A rail damage identification and location method

Abstract

The present invention discloses a method for identifying and locating rail damage, which comprises the following steps: establishing a rail wave characteristic equation to obtain a rail dispersion characteristic equation; establishing a two-dimensional high-order spectral element method model for the rail to obtain a rail guided wave dispersion curve; analyzing the rail detection frequency and specific modes and obtaining guided wave excitation signals and receiving signals for the rail in an undamaged state and a damaged state; obtaining the difference between the guided wave dispersion characteristic parameters for the undamaged state and the damaged state as the guided wave dispersion characteristic variation; constructing a nonlinear perturbation relationship between the variation of rail damage and the guided wave dispersion characteristic variation to determine whether the rail to be tested is damaged and the degree of damage; and if damaged, locating the damage using the excitation signal and receiving signal of the ultrasonic guided wave detection system. The present invention has the following beneficial effects: reducing the number of rail inspections and enabling simple and accurate detection of the damage condition and location of seamless line rails.

Description

Technical Field

[0001] The present invention relates to the technical field of nondestructive testing and monitoring, and in particular to a method for identifying and locating rail damage. Background Art

[0002] Seamless rails are a crucial component of high-speed rails. These rails, defined as those with no gaps between standard-length rails, ensure smoother and safer travel, while also reducing operating and maintenance costs. However, rail wear from trains, fatigue damage from dynamic loads, and erosion from environmental factors can easily lead to core damage, other damage, and even rail breakage, posing safety risks. Therefore, nondestructive testing methods that can accurately identify and locate rail damage in real time are urgently needed to ensure the safe operation of high-speed rails.

[0003] Traditional inspection and monitoring technologies include using hand-pushed rail flaw detection trolleys to inspect rails, using track circuits for rail safety monitoring, and manually inspecting rails during patrols. These methods often have drawbacks. For example, the circuit loop system on the rails is significantly affected by roadbed data. Furthermore, track circuits are generally not used in certain railway operating environments, such as tunnel sections with low rail-roadbed impedance or water accumulation. Manual inspection of long sections of rail lines using hand-pushed rail flaw detection trolleys is time-consuming, requires occupancy of operating railway lines, is subject to operational and environmental constraints, and can be affected by the proficiency and work enthusiasm of maintenance personnel. Ultrasonic guided wave inspection technology, with its advantages of sensitivity to damage, large detection range, long transmission distance, and fast detection speed, offers significant advantages for detecting and locating rail damage on seamless lines.

[0004] The existing ultrasonic guided wave rail damage detection technology requires multiple tests and confirmations during the actual detection process. The process is cumbersome and cannot accurately detect the degree and location of damage to any rail. There are certain errors, which is not conducive to promotion and application.

[0005] The present invention analyzes the wave guiding characteristics of rails by using a semi-analytical spectral element method, and proposes the relationship between the degree of rail damage and the change of wave guiding characteristics using nonlinear perturbation theory, and directly determines the wave guiding characteristic perturbation theory formula related to the degree of rail damage based on the change of the wave guiding characteristics; and provides a method for accurately locating rail damage; the present invention can accurately determine the degree of rail damage and accurately locate the damaged position of seamless rail lines, and is suitable for long-distance detection and real-time monitoring of the damage status of seamless rail lines, so as to solve the safety hazards caused by excessive damage to seamless lines for relevant departments and provide timely warnings. Summary of the Invention

[0006] In order to overcome the deficiencies in the prior art, the present invention aims to provide a rail damage identification and location method, which is based on the characteristics of ultrasonic guided waves and nonlinear perturbation theory, so as to effectively and accurately judge and detect the real-time rail damage degree and precise location of seamless line rails, and is suitable for long-distance detection and real-time monitoring of the damage status of seamless line rails.

[0007] In order to achieve the above object, the present invention adopts the following technical solution: a method for identifying and locating rail damage, comprising the following steps:

[0008] Step S1: Using the semi-analytical spectral element method of ultrasonic guided waves to establish the rail wave characteristic equation and the two-dimensional high-order spectral element method model, inputting rail-related parameters to obtain the rail guided wave dispersion characteristic equation and the wavenumber dispersion curve, phase velocity dispersion curve, and group velocity dispersion curve of the rail;

[0009] Step S2, using guided wave nonlinear perturbation theory to construct a perturbation equation for the change in rail damage and the change in rail dispersion characteristic parameters, and establish a relationship between the change in rail damage and the change in rail dispersion characteristic parameters at different damage levels;

[0010] Step S3, obtaining the rail detection frequency and rail specific mode according to the wave number dispersion curve, phase velocity dispersion curve and group velocity dispersion curve of the rail in step S1;

[0011] Step S4: Input the rail detection frequency obtained in step S3 into the ultrasonic guided wave detection system for detection, and obtain the guided wave excitation signal and received signal of the original rail state, i.e., the undamaged rail state, and the guided wave excitation signal and received signal of the rail to be tested under the specific rail mode;

[0012] Step S5, identifying the guided wave excitation signals and received signals of the undamaged rail and the rail to be tested in step S4, and determining whether there is a difference in guided wave dispersion characteristics between the undamaged rail and the rail to be tested; analyzing and determining whether the rail to be tested is damaged and the extent of the damage based on the relationship between the change in the amount of rail damage and the change in the guided wave dispersion characteristic parameter;

[0013] Step S6: After determining whether the rail to be tested is damaged and the extent of the damage in step S5, the position of the damage to the rail to be tested is accurately located using the ultrasonic guided wave detection system and the rail damage location method.

[0014] Furthermore, in step S1, the ultrasonic guided wave semi-analytical spectral element method is improved by introducing a spectral unit. In the process of calculating the total stiffness matrix and the total mass matrix, the shape function is used to express it as follows:

[0015] N(ζ,η)=h(ζ)h(η) (1);

[0016] Where: N(ζ,η) is the unit shape function, where ζ and η are the parameter variables of the basis function in two directions in the physical space, and h(ζ) and h(η) are the two basis functions in two directions in the physical space;

[0017] The W-order basis function based on the Gauss-Lobato-Legendre integral collocation point in the one-dimensional reference coordinate system is obtained by using Legendre polynomial interpolation as follows:

[0018]

[0019] Where: h j (ζ) is the W-order basis function of the collocation point j based on the Gauss-Lobato-Legendre integral, W is the node order of the spectral element method, P W (ζ j ) is node ζ j The value of the Nth-order Legendre orthogonal polynomial, P′ W (ζ) is the Nth order Legendre orthogonal polynomial P W The first derivative of (ζ), ζ j is the zero point of formula (5), i.e., the node in the spectral element method, j = 0, 1, 2, ... W;

[0020] (1-ζ 2 )P′ W (ζ)=0 (3);

[0021] Where: P′ W (ζ) is the Nth order Legendre orthogonal polynomial P W The first derivative of (ζ).

[0022] Furthermore, in step S2, the perturbation equation of the change in rail damage and the change in rail dispersion characteristic parameters is constructed using the guided wave nonlinear perturbation theory, and the perturbation of the eigenvalue Δξ and the perturbation of the eigenvector corresponding to the eigenvalue in the wave equation after rail damage are calculated. The relationship between the transformation of the m-th order mode wave number of ultrasonic guided waves in the rail and the rail damage is obtained:

[0023]

[0024] Where Δξ m 、 are the perturbations of the mth-order modal eigenvalue and its eigenvector caused by the change of stiffness, ξ m represents the wave number of the mth mode, are the mth-order modal eigenvalue and eigenvector after rail damage, i.e., the wave number and node displacement vector, respectively. K1, K2, and K3 are three different total stiffness matrices of the rail. ΔK1, ΔK2, and ΔK3 are the three structural stiffness changes caused by rail damage. is the mth-order modal eigenvector The transpose of

[0025] Where,

[0026] Where,

[0027] Where, To eliminate the total stiffness matrix of the imaginary term i, is the displacement vector of the mth-order guided wave mode at each node of the rail after being multiplied on the left by the auxiliary matrix H, i is an imaginary number, H T is the transpose of the auxiliary matrix H of the rail.

[0028] Furthermore, in step S2, the rail stiffness decreases after the rail is damaged, and the phase velocity and group velocity of the guided wave change. The relationship between the change in the phase velocity of the ultrasonic guided wave in the rail and the rail damage is derived and calculated:

[0029]

[0030] Where, C p and are the phase velocities before and after rail damage, respectively;

[0031] Similarly, the relationship between the change in the ultrasonic guided wave group velocity in the rail and the rail damage is obtained:

[0032]

[0033] Where, C g and are the group velocities before and after rail damage, respectively.

[0034] Furthermore, in step S3, the wave number dispersion curve, phase velocity dispersion curve and group velocity dispersion curve of the rail are analyzed to obtain that the optimal detection frequency of the rail is in the range of 20 to 40 kHz, and the specific modes corresponding to the rail at different frequencies are obtained.

[0035] Furthermore, in step S4, the ultrasonic guided wave detection system includes an excitation output channel and two receiving input channels, and the receiving signals of the original rail state, i.e., the undamaged state, and the rail to be tested are obtained under the specific mode of the rail as the receiving signals of the second receiving transducer.

[0036] Furthermore, the received signals of the original rail state, i.e., the undamaged state, and the rail to be tested in step S4 are identified, and the guided wave dispersion characteristics between the undamaged rail and the rail to be tested are obtained, including the group velocity of the rail and the group velocity of the rail to be tested. The group velocity of the original rail and the group velocity of the rail to be tested are detected by the ultrasonic guided wave detection system, specifically:

[0037]

[0038] Where: C g is the group velocity of the rail to be measured, L1 is the distance from the excitation transducer to the second receiving transducer, t s2 is the time when the second receiving transducer of the rail guided wave receives the signal, t off is the moment of obtaining the rail guided wave excitation signal;

[0039] The group velocity of the original rail detected by the ultrasonic guided wave detection system is recorded as C g0 ;

[0040] The rail group velocity variation ΔC of the tested rail and the undamaged rail is obtained through experimental analysis. g =C g -C g0 By establishing the relationship between the variation of rail damage at different damage levels and the variation of the rail dispersion characteristic parameter in step S2, it is possible to analyze and determine whether the rail to be tested is damaged and the degree of damage.

[0041] Furthermore, in step S6, after determining whether the rail to be tested is damaged and the extent of the damage in step S5, the ultrasonic guided wave detection system and the rail damage location method are used to accurately locate the location of the damage in the rail to be tested. The calculation formula for locating the damage in the rail is:

[0042]

[0043] Where: Ls is the distance from the excitation transducer to the damage, L0 is the distance from the excitation transducer to the first receiving transducer, t s is the time when the damage reflection wave packet signal of the first receiving transducer of the rail guided wave is obtained, t off is the moment when the rail guided wave excitation signal is obtained.

[0044] Furthermore, in step S1, a two-dimensional high-order spectral element method model of the rail is established using the semi-analytical spectral element method and the wave characteristic equation is listed, as shown in formula (9);

[0045]

[0046] Formula (9) is expressed as a first-order eigenvalue equation, as shown in formula (10);

[0047] (A-ξB)q=0 (10);

[0048] Where: A and B are two symmetric matrices of the first-order eigenvalue equation; q is the eigenvector set of the first-order eigenvalue equation, that is, the node displacement vector set; where:

[0049]

[0050] Where,

[0051] Where,

[0052] Where K1, K2 and K3 are three different total stiffness matrices of the rail, M is the total mass matrix of the rail, ξ is the wave number, ω is the angular frequency; U is the displacement vector of each node of the guided wave in the rail, H is the auxiliary matrix, To eliminate the total stiffness matrix of the imaginary term i, is the displacement vector of each node in the rail after the auxiliary matrix H is multiplied on the left, i is an imaginary number, H T is the transpose of the auxiliary matrix of the rail.

[0053] Furthermore, in step S1, the phase velocity and group velocity of the guided wave propagating in the rail are obtained according to the first-order eigenvalue equation of the rail, as shown in formula (11) and formula (12);

[0054]

[0055]

[0056] Where C p is the phase velocity of the rail, C g is the group velocity of the rail, are the left eigenvector and the right eigenvector of the rail respectively.

[0057] By solving the first-order eigenvalue equation of formula (10) to all eigenvalue solutions, namely the wave number ξ and the calculation formulas (11)-(12) of the phase velocity and group velocity of the rail, the wave number dispersion curve, phase velocity dispersion curve and group velocity dispersion curve of the rail at different frequencies are obtained.

[0058] Furthermore, in step S2, the perturbation equation of the change in rail damage and the change in rail dispersion characteristic parameters is constructed using the guided wave nonlinear perturbation theory, and the relationship between the change in damage at different damage levels and the change in rail dispersion characteristic parameters is established. The relationship between the structural parameters (such as stiffness and mass) and guided wave characteristic parameters (such as wave number, phase velocity and group velocity) of the structural dynamic system can be expressed by the characteristic equation of the system, see formulas (9)-(12). It can be seen from the wave equation of the rail that when the rail is damaged, its structural parameters (K, M) will change, thereby causing the guided wave characteristic related parameters (ξ m ,C p ,C g). Therefore, a precise relationship between the perturbation of rail structural parameters and the perturbation of guided wave characteristic parameters can be established to analyze the changes in the stiffness caused by different rail damage on the wave number, phase velocity and group velocity of guided wave modes. Specifically:

[0059] The structural stiffness changes caused by rail damage are ΔK1, ΔK2, and ΔK3. Therefore, the stiffness matrix after damage is expressed as:

[0060]

[0061] The wave equation of the damaged structure can be expressed as:

[0062]

[0063] Where, ξ * =ξ+Δξ,

[0064] Where, They are the three stiffness matrices after stiffness damage, Δξ, are the perturbations of the eigenvalues and their corresponding eigenvectors caused by the change in stiffness, ξ * 、 are the eigenvalue and eigenvector of the rail after damage, namely the wave number and node displacement vector.

[0065] Furthermore, the first-order eigenvalue problem of formula (10) can be rewritten as:

[0066] [(A+ΔA)-(ξ+Δξ)(B+ΔB)](q+Δq)=0 (15);

[0067] Where:

[0068] Where: ΔA and ΔB are the perturbations of the symmetric matrix of the first-order eigenvalue equation after rail damage; Δq is the perturbation of the eigenvector set of the first-order eigenvalue equation after rail damage, that is, the perturbation of the node displacement vector set;

[0069] For the mth mode after damage, ξ m represents the wave number of the mth mode, q m represents the m-th order modal eigenvector, represents the transpose of the m-th order modal eigenvector, represents the mth-order modal eigenvector after damage, Δq m represents the perturbation of the m-th order modal eigenvector, and formula (10) is multiplied on the left by the transposed vector of the damaged eigenvector Then by transposing the equation we can get:

[0070]

[0071] Because any multiple of the damaged eigenvector is also the damaged eigenvector, in order to ensure the uniqueness of the modal vibration shape of the structural system after damage, regularization is performed based on the damaged eigenvector, and its form is defined as:

[0072]

[0073] According to the basic equation of guided wave perturbation theory, the perturbation of the eigenvalue Δξ and the perturbation of the eigenvector corresponding to the eigenvalue in the wave equation after rail damage can be calculated. According to formula (17), the relationship between the change in the m-th order modal wave number of the ultrasonic guided wave in the rail and the rail damage can be obtained.

[0074] The beneficial effects of the present invention are as follows: (1) The present invention is easy to operate. The optimal excitation point, detection frequency and specific mode of the rail are obtained theoretically. In actual test measurement, only one excitation point and two receiving points need to be arranged. The nonlinear perturbation relationship between different degrees of damage to the rail and the variation of the dispersion characteristic is obtained theoretically. In addition, it can judge whether the rail is damaged and the degree of damage, and accurately locate the location of the damage to the rail. The measurement range is large and the measurement results are accurate. It is suitable for long-distance detection and real-time monitoring of the damage status of the rails of seamless lines. (2) The present invention reduces the number of detections, can simply and accurately judge whether the rail is damaged and the degree of damage, and accurately locate the location of the damage to the rails. It is suitable for long-distance detection and real-time monitoring of the damage status of the rails of seamless lines, and can solve the safety hazards caused by different degrees of damage to the seamless line and provide timely warnings. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a schematic flow diagram of the method of the present invention.

[0076] Figure 2 2. It is a two-dimensional high-order spectral element method model diagram of the rail in an embodiment of the present invention.

[0077] Figure 3 Schematic diagram of the wave number dispersion curve of the rail in an embodiment of the present invention.

[0078] Figure 4 Schematic diagram of the phase velocity dispersion curve of the rail in an embodiment of the present invention.

[0079] Figure 5 Schematic diagram of the rail group velocity dispersion curve in an embodiment of the present invention.

[0080] Figure 6 Schematic diagram of model parameters for rails with different damage degrees in an embodiment of the present invention.

[0081] Figure 7 Schematic diagram of the relationship between different damage degrees and group velocity changes in an embodiment of the present invention.

[0082] Figure 8 Schematic diagram of a seamless rail detection system in an embodiment of the present invention.

[0083] Figure 9 Schematic diagram of the excitation signal obtained by the rail specimen to be tested and the receiving signal of the receiving transducer 2 in an embodiment of the present invention.

[0084] Figure 10 Schematic diagram of the excitation signal, the receiving transducer 1 and the received signal reflected by the damage obtained by the rail specimen to be tested in an embodiment of the present invention. DETAILED DESCRIPTION

[0085] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0086] like Figure 1 The present invention is a flow chart of the method. In this embodiment, a rail damage identification and location method based on waveguide characteristics and nonlinear perturbation theory is provided. The existing semi-analytical finite element method is improved according to the geometric structure of long and thin rods such as rails. A spectral unit is introduced to form a two-dimensional semi-analytical spectral element method suitable for long and thin rod waveguide media. The dispersion characteristics of rail waveguides are combined with nonlinear perturbation theory. The nonlinear perturbation theory of waveguides is used to construct a perturbation equation for the change in rail damage and the change in the parameters of the rail waveguide dispersion characteristics. The relationship between the change in damage at different damage levels and the change in the parameters of the rail waveguide dispersion characteristics is established.

[0087] Furthermore, in step S1, the semi-analytical spectral element method is a semi-analytical method for solving the dispersion problem in the waveguide medium of a long and slender rod. When using the semi-analytical spectral element method to solve the dispersion solution, it is only necessary to perform finite element discretization on the cross section of the waveguide medium and perform analytical processing on the propagation direction of the waveguide medium using simple harmonic vibration modes. Taking the elastic isotropic CHN60 rail as an example, the cross section is defined as the yz plane, and the waveguide propagation direction along the longitudinal direction of the rail is defined as the x direction. The spatial distribution function u can be used to represent the displacement value of any point in the waveguide medium, and the expression is:

[0088]

[0089] Where: u (e)(x, y, z, t) is the displacement of the node of the rail section at any point in the Cartesian coordinate system, N(y, z) is the shape function of the unit, x is the coordinate value of the unit node on the rail section in the x-axis direction, y and z are the coordinate values of the unit node on the rail section in the y and z directions respectively, q (e) is the unit node displacement vector, ξ is the wave number, ω is the angular frequency, t is the time, and i represents the imaginary unit.

[0090] Furthermore, in step S1, the shape function of the spectral element method used in formula (18) and in the process of calculating the total stiffness matrix and the total mass matrix is expressed as follows:

[0091] N(ζ,η)=h(ζ)h(η) (1);

[0092] Where: N(ζ,η) is the unit shape function, where ζ and η are the parameter variables of the basis function in two directions in the physical space, and h(ζ) and h(η) are the two basis functions in two directions in the physical space;

[0093] The W-order basis function based on the Gauss-Lobato-Legendre integral collocation point in the one-dimensional reference coordinate system is obtained by using Legendre polynomial interpolation as follows:

[0094]

[0095] Where: h j (ζ) is the W-order basis function based on the Gauss-Lobato-Legendre integral collocation point j, ζ j (j=0, 1, 2, ... W) are the zeros of the following formula, i.e., the nodes in the spectral element method, and W is the node order of the spectral element method;

[0096] (1-ζ 2 )P′ W (ζ)=0 (3);

[0097] Where: P′ W (ζ) is the Nth order Legendre orthogonal polynomial P W The first derivative of (ζ).

[0098] Furthermore, in step S1, a two-dimensional high-order spectral element method model of the rail is established using the semi-analytical spectral element method and the wave characteristic equation is listed, as shown in formula (9);

[0099]

[0100] Formula (9) is expressed as a first-order eigenvalue equation, as shown in formula (10);

[0101] (A-ξB)q=0 (10);

[0102] Where: A and B are two symmetric matrices of the first-order eigenvalue equation; q is the eigenvector set of the first-order eigenvalue equation, that is, the node displacement vector set; where:

[0103]

[0104] Where,

[0105] Where,

[0106] Where K1, K2 and K3 are three different total stiffness matrices of the rail, M is the total mass matrix of the rail, ξ is the wave number, ω is the angular frequency; U is the displacement vector of each node of the guided wave in the rail, H is the auxiliary matrix, To eliminate the total stiffness matrix of the imaginary term i, is the displacement vector of each node in the rail after the auxiliary matrix H is multiplied on the left, i is an imaginary number, H T is the transpose of the auxiliary matrix H of the rail.

[0107] Furthermore, in step S1, the phase velocity and group velocity of the guided wave propagating in the rail are obtained according to the first-order eigenvalue equation of the rail, as shown in formula (11) and formula (12);

[0108]

[0109]

[0110] Where C p is the phase velocity of the rail, C g is the group velocity of the rail, are the left eigenvector and the right eigenvector of the rail respectively.

[0111] By solving the first-order eigenvalue equation of formula (10) to all eigenvalue solutions, namely the wave number ξ and the calculation formulas (11)-(12) of the phase velocity and group velocity of the rail, the wave number dispersion curve, phase velocity dispersion curve and group velocity dispersion curve of the rail at different frequencies are obtained.

[0112] Furthermore, in step S2, the perturbation equation of the change in rail damage and the change in rail dispersion characteristic parameters is constructed using the guided wave nonlinear perturbation theory, and the relationship between the change in damage at different damage levels and the change in rail dispersion characteristic parameters is established. The relationship between the structural parameters (such as stiffness and mass) and guided wave characteristic parameters (such as wave number, phase velocity and group velocity) of the structural dynamic system can be expressed by the characteristic equation of the system, see formulas (9)-(12). It can be seen from the wave equation of the rail that when the rail is damaged, its structural parameters (K, M) will change, thereby causing the guided wave characteristic related parameters (ξ m,C p ,C g ). Therefore, a precise relationship between the perturbation of rail structural parameters and the perturbation of guided wave characteristic parameters can be established to analyze the changes in the stiffness caused by different rail damage on the wave number, phase velocity and group velocity of guided wave modes. Specifically:

[0113] The structural stiffness changes caused by rail damage are ΔK1, ΔK2, and ΔK3. Therefore, the stiffness matrix after damage is expressed as:

[0114]

[0115] The wave equation of the damaged structure can be expressed as:

[0116]

[0117] Where, ξ * =ξ+Δξ,

[0118] Where, They are the three stiffness matrices after stiffness damage, Δξ, are the perturbations of the eigenvalues and their corresponding eigenvectors caused by the change in stiffness, ξ * 、 are the eigenvalue and eigenvector of the rail after damage, namely the wave number and node displacement vector.

[0119] Furthermore, the first-order eigenvalue problem of formula (10) can be rewritten as:

[0120] [(A+ΔA)-(ξ+Δξ)(B+ΔB)](q+Δq)=0 (15);

[0121] Where:

[0122] Where: ΔA and ΔB are the perturbations of the symmetric matrix of the first-order eigenvalue equation after rail damage; Δq is the perturbation of the eigenvector set of the first-order eigenvalue equation after rail damage, that is, the perturbation of the node displacement vector set;

[0123] For the mth mode after damage, ξ m represents the wave number of the mth mode, q m represents the m-th order modal eigenvector, represents the transpose of the m-th order modal eigenvector, represents the mth-order modal eigenvector after damage, Δq m represents the perturbation of the m-th order modal eigenvector, and formula (10) is multiplied on the left by the transposed vector of the damaged eigenvector Then by transposing the equation we can get:

[0124]

[0125] Because any multiple of the damaged eigenvector is also the damaged eigenvector, in order to ensure the uniqueness of the modal vibration shape of the structural system after damage, regularization is performed based on the damaged eigenvector, and its form is defined as:

[0126]

[0127] According to the basic equation of guided wave perturbation theory, the perturbation of the eigenvalue Δξ and the perturbation of the eigenvector corresponding to the eigenvalue in the wave equation after rail damage can be calculated. According to formula (17), the relationship between the transformation of the m-th order mode wave number of ultrasonic guided waves in the rail and the rail damage can be obtained:

[0128]

[0129] Where Δξ m 、 are the perturbations of the mth-order eigenvalue and its eigenvector caused by the change of stiffness, are the mth order eigenvalue and eigenvector after rail damage, namely the wave number and node displacement vector.

[0130] Furthermore, in step S2, after the rail is damaged, its material stiffness decreases, which also causes the guided wave phase velocity and group velocity to change. By derivation and calculation, the relationship between the change in the ultrasonic guided wave phase velocity in the rail and the rail damage can be obtained:

[0131]

[0132] Where, C p and are the phase velocities of the rail before and after damage, respectively.

[0133] Furthermore, in step S2, the relationship between the change in the ultrasonic guided wave group velocity in the rail and the rail damage can be obtained in the same way:

[0134]

[0135] Where, C g and are the group velocities before and after rail damage, respectively.

[0136] Furthermore, in step S2, a relationship model between different assumed degrees of rail damage and changes in waveguide characteristic parameters can be established, providing a theoretical basis for determining the degree of rail damage based on the changes in waveguide characteristic parameters measured later.

[0137] This example uses CHN60 rails as an example. The relationship between the change in ultrasonic and guided wave group velocity after rail damage is established. The extent of rail damage is determined based on the change in group velocity of the rail being tested. The ultrasonic guided wave detection system and positioning method are then used to accurately locate the rail damage. The rail has an elastic modulus of E = 210 GPa, a Poisson's ratio μ = 0.3, and a density of ρ = 7800 kg / m 3 , the rail cross section is discretized using the fourth-order spectral unit as follows Figure 2 As shown, the above rail parameters are substituted into equations (10)-(12) to obtain the wave number, phase velocity and group velocity dispersion curves of the rail, as shown in Figure 3-Figure 5 As shown in the figure. From the dispersion curve, it can be seen that each dispersion curve represents the same waveguide propagation mode. For the same waveguide mode, its propagation speed tends to be stable as the frequency increases, that is, the dispersion phenomenon weakens. And as the excitation frequency increases, the number of waveguide modes that can propagate in the rail at the same frequency gradually increases. When using waveguides to identify and locate steel damage, the best excitation frequency is in the range of 20 to 40 kHz. Taking the excitation frequency of 35 kHz as an example, Figure 3-Figure 5 It shows that there are 23 modes at this frequency. Figure 6 The figure is used as an example to illustrate. In order to compare the influence of damage degree on the dispersion characteristics of ultrasonic guided waves, fatigue damage models of the middle part of the rail waist were established. The size and parameters of the damage models are shown in Table 1.

[0138] Table 1 Model parameters for different damage levels

[0139]

[0140]

[0141] The presence of bolt holes in the rail waist can easily cause fatigue damage under the impact load of the train. After repeated load action, the rail may even break, seriously affecting the safety of train operation. Therefore, determining the extent of fatigue damage is of great significance to the operation and maintenance of the rail. The group velocity difference is used as an indicator to evaluate the sensitivity of the guided wave mode, and the sensitivity of each guided wave mode to different degrees of damage to the rail waist is studied. The group velocity difference of each guided wave mode at 35kHz is calculated by the group velocity variation perturbation equation. For most modes, the group velocity variation increases with the increase of the damage degree. Mode 17 is sensitive to rail waist damage and has the most regular identification. Table 2 lists the group velocity variation of mode 17 at different damage degrees and undamaged rails.

[0142] Table 2 Group velocity changes of models with different damage degrees and those without damage

[0143] serial number Elastic modulus reduction ratio Group velocity change (m / s) 1 0％ 0 2 10％ -80.79 3 30％ -304.35 4 50％ -628.54

[0144] In an embodiment, Figure 7 Figure 17 shows the relationship between different damage degrees and the change in group velocity of mode 17. It can be seen that the relationship between the change in group velocity of the guided wave mode and the damage degree is not linear, and its slope increases with the increase in the damage degree. Therefore, the sensitivity of the ultrasonic guided wave mode further increases with the aggravation of rail fatigue damage.

[0145] In an embodiment, Figure 8 As shown in the figure, in order to identify whether there is damage and the degree of damage in the actual operation of seamless rails, it is necessary to first detect the group velocity of the tested rail and the group velocity of the original rail through the ultrasonic guided wave detection system, and solve their difference to obtain the change in group velocity. Figure 8 The ultrasonic guided wave detection system shown in the figure includes an excitation output channel and two receiving input channels. The rail detection frequency obtained in step S3 is input into the ultrasonic guided wave detection system to perform experimental detection on the original rail (undamaged rail) and the rail to be tested, and the guided wave excitation signal of the original rail (undamaged rail) and the received signal of the second receiving transducer, and the guided wave excitation signal of the rail to be tested and the received signal of the second receiving transducer are respectively obtained.

[0146] Furthermore, in step S5, the received signals of the second receiving transducer of the original rail (undamaged rail) and the rail to be tested in step S4 are identified, and the group velocity of the original rail and the group velocity of the rail to be tested are detected by the ultrasonic guided wave detection system, specifically:

[0147]

[0148] Where: C g To measure the group velocity of the rail, L1 is the distance from the excitation transducer to the second receiving transducer, t s2 is the time when the second receiving transducer of the rail guided wave receives the signal, t off is the moment of obtaining the rail guided wave excitation signal;

[0149] The same method is used to detect the group velocity of the original rail, which is recorded as C g0 Through experimental analysis, the rail group velocity variation ΔC under the two states of the tested rail and the undamaged rail can be obtained. g =C g -C g0 , through the relationship between the variation of different rail damage and guided wave dispersion characteristic parameters established in step S2, such as Figure 7 As shown, analyze and judge whether the rail to be tested is damaged and the degree of damage.

[0150] Furthermore, after determining that the rail to be tested is damaged in step S5, the ultrasonic guided wave detection system and the rail damage location method are used to accurately locate the damaged position of the rail to be tested. The calculation formula for locating the damage in the rail is:

[0151]

[0152] Where: Ls is the distance from the excitation transducer to the damage, L0 is the distance from the excitation transducer to the first receiving transducer, t s is the time when the damage reflection wave packet signal of the first receiving transducer of the rail guided wave is obtained, t off is the moment when the rail guided wave excitation signal is obtained.

[0153] Although the above embodiments have described in detail the concepts and embodiments of the present invention, those skilled in the art will recognize that various improvements and modifications can be made to the present invention without departing from the scope of the claims, so they will not be described in detail here.

Claims

1. A rail damage identification and location method, characterized by: The following steps are involved: Step S1: Using the semi-analytical spectral element method of ultrasonic guided waves to establish the rail wave characteristic equation and the two-dimensional high-order spectral element method model, inputting rail-related parameters to obtain the rail guided wave dispersion characteristic equation and the wavenumber dispersion curve, phase velocity dispersion curve, and group velocity dispersion curve of the rail; Step S2, using guided wave nonlinear perturbation theory to construct a perturbation equation for the change in rail damage and the change in rail dispersion characteristic parameters, and establish a relationship between the change in rail damage and the change in rail dispersion characteristic parameters at different damage levels; Step S3, obtaining the rail detection frequency and rail specific mode according to the wave number dispersion curve, phase velocity dispersion curve and group velocity dispersion curve of the rail in step S1; Step S4: Input the rail detection frequency obtained in step S3 into the ultrasonic guided wave detection system for detection, and obtain the guided wave excitation signal and received signal of the original rail state, i.e., the undamaged rail state, and the guided wave excitation signal and received signal of the rail to be tested under the specific rail mode; Step S5, identifying the guided wave excitation signals and received signals of the undamaged rail and the rail to be tested in step S4, and determining whether there is a difference in guided wave dispersion characteristics between the undamaged rail and the rail to be tested; analyzing and determining whether the rail to be tested is damaged and the extent of the damage based on the relationship between the change in the amount of rail damage and the change in the guided wave dispersion characteristic parameter; Step S6: After determining whether the rail to be tested is damaged and the extent of the damage in step S5, the position of the damage on the rail to be tested is accurately located using an ultrasonic guided wave detection system and a rail damage location method; In step S1, the ultrasonic guided wave semi-analytical spectral element method is improved by introducing a spectral unit. In the process of calculating the total stiffness matrix and the total mass matrix, the shape function is used to express it as follows: （1）； Where: is the unit shape function, where are the parameter variables of the basis function in two directions in the physical space, 、 are two basis functions in two directions of physical space; The W-order basis function based on the Gauss-Lobato-Legendre integral collocation point in the one-dimensional reference coordinate system is obtained by using Legendre polynomial interpolation as follows: （2）； Where: Assign points to Gauss-Lobato-Legendre quadrature W-order basis function, W is the node order of the spectral element method, For nodes The value of the Nth order Legendre orthogonal polynomial, is the Nth-order Legendre orthogonal polynomial The first derivative of is the zero point of formula (5), that is, the node in the spectral element method, ; （3）； Where: is the Nth-order Legendre orthogonal polynomial The first derivative of .

2. The rail damage identification and location method according to claim 1, characterized in that: In step S2, the perturbation equation of the change in rail damage and the change in rail dispersion characteristic parameters is constructed using the guided wave nonlinear perturbation theory, and the perturbation of the eigenvalue in the wave equation after rail damage is calculated. And the perturbation of the eigenvalue corresponding to the eigenvector , get the ultrasonic guided wave in rail The relationship between the transformation of the modal wave number and rail damage: （4）； Where, They are the first The perturbation of the first-order mode eigenvalue and its eigenvector, Indicates the The wave number of the first mode, The first The modal eigenvalues and eigenvectors are the wave numbers and node displacement vectors, 、 and are three different total stiffness matrices of the rail, are the three structural stiffness changes caused by rail damage, For the The first-order mode eigenvector The transpose of Where, ; Where, ; Where, To eliminate imaginary terms The total stiffness matrix of is the left multiplication auxiliary matrix The next waveguide The displacement vector of the order mode at each node of the rail, is an imaginary number, is the auxiliary matrix of the rail The transpose of .

3. The rail damage identification and location method according to claim 2, characterized in that: In step S2, the rail stiffness decreases after the rail is damaged, and the phase velocity and group velocity of the guided wave change. The relationship between the change in the phase velocity of the ultrasonic guided wave in the rail and the rail damage is derived and calculated: （5）； Where, , and are the phase velocities before and after rail damage, respectively; Similarly, the relationship between the change in the ultrasonic guided wave group velocity in the rail and the rail damage is obtained: （6）； Where, , and are the group velocities before and after rail damage, respectively.

4. The rail damage identification and location method according to claim 1, characterized in that: In step S3, the wave number dispersion curve, phase velocity dispersion curve, and group velocity dispersion curve of the rail are analyzed to obtain the optimal detection frequency range of the rail to be 20-40 kHz, and the specific modes corresponding to the rail at different frequencies are obtained.

5. The rail damage identification and location method according to claim 1, characterized in that: In step S4, the ultrasonic guided wave detection system includes an excitation output channel and two receiving input channels, and the receiving signals of the original rail state, i.e., the undamaged state, and the rail to be tested are obtained in the specific rail mode as the receiving signals of the second receiving transducer.

6. The rail damage identification and location method according to claim 5, characterized in that: The received signals of the original rail state, i.e., the undamaged state, and the rail to be tested in step S4 are identified, and the guided wave dispersion characteristics between the undamaged rail and the rail to be tested are obtained, including the group velocity of the rail and the group velocity of the rail to be tested. The group velocity of the original rail and the group velocity of the rail to be tested are detected by the ultrasonic guided wave detection system, specifically: （7）； Where: is the group velocity of the rail to be measured, L1 is the distance from the excitation transducer to the second receiving transducer, The moment when the second receiving transducer of the rail guided wave receives the signal is obtained. is the moment of obtaining the rail guided wave excitation signal; The group velocity of the original rail detected by the ultrasonic guided wave detection system is recorded as ; The rail group velocity variation of the tested rail and the undamaged rail is obtained through experimental analysis. By establishing the relationship between the variation of rail damage at different damage levels and the variation of the rail dispersion characteristic parameter in step S2, it is possible to analyze and determine whether the rail to be tested is damaged and the degree of damage.

7. The rail damage identification and location method according to claim 1, characterized in that: In step S6, after determining whether the rail to be tested is damaged and the extent of the damage in step S5, the ultrasonic guided wave detection system and the rail damage location method are used to accurately locate the location of the damage in the rail to be tested. The calculation formula for locating the damage in the rail is: （8）； Where: Ls is the distance from the excitation transducer to the damage, L0 is the distance from the excitation transducer to the first receiving transducer, is the moment when the damage reflection wave packet signal of the first receiving transducer of the rail guided wave is obtained, is the moment when the rail guided wave excitation signal is obtained.

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