows:

[0086]

[0087] To ensure that the eigenvalue problem in equation (7) has a non-zero solution, the determinant of the matrix should be equal to 0, i.e.,

[0088]

[0089] By If considered as a whole, four real roots can be naturally obtained from equation (8). It represents the first double-beam model. n The natural frequencies of the first mode. For convenience, some new parameters are defined here, namely... and , which are listed in equations (A9) to (A10).

[0090] Considering the complexity of the coupled equations (4a) to (4d), solving them directly in the time domain is impractical. Therefore, under the assumption of zero initial conditions, a Laplace transform is used to process these equations. This allows for an efficient transformation of these equations from the time domain to... s A field is represented as:

[0091]

[0092] in, and The first two characters represent the vertical and torsional responses of the track and bridge, respectively. n First modal coordinates; s Let be a complex variable. Therefore, we can obtain... s Relevant vertical responses of tracks and bridges within the domain:

[0093]

[0094] Using the inverse Laplace transform, the equations (10a) and (10b) given in equation (10b) can be transformed into the equations (10a) and (10b). s The solution in the time domain, when transformed back to the time domain, yields the following expression:

[0095]

[0096] Among them, the correlation coefficient , , , , , , , , and Listed in equations (A11) to (A20).

[0097] Based on the modal coordinates in equations (11a) and (11b), the vertical time-domain displacement can be derived using equations (3a) and (3c). For simplicity, explicit expressions for the vertical displacements of the bridge and track are not given here. Furthermore, since this invention focuses only on the vertical response, the relevant torsional responses of the track and bridge in the time domain are not shown here.

[0098] By order x = vt The vertical displacement of the contact point can be obtained from equation (11a), that is... Z c ( t )= Z r ( vt , t ), and thus time t Find the second derivative to obtain the acceleration. for:

[0099]

[0100] Subsequently, the contact displacement Z c ( t Substituting into equation (2), the vehicle displacement can be directly solved. q v ( t ), represented as:

[0101]

[0102] Among them, the correlation coefficient ~ Listed in equations (A21) to (A32).

[0103] Similarly, vehicle acceleration The result can be obtained by taking the second derivative of equation (12):

[0104]

[0105] From the observations of equations (12) and (14), it can be seen that the frequency corresponding to the double-beam system is... and It is closely related to the contact point and vehicle acceleration response. This indicates that either the contact point response or the vehicle response can be effectively used to extract key parameters such as track and bridge frequencies and track stiffness.

[0106] In one specific embodiment, the orbital modulus extraction process is as follows:

[0107] Based on the closed-form solution derived above, the track modulus exists in the coupling frequency of the track-bridge system, i.e. and This means that once the coupling frequency is determined, the track modulus can be extracted naturally. Based on this, the process of extracting the track modulus can be summarized into the following three steps: (1) calculate or measure the vehicle response or contact point response when the vehicle passes through the curved track-bridge system; (2) extract the frequency of the coupling system from the response; and (3) use the extracted frequency to identify the track modulus.

[0108] To extract the orbital modulus, only the first-order vibration mode is used here, and the inequalities are... This still holds true. Therefore, analysis shows that the frequency parameter equations in equations (A9) and (A10) can be simplified to: Based on this, equation (7) can be rewritten as:

[0109]

[0110] Clearly, the four roots appearing in equation (15) can be expressed as: Approaching zero Furthermore, the track modulus can be obtained through the fourth frequency component of the first-order mode of the track-bridge system. To achieve efficient recognition, the expression is:

[0111]

[0112] According to equation (16), it is easy to see that once the fourth frequency component of the first-order mode is predetermined... This allows us to inversely calculate the orbital modulus. Typically, the frequency... The frequency is clearly located in the initial high-frequency domain, which helps in identifying the track modulus. However, in reality, under the influence of a moving vehicle, the frequency of the coupled system varies with time. Therefore, a parameter is introduced... Let's consider the change in frequency. Equation (16) can be restated as follows:

[0113]

[0114] in, This represents the predicted value of the orbital modulus. When... When the value falls within the range of 0.98-1.02, the ratio between the predicted and actual values ​​of the orbital modulus is... / A value between 0.95 and 1.05 meets engineering requirements. Within this range, the proposed technique can be used to obtain the orbital modulus through frequency peaks in actual field tests.

[0115] Theoretically, for a curved track-beam coupled system, the fourth frequency component of the first-order mode of the vehicle response can be used as a reference. Obtain the orbital modulus Θ In this section, we will evaluate the effects of these two responses on extracting first-order frequencies. Performance differences in terms of orbital modulus Θ.

[0116] Vehicle frequency Included in vehicle response In the middle, the contact point response This frequency is not included. Therefore, the contact point response is the extracted fourth frequency component of the first-order mode. and orbital modulus Θ A better option.

[0117] Next, we will discuss the fourth frequency component of the first mode. Further performance comparisons were conducted regarding amplitude. It is well known that if the amplitude of a specific frequency is significantly higher than other frequencies, it is easier to identify. For the fourth frequency component of the first-order mode, its amplitude can be obtained from the contact point response and the vehicle response:

[0118]

[0119] Accordingly, and The amplitude ratio is defined as:

[0120]

[0121] For the first-order vibration mode, at a moderate driving speed of the test vehicle... much smaller or Therefore, equation (19) can be further simplified to:

[0122]

[0123] Under normal circumstances, The frequency value is much greater than This means that the amplitude ratio can be simplified to:

[0124]

[0125] From the two perspectives mentioned above, there is sufficient evidence to show that the contact point response outperforms the vehicle response in extracting the fourth frequency component of the first-order mode.

[0126] In one specific embodiment, the method for obtaining the contact point response during field testing is as follows:

[0127] Because the vehicle-rail contact point has time-varying characteristics, the acceleration at the contact point cannot be directly measured during field testing. However, the vehicle response can be obtained from on-site test records. The inverse calculation can be easily obtained. Based on the vehicle control equation and the central difference method in equation (2), the inverse calculation formula for the contact point response can be expressed as:

[0128]

[0129] in, Indicates the sampling point, while This indicates the sampling interval.

[0130] Specifically, the parameters involved in equations (18) to (22) are:

[0131]

[0132]

[0133]

[0134] Example 2:

[0135] This embodiment will briefly introduce a curved vehicle-rail-bridge (VTB) interaction element suitable for single-axle vehicles (including vertical and torsional motion) to verify the reliability and accuracy of the above analytical solution. The curved VTB element is as follows: Figure 2 As shown. The curve VTB cell consists of a length of L e , radius is R The curved track and bridge unit are coupled together in the local coordinate system through distributed springs and dampers. (Using superscript...) r and b The track and bridge units shown are, in such a way Figure 2 Use superscript i and j The two endpoints shown each have three degrees of freedom, namely one translational displacement. z and two rotational displacements θ x and θ y .

[0136] To obtain the displacement form function of the curved beam element, the displacement coefficient matrix of vertical-torsional vibration is introduced here. H The expression is as follows:

[0137]

[0138] Among them, H q ( q =1,2,3) represents the coefficient matrix corresponding to the three degrees of freedom. Displacement shape functions NDefined as:

[0139]

[0140] in, and Representing vertical deflection and corresponding values ​​respectively. x Shape functions of torsional displacement along the y-axis and y-axis. Let be the local axial coordinates of the beam. Integral expressions for the element mass matrix and stiffness matrix were established. Subsequently, these expressions were integrated into the overall global mass matrix and stiffness matrix.

[0141] Furthermore, the global damping matrix is ​​established based on the Rayleigh damping assumption. Following the energy principle, the global equations of motion for the vehicle-track-bridge (VTB) interaction system considering track irregularities can be constructed:

[0142]

[0143] in, , and These represent the mass matrix, damping matrix, and stiffness matrix, respectively. (Subscript ') v '、' r 'and' b 'These represent the physical quantities corresponding to vehicles, tracks, and bridges, respectively;' vr 'and' rv 'represent the coupling matrices between the vehicle and the track, respectively, while' rb 'and' br 'Represents the coupling matrix between the track and the bridge, respectively. Represents the displacement vector. The load vector is used. VTB interacting elements are assembled with other track-bridge elements without vehicle interaction to form a global VTB system. Subsequently, Newmark- β Law( β =0.25, γ =0.5) Calculate the motion equations of the global VTB system step by step, with the time step set to 0.0001 seconds.

[0144] Specifically, this embodiment 2 numerically verifies the closed-loop solution proposed in embodiment 1. The parameters of the selected test vehicle, horizontal curved track, and bridge are listed in Table 1. Utilizing these characteristics, the vehicle frequency... The frequency is 11.25 Hz, and the travel speed is 20 m / s. In the numerical analysis, the bridge is divided into 32 equal elements, each element being 1 m long. To verify the reliability of the proposed solution, track irregularities are temporarily disregarded. It is worth noting that, for simplicity, only the displacement and acceleration results for the curved track and the mid-span of the bridge are given.

[0145] Table 1. Characteristic parameters of vehicles, tracks, and bridges

[0146]

[0147]

[0148] Referring to Figures 3(a)-3(c), the accuracy of the closed-loop solution may be affected by the number of modes considered in the analysis. To investigate this effect, this section evaluates five different levels of mode count. Regarding convergence evaluation, Figures 3(a)-3(c) show the calculated vertical displacements of the vehicle, track, and bridge at different modes. Clearly, the response gradually stabilizes as the number of modes included in the analysis increases. Specifically, the bridge vertical displacement converges when the number of modes reaches 10; while the vertical displacements of the track and vehicle require at least 30 modes to converge. This can be attributed to the relatively higher frequencies of the track and vehicle compared to the bridge frequency-vehicle frequency. The first frequency of the bridge's first-order mode is 11.25 Hz. The frequency was only 3.89 Hz. Therefore, 30 modes were used in subsequent studies.

[0149] Figures 4(a)-4(b), 5(a)-5(b), 6(a)-6(b), and 7(a)-7(b) compare the results of the proposed method for identifying the support stiffness of a curved track-bridge coupling system based on vehicle scanning with the numerical results of the finite element method (FEM). These figures involve the test vehicle, contact point, curved track, and curved bridge. Notably, the acceleration of the vehicle and contact point in the frequency domain was calculated using time-history data and Fast Fourier Transform (FFT). It can be clearly seen that the analytical results agree well with the finite element results, with only minor differences in acceleration, which is acceptable for the frequencies of the system under study extracted in the frequency domain. Therefore, all analytical results highly match the numerical results in both the time and frequency domains, confirming the accuracy and reliability of the identification results of this invention.

[0150] The vehicle acceleration spectrum is shown in Figure 8(a). Its acceleration amplitude peaks at 11.25 Hz, which is consistent with the analytical value. ω vEqual. However, the peak amplitude caused by the vehicle frequency is significantly higher than all other frequency components of the curved track-bridge system, including the fourth frequency component of the first mode. Conversely, as can be seen from the magnified view of the contact point acceleration spectrum in the 100Hz to 200Hz frequency band in Figure 8(b), there is a dense distribution of high-frequency components in this region. The analytical value of the fourth frequency component of the first mode, derived from Equation (7), is 119.24Hz. In order to ensure a 5% error range for the predicted track modulus, the frequency can vary between 116.22Hz and 122.18Hz. Specifically, the maximum value of the fourth frequency component of the first mode, which can be clearly identified in this range, is 121.88Hz, which is very close to the analytical value. The analysis shows that although the fourth frequency component of the first mode exists in the vehicle acceleration spectrum, it is obscured by the masking effect of the vehicle's own frequency and is difficult to identify directly.

[0151] Once the fourth frequency component of the first mode is determined in the acceleration spectrum at the contact point, the orbital modulus can be obtained using equation (16). In this invention, the extracted orbital modulus is 33.07 × 10⁻⁶. 6 N / m², compared to the assumed value of 33.33 × 10 6 The N / m² values ​​show a good agreement. This result confirms the feasibility of using contact point response for track modulus identification. This invention uses contact point response as the sole input for modulus extraction, which has the advantage of outstanding implementation efficiency and is suitable for the effective identification of curved track-bridge coupled systems.

[0152] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0153] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for identifying the support stiffness of a curved track-bridge coupled system based on vehicle scanning, characterized in that, include: Step 1: Establish a mechanical model of a curved double-beam system with a moving elastic mass; Step 2: Derive the control equations based on the mechanical model, including the vertical and torsional vibration control equations for curved rails and bridges, as well as the vibration equations for vehicles; Step 3: The displacements of the track and bridge are represented by the modal superposition method, and the vertical responses of the track and bridge are obtained by solving the Laplace transform. Step 4: Based on the vertical response of the track and bridge, obtain the vertical displacement and acceleration of the contact point, and obtain the vehicle displacement and acceleration, clarifying the relationship between the key parameters of the contact point response or vehicle response and the support stiffness; Step 5: Extract the frequency of the coupled system from the contact point response or vehicle response based on the correlation results, and identify the track modulus through the fourth frequency component of the first-order mode; In the mechanical model of the curved double beam system, the double beam is modeled as a warp-free Bernoulli-Euler beam, and based on linear deformation, the discrete fastener-sleeper system is equivalent to a uniformly distributed spring-damper unit. The expressions for the vertical and torsional vibration control equations of curved rails and bridges are as follows: In the formula, and These represent the vertical and torsional displacements of the rail and the bridge, respectively. The subscript 'r' represents the rail, and the subscript 'b' represents the bridge. R is the radius of curvature. Θ For the track support stiffness, E and G represent the elastic modulus and shear modulus, respectively; y express y The moment of inertia of the shaft, J represents the torsional moment of inertia, and ρ represents the mass per unit length of the track or bridge; The expression for the vehicle's vibration equation is: ； In the formula, Indicates vertical displacement. The natural frequency of the vehicle, , For the spring stiffness, and For the quality of the vehicle; The displacements of the track and bridge are represented using the modal superposition method, and the vertical responses of the track and bridge are obtained by solving the Laplace transform, including: The vertical and torsional displacements of the track and bridge are expressed using the modal superposition method as follows: ； ； ； ； In the formula, and These represent the vertical and torsional displacements of the rail and the bridge, respectively. The subscript 'r' represents the rail, and the subscript 'b' represents the bridge. and Vertical displacement and The generalized coordinates of the corresponding nth mode, and and These are respectively torsional displacements and The generalized coordinates of the nth mode. ; The vertical responses of the track and bridge are obtained by solving the Laplace transform, and the expressions are as follows: ； ； ； ； In the formula, and These represent the nth-order modal coordinates of the vertical and torsional responses of the track and bridge, respectively; s is a complex variable. , , , , , These represent the coupled and uncoupled frequencies of the track and bridge, respectively. For vehicle quality, It is the acceleration due to gravity. This refers to the vehicle's driving frequency.

2. The method for identifying the support stiffness of a curved track-bridge coupling system based on vehicle scanning as described in claim 1, characterized in that, The key parameters for the support stiffness include: track and bridge frequencies, and track stiffness.

3. The method for identifying the support stiffness of a curved track-bridge coupling system based on vehicle scanning as described in claim 1, characterized in that, The method of identifying the orbital modulus through the fourth frequency component of the first-order mode includes obtaining the orbital modulus by reversing the closed-loop solution.

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