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

Abstract

The invention discloses a curve track-bridge coupling system support stiffness identification method based on a vehicle scanning method, which belongs to the field of engineering structure monitoring, and comprises the following steps: establishing a curve double-beam system mechanical model with moving elastic mass, deducing a control equation, and solving by adopting a modal superposition method and Laplacian transformation to obtain the support stiffness of a curve track-bridge coupling system. Coupled system frequencies are extracted from contact points or vehicle responses, in particular track moduli are efficiently identified using fourth frequency components of first order modalities. The method has the advantages of being high in operation maneuverability, high in cost-benefit ratio and outstanding in implementation efficiency, and is suitable for health monitoring of the curve track-bridge coupling system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of engineering structure monitoring, and more particularly to a support stiffness identification method for a curved track-bridge coupling system based on a vehicle scanning method. BACKGROUND

[0002] Currently, dynamic detection methods are mainly divided into two categories: direct measurement method and indirect measurement method. The direct measurement method evaluates the structural dynamic characteristics by analyzing the vibration data obtained from the sensors permanently installed on the structure, but this method has some defects: including high installation cost, excessive data volume, and sensor life far lower than the structure life, etc., and is mainly applied to long-span bridges, with limited application in medium and short-span bridges.

[0003] The traditional static load test method needs to interrupt the operation and cannot simulate dynamic effects; the dynamic test method based on the finite element model relies on a large number of accurate parameters and takes a long time to calculate; the method based on vibration sensors has high requirements for sensor arrangement and is easily disturbed by environmental noise.

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

[0005] Therefore, the present application provides a support stiffness identification method for a curved track-bridge coupling system based on a vehicle scanning method, which aims to solve the above problems and achieve uninterrupted operation, accurate dynamic simulation, reduced parameter dependence, strong anti-interference, and real-time and efficient identification.

[0006] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0007] A support stiffness identification method for a curved track-bridge coupling system based on a vehicle scanning method, comprising:

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

[0009] Step 2: deriving control equations according to the mechanical model, including vertical and torsional vibration control equations of the curved steel rail and the bridge, and vibration equations of the vehicle;

[0010] Step 3: using the modal superposition method to represent the displacement of the track and the bridge, and solving the vertical response of the track and the bridge through Laplace transform;

[0011] Step 4: obtaining the vertical displacement and acceleration of the contact point based on the vertical response of the track and the bridge, and obtaining the displacement and acceleration of the vehicle, and clearly defining the correlation between the key parameters of the contact point response or the vehicle response and the support stiffness;

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

[0013] Further, in the curved double-beam system mechanics model, the double-beam is modeled as a Bernoulli-Euler beam without warping, and the discrete fastener-sleeper system is equivalent to a uniformly distributed spring-damper unit based on linear deformation.

[0014] Further, the expressions of the vertical and torsional vibration control equations of the curved rail and the bridge are:

[0015]

[0016] where Z r ,Z b ,Φ r andΦ b represent the vertical displacement and torsional displacement of the rail and the bridge, respectively, subscript r represents the rail, subscript b represents the bridge, R is the radius of curvature, Θ is the track support stiffness, E and G represent the elastic modulus and shear modulus, respectively; I y represents the moment of inertia of the y-axis, J represents the torsional moment of inertia, and p represents the mass per unit length of the track or the bridge.

[0017] Further, the expression of the vibration equation of the vehicle is:

[0018]

[0019] where q v represents the vertical displacement, ω v is the natural frequency of the vehicle, k v is the spring stiffness, and M v is the mass of the vehicle.

[0020] Further, the displacements of the track and the bridge are expressed by the modal superposition method, and the vertical responses of the track and the bridge are obtained by solving through Laplace transform, including:

[0021] The vertical displacement and torsional displacement of the track and the bridge are expressed by the modal superposition method as:

[0022]

[0023] where Z r ,Z b ,Φ r andΦ b represent the vertical displacement and torsional displacement of the rail and the bridge, respectively, subscript r represents the rail, subscript b represents the bridge, q rn and q bn are the vertical displacements Z r and Zb the corresponding generalized coordinate of the nth modal of the bridge, respectively and Φn(t) and Φn(t) are the generalized coordinates of the nth modal of the torsional displacement Φ r and Φ b of the bridge, respectively, x represents space, and t represents time;

[0024] The vertical responses of the track and the bridge are obtained by solving by Laplace transform, and the expression is:

[0025]

[0026] In the formula, and respectively represent the nth modal coordinates of the vertical and torsional responses of the track and the bridge; s is a complex variable. respectively represent the coupled and uncoupled frequencies of the track and the bridge; M v is the mass of the vehicle, g is the acceleration of gravity, and Ω n is the driving frequency of the vehicle.

[0027] Further, the key parameters of the support stiffness include the track and bridge frequencies and the track stiffness.

[0028] Further, the track modulus is identified through the fourth frequency component of the first modal, including obtaining the track modulus by reverse closed solution.

[0029] According to the technical solution, compared with the prior art, the present application provides a curve track-bridge coupling system support stiffness identification method based on a vehicle scanning method. By establishing a curve double-beam system mechanical model with a moving elastic mass, the control equation is derived and solved by using the modal superposition method and Laplace transform. The coupling system frequency is extracted from the contact point or the vehicle response. In particular, the track modulus is efficiently identified by using the fourth frequency component of the first modal. The method has the advantages of strong operation flexibility, high cost-benefit ratio, and high implementation efficiency. It can realize uninterrupted operation, accurate dynamic simulation, reduced parameter dependence, strong anti-interference, and real-time and efficient identification, and is suitable for health monitoring of curve track-bridge coupling systems. BRIEF DESCRIPTION OF DRAWINGS

[0030] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without creative labor.

[0031] Figure 1Fig. 1 is a schematic diagram of a mechanical model of a curved double-beam system with moving elastic mass for a vehicle-track-bridge system;

[0032] Figure 2 Fig. 2 is a schematic diagram of a vehicle-track-bridge (VTB) unit structure;

[0033] Fig. 3(a) is a schematic diagram of track convergence under different modal numbers;

[0034] Fig. 3(b) is a schematic diagram of bridge convergence under different modal numbers;

[0035] Fig. 3(c) is a schematic diagram of vehicle convergence under different modal numbers;

[0036] Fig. 4(a) is a schematic diagram of vertical displacement response in a curved bridge span;

[0037] Fig. 4(b) is a schematic diagram of vertical acceleration response in a curved bridge span;

[0038] Fig. 5(a) is a schematic diagram of vertical displacement response in a curved track span;

[0039] Fig. 5(b) is a schematic diagram of vertical acceleration response in a curved track span;

[0040] Fig. 6(a) is a schematic diagram of vehicle vertical acceleration response;

[0041] Fig. 6(b) is a vehicle vertical acceleration spectrum diagram;

[0042] Fig. 7(a) is a schematic diagram of contact point vertical acceleration response;

[0043] Fig. 7(b) is a contact point vertical acceleration spectrum diagram;

[0044] Fig. 8(a) is a vehicle acceleration spectrum diagram;

[0045] Fig. 8(b) is a contact point acceleration spectrum diagram;

[0046] Figure 9 Fig. 9 is a schematic diagram of a method of the present application. DETAILED DESCRIPTION

[0047] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0048] Embodiment 1:

[0049] Reference is made to Figure 9This invention discloses a method for identifying the support stiffness of a curved track-bridge coupling system based on vehicle scanning, comprising:

[0050] Step 1: Establish a mechanical model of a curved double-beam system with a moving elastic mass;

[0051] 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;

[0052] 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.

[0053] 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;

[0054] 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.

[0055] Specifically, such as Figure 1 As shown, the rail-bridge system is simulated as a horizontal curved double-beam model, where the upper and lower beams represent the rail and bridge, respectively, both having a uniform length L and radius of curvature R. The 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 Θ and damping coefficient C. The detection vehicle, moving at a constant speed v on the rail, is characterized by stiffness k. v The concentrated mass M supported by the spring 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.

[0056] Specifically, to derive the closed-form solution, a right-handed coordinate system is established, where the x-axis is tangent to the centroidal axis of the beam, and the y-axis and z-axis correspond to the horizontal and vertical axes of the beam's cross-section, respectively. Furthermore, Z... r Z b ,Φ r and Φ b 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.

[0057] 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:

[0058]

[0059] The interaction load is expressed as,

[0060]

[0061] where subscript r denotes the rail, subscript b denotes the bridge, R is the radius of curvature; m denotes the mass per unit length of the track and bridge. E and G denote the elastic modulus and shear modulus, respectively; I y denotes the moment of inertia about the y-axis, J denotes the torsional moment of inertia, and p denotes the mass per unit length of the track and bridge; x c denotes the contact point coordinates, g denotes the gravitational acceleration, Θ denotes the track support stiffness, i.e., the foundation stiffness of the rail, and δ denotes the Dirac function.

[0062] Meanwhile, the equation of the vehicle can be expressed as

[0063]

[0064] where q v denotes the vertical displacement, ω v is the natural frequency of the vehicle, which can be calculated using k v is the spring stiffness, and M v is the mass of the vehicle.

[0065] For the simply supported boundary problem, the vertical and torsional displacements of the track and bridge can be expressed by the modal superposition method as:

[0066]

[0067] where q rn and q bn are the generalized coordinates of the nth mode of the vertical displacement Z r and Z b , respectively, and and are the generalized coordinates of the nth mode of the torsional displacement Φ r and Φ b , respectively.

[0068] Substituting equations (3a) to (3d) into equations (la) to (Id), multiplying both sides of the equations by sin(nxπ / L), and integrating with respect to x from 0 to L, the following modal motion equations for thin-walled beams can be obtained:

[0069]

[0070] For the speed parameter of the vehicle speed v,

[0071]

[0072] where the dot (·) denotes differentiation with respect to time t; parameters and are listed in Equations (Al) to (A8).

[0073] By letting and The homogeneous part of Equations (3a) to (3d) can be expressed as (i is the imaginary unit):

[0074]

[0075] In matrix form:

[0076]

[0077] For the eigenvalue problem in Equation (7) to have non-zero solutions, the determinant of the matrix should be equal to zero, i.e.,

[0078]

[0079] By considering as a whole, four real roots can be naturally obtained from Equation (8) which represents the natural frequency of the nth mode of the double-beam model. For convenience, some new parameters are defined here, i.e., and which are listed in Equations (A9) to (A10).

[0080] Considering the complexity of the coupled Equations (4a) to (4d), it is not practical to solve them directly in the time domain. Therefore, these equations are processed using the Laplace transform under the assumption of zero initial conditions. Thus, these equations can be effectively transformed from the time domain to the s domain, expressed as:

[0081]

[0082] where and represent the nth mode coordinate of the track and bridge vertical and torsional responses, respectively; s is a complex variable. From this, the relevant vertical responses of the track and bridge in the s domain can be obtained:

[0083]

[0084] Using the inverse Laplace transform, the solution in the s domain given by Equations (10a) and (10b) can be converted back to the time domain, resulting in the expression:

[0085]

[0086] where the relevant coefficients A n1 ,A n2 ,An3 A n4 A n5 B n1 B n2 B n3 B n4 and B n5 Listed in equations (A11) to (A20).

[0087] 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.

[0088] By setting x = vt, the vertical displacement of the contact point can be obtained from equation (11a), i.e., Z. c (t)=Z r (vt,t), and then taking the second derivative with respect to time t, we obtain the acceleration. for:

[0089]

[0090] Subsequently, the contact displacement Z c Substituting (t) into equation (2), the vehicle displacement q can be directly solved. v (t), represented as:

[0091]

[0092] Among them, the correlation coefficient D n1 ~D n11 Listed in equations (A21) to (A32).

[0093] Similarly, vehicle acceleration The result can be obtained by taking the second derivative of equation (12):

[0094]

[0095] From the observations of equations (12) and (14), it can be seen that the frequency corresponding to the double-beam system, i.e., ω n1 ,ω n2 ,ω n3 and ω n4 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.

[0096] In one specific embodiment, the orbital modulus extraction process is as follows:

[0097] Based on the derived closed-form solution, the track moduli exist in the coupled frequencies of the track-bridge system, i.e., ω n1 , ω n2 , ω n3 , and ω n4 , which means that once the coupled frequencies are determined, the track moduli can be naturally extracted. Based on this, the extraction procedure of the track moduli can be summarized as the following three steps: (1) calculate or measure the vehicle response or the response of the contact point when the vehicle passes through the curved track-bridge system; (2) extract the frequencies of the coupled system from the response; (3) identify the track moduli using the extracted frequencies.

[0098] For the extraction of the track moduli, only the first-order vibration mode is adopted here, and the inequality

[0099] still holds. Therefore, it can be known from the analysis that the frequency parameter equation in the equations (A9) and (A10) can be simplified as: Based on this, the equation (7) can be rewritten as:

[0100]

[0101] Obviously, the four roots appearing in the equation (15) can be expressed as: tend to zero, In addition, the track moduli can be efficiently identified by the fourth frequency component ω of the first-order mode of the track-bridge system, and the expression is:

[0102]

[0103] According to the equation (16), it is not difficult to see that once the fourth frequency component ω 14 of the first-order mode is determined in advance, the track moduli can be inversely solved. Generally, the frequency ω 14 is obviously located in the initial high-frequency domain, which is helpful for the identification of the track moduli. However, in practice, the frequency of the coupled system changes with time under the action of the moving vehicle. For this reason, the parameter ε is introduced to consider the change of the frequency. The equation (16) can be re-expressed as follows:

[0104]

[0105] where represents the predicted value of the track moduli. When μ falls within the range of 0.98-1.02, the ratio between the predicted value and the actual value of the track moduli is between 0.95 and 1.05, which meets the engineering requirements. Within this range, the track moduli can be obtained by the frequency peak value in the actual field test by using the proposed technology.

[0106] Theoretically, for a curved track-beam coupled system, the fourth frequency component ω of the first mode of the vehicle response can be used as a reference. 14 The orbital modulus Θ is obtained. In this section, the effects of these two responses on extracting the first-order frequency ω will be evaluated. 14 Performance differences in terms of orbital modulus Θ.

[0107] Vehicle frequency ω v 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 ω of the first-order mode. 14 A better choice of orbital modulus Θ.

[0108] Next, we will discuss the fourth frequency component ω of the first-order mode. 14 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:

[0109]

[0110] Accordingly, and The amplitude ratio is defined as:

[0111]

[0112] For the first-order vibration mode, at a moderate driving speed of the test vehicle, Ω1 is much smaller than ω. 14 -Ω1 or ω 14 +Ω1. Therefore, equation (19) can be further simplified to:

[0113]

[0114] Under normal circumstances, ω 14 The frequency value is much greater than ω v This means that the amplitude ratio can be simplified to:

[0115] λ>>1 (21)

[0116] 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.

[0117] In one specific embodiment, the method for obtaining the contact point response during field testing is as follows:

[0118] 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:

[0119]

[0120] in, Δt represents the sampling point, while Δt represents the sampling interval.

[0121] Specifically, the parameters involved in equations (18) to (22) are:

[0122]

[0123]

[0124]

[0125]

[0126] Example 2:

[0127] 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. This curve VTB cell consists of a length of L e The system consists of a curved track and a bridge unit with radius R, coupled together in a local coordinate system via distributed springs and dampers. As shown by the superscripts r and b, the track and bridge unit, in... Figure 2 The two endpoints, indicated by superscripts i and j, each have three degrees of freedom: one translational displacement z and two rotational displacements θ. x With θ y .

[0128] To obtain the displacement shape function of the curved beam element, the displacement coefficient matrix H of the vertical-torsional vibration is introduced here, and its expression is as follows:

[0129]

[0130] Among them, H q (q = 1, 2, 3) represents the coefficient matrix corresponding to the three degrees of freedom. The displacement shape function N is defined as:

[0131]

[0132] Where, N z , and N(x) = sin(nπx / L), n = 1, 2, 3,..., N (1) where N(x) represents the shape function of vertical deflection and corresponding torsional displacement about x and y axes, respectively. ζ ∈ [0, L] is the local axial coordinate of the beam. The integral expressions of element mass and stiffness matrices are established. Subsequently, they are incorporated into the total global mass and stiffness matrices. e ] for the beam. The integral expressions of element mass and stiffness matrices are established. Subsequently, they are incorporated into the total global mass and stiffness matrices.

[0133] In addition, the global damping matrix is established based on Rayleigh damping assumption. Following the energy principle, the global motion equation of the vehicle-track-bridge (VTB) interaction system considering track irregularity can be constructed as:

[0134]

[0135] where [M], [C] and [K] represent the mass, damping and stiffness matrices, respectively. Subscripts 'v', 'r' and 'b' represent the physical quantities corresponding to vehicle, track and bridge, respectively; 'vr' and 'rv' represent the coupling matrices between vehicle and track, while 'rb' and 'br' represent the coupling matrices between track and bridge. {q} represents the displacement vector, and {F(t)} is the load vector. The VTB interaction elements are assembled with other track-bridge elements without vehicle action to form the global VTB system. Subsequently, the Newmark-β method (β = 0.25, γ = 0.5) is employed to calculate the motion equation of the global VTB system step by step, with the time step set as 0.0001 s.

[0136] Specifically, the present embodiment 2 numerically verifies the closed-form solution proposed in embodiment 1. The parameters of the selected test vehicle, horizontal curve track and bridge are listed in Table 1. With these characteristics, the vehicle frequency f v is 11.25 Hz, and the travelling speed is 20 m / s. In the numerical analysis, the bridge is equally divided into 32 elements, each with a length of 1 m. To verify the reliability of the proposed solution, the track irregularity factor is not considered. It is worth noting that, for the sake of brevity, only the displacement and acceleration results at the mid-span position of the curve track and bridge are given.

[0137] Table 1. Characteristics of vehicle, track and bridge

[0138]

[0139]

[0140] Referring to Figures 3(a)-3(c) , the accuracy of the closed-form solution can be affected by the number of modes considered in the analysis. To investigate this effect, five different levels of mode number are evaluated in this section. In terms of convergence evaluation, Figures 3(a)-3(c)The vertical displacements of the vehicle, track and bridge mid-span are given for different number of modes. It is clear that the responses gradually converge as the number of modes included in the analysis increases. Specifically, the vertical displacement of the bridge has converged 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 fact that the frequencies of the track and vehicle are relatively higher than the frequencies of the bridge - the vehicle frequency f v is 11.25 Hz, while the first frequency f 11 of the first mode of the bridge is only 3.89 Hz. Therefore, 30 modes are used in the subsequent study.

[0141] Figures 4(a)-4(b) 、 Figures 5(a)-5(b) 、 Figures 6(a)-6(b) 、 Figures 7(a)-7(b) The results of the proposed method are compared with the numerical results of the finite element method (FEM) in the case study, involving the test vehicle, contact point, curved track and curved bridge. It is noted that the accelerations of the vehicle and contact point in the frequency domain are calculated from the time history data and fast Fourier transform (FFT). It can be clearly seen that the analytical results agree well with the FEM results, with only minor differences in the accelerations, which are acceptable for the frequencies of the system under study extracted in the frequency domain. Therefore, all the analytical results in the time and frequency domains match well with the numerical results, confirming the accuracy and reliability of the identification results.

[0142] The vehicle acceleration spectrum is shown in Fig. 8(a), which reaches a peak value at the frequency of 11.25 Hz, which is equal to the analytical value ω v . However, the amplitude peak 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. In contrast, it can be seen from the local magnification of the contact point acceleration spectrum in the frequency band of 100 Hz to 200 Hz in Fig. 8(b) that 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 119.24 Hz. To ensure a 5% error range for the predicted track modulus, the frequency can vary between 116.22 Hz and 122.18 Hz. Specifically, the maximum value of the fourth frequency component of the first mode within this interval can be clearly identified as 121.88 Hz, which is highly close to the analytical value. The analysis shows that although the fourth frequency component of the first mode is present in the vehicle acceleration spectrum, it is masked by the covering effect of the vehicle's own frequency and is difficult to identify directly.

[0143] Once the fourth frequency component of the first mode is determined in the contact point acceleration spectrum, the track modulus can be obtained by equation (16). In the present invention, the extracted track modulus is 33.07 x 106 N / m 2 , the assumed value 33.33 x 10 6 N / m 2 Good agreement. The results confirm the feasibility of track modulus identification using contact point responses. The present application uses contact point responses as the only input for modulus extraction, and has the advantage of high implementation efficiency. It is suitable for effective identification of curve track-bridge coupling systems.

[0144] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be mutually referred to. For the apparatus disclosed by the embodiments, since it corresponds to the method disclosed by the embodiments, the description is relatively simple, and the relevant parts can be referred to the method part.

[0145] The above description of disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to 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.

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, 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.

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 expressions for the vertical and torsional vibration control equations of curved rails and bridges are as follows: In the formula, Z r Z b ,Φ r and Φ b These represent the vertical and torsional displacements of the rail and bridge, respectively. The subscript *r* represents the rail, and the subscript *b* represents the bridge. *R* is the radius of curvature, *Θ* is the rail support stiffness, and *E* and *G* represent the elastic modulus and shear modulus, respectively. y ρ represents the moment of inertia along the y-axis, J represents the torsional moment of inertia, and ρ represents the mass per unit length of the track or bridge.

4. 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 expression for the vehicle's vibration equation is: In the formula, q v Represents vertical displacement, ω v The natural frequency of the vehicle, k v M is the spring stiffness. v For the quality of the vehicle.

5. The method for identifying the support stiffness of a curved track-bridge coupled system based on vehicle scanning as described in claim 1, characterized in that, 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, Z r Z b ,Φ r and Φ b 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. rn and q bn The vertical displacement Z is respectively r and Z b The generalized coordinates of the corresponding nth mode, and and These are the torsional displacements Φ r and Φ b The generalized coordinates of the nth mode, where x represents space and t represents time; 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; M v Let Ω be the mass of the vehicle, g be the acceleration due to gravity, and Ω be the acceleration due to gravity. n This refers to the vehicle's driving frequency.

6. 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.

7. The method for identifying the support stiffness of a curved track-bridge coupled 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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