Steel rail defect quantification method based on pulsed eddy current thermal imaging

Abstract

The invention relates to the technical field of nondestructive testing, in particular to a steel rail defect quantification method based on pulsed eddy current thermal imaging, which comprises the following steps: S1, applying an alternating magnetic field to a steel rail to be detected to generate eddy current inside the steel rail; s2, measuring temperature field data of the surface of the steel rail; and S3, solving a heat conduction inverse problem according to the temperature field data, and determining the crack distribution of the steel rail. According to the method, eddy current is generated through pulsed eddy current excitation, temperature field change is formed in a crack area, and quantification of crack parameters is realized by utilizing heat conduction inverse problem solution, so that the crack detection precision and the calculation efficiency are improved. The method is suitable for various detection conditions, is especially suitable for steel rail in-service detection, and solves the problems of insufficient detection precision and poor real-time performance in the prior art.

Description

Technical Field

[0001] The invention relates to the technical field of nondestructive testing, and in particular to a rail defect quantification method based on pulsed eddy current thermal imaging. Background Art

[0002] During the operation of the train, the rails are subjected to huge pressure and impact from the wheels, resulting in wavy wear and plastic deformation on their surfaces. These conditions often cause rolling contact fatigue (RCF) cracks in the rails, which can be more than 10 mm in horizontal length and gradually expand over time, eventually leading to crack spalling or even rail breakage. Therefore, timely prediction and quantitative analysis of these cracks are crucial to ensure the safe operation of the railway.

[0003] At present, commonly used rail crack detection methods include ultrasonic testing, magnetic particle testing and conventional eddy current testing. However, these technologies have their limitations: although ultrasonic testing is suitable for detecting internal defects, it has low sensitivity when identifying small surface cracks. Magnetic particle testing is mainly used for the detection of surface defects, but its ability to identify deep or fine cracks is limited. Conventional eddy current testing can detect surface cracks in conductive materials, but it is difficult to accurately quantify the depth and angle of the cracks. These methods generally have the shortcomings of low detection accuracy, poor real-time performance and the inability to quantify cracks. With the continuous development of rail materials and the increasing complexity of structures, existing detection methods face more severe challenges.

[0004] Pulsed eddy current thermography (ECPT) is a nondestructive testing method that combines electromagnetic induction with infrared thermal imaging technology. It excites eddy currents through an alternating magnetic field, causing the Joule heat generated in the material to form temperature changes on the surface, reflecting the location and characteristics of the defect. However, due to the pathological nature of the inverse problem of thermal conductivity, the current pulsed eddy current thermography is mostly limited to two-dimensional analysis in crack quantitative reconstruction, or can only achieve reconstruction of a single parameter. Existing quantitative methods are mainly divided into two categories: black box method and model method. Black box methods rely on machine learning or deep learning models (such as neural networks, support vector machines, etc.) to predict crack parameters. Although these methods can quickly provide estimation results after establishing a sufficient sample database, their disadvantages are that they require a large amount of training data and the parameters of the model lack physical interpretation. Once the inspection conditions change, the model may fail and must be retrained. The model rule solves the positive problem through optimization algorithms (such as Newton's method, conjugate gradient method, genetic algorithm). Although the model method has a strong physical interpretation, each iteration requires solving complex computational problems, resulting in a long calculation time.

[0005] Patent CN201910019827 introduces a method for infrared thermal image defect feature recognition based on dynamic multi-objective optimization. Defect features are extracted through multi-objective optimization and pulse coupled neural network. Although the detection accuracy is improved, it relies on a large amount of thermal image data training and requires a complex multi-objective optimization process in a dynamic environment, with high computational costs.

[0006] "Liang Yuanyuan, Yang Shengsheng, Wen Xuan, et al. Research on defect quantification technology in pulsed eddy current nondestructive testing [J]. Chinese Journal of Scientific Instrumentation, 2018, 39(11):9" proposed a pulsed eddy current detection method based on tunnel magnetoresistance sensor, using BP neural network algorithm to quantitatively evaluate the defect depth. However, this method requires training networks for defects of different shapes, has poor generalization, and needs to retrain the model when the detection conditions change, resulting in high application costs. Summary of the invention

[0007] The present invention aims to overcome the shortcomings of the prior art, such as low detection accuracy, slow calculation speed, poor system adaptability and stability, and provides a rail defect quantification method based on pulsed eddy current thermal imaging, which specifically includes: improving the detection accuracy by realizing multi-parameter precise quantification of crack depth and angle; simplifying the solution process by an equivalent acceleration method, significantly reducing the calculation time; using an algorithm with good generalization ability, it is suitable for different detection conditions without the need to retrain the model, thereby improving the adaptability of the system; and improving the detection stability in a dynamic environment by combining an optimization algorithm with multi-parameter analysis.

[0008] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions: A rail defect quantification method based on pulsed eddy current thermal imaging comprises the following steps: S1. Apply an alternating magnetic field to the rail to be tested to generate eddy currents inside it; S2. Measuring the temperature field data of the rail surface; S3. Solving the inverse heat conduction problem according to the temperature field data to determine the crack distribution of the rail.

[0009] Preferably, the alternating magnetic field is a high-frequency pulse alternating magnetic field, and its frequency range is 10kHz to 1MHz; the alternating magnetic field is generated by an excitation coil; and the temperature field distribution data is measured by an infrared thermal imager. This preferred solution provides the frequency range of the alternating magnetic field and the type of excitation source, excites eddy currents by a high-frequency pulse alternating magnetic field (10kHz to 1MHz), and measures the temperature field by an infrared thermal imager. This frequency range and infrared measurement method can ensure the acquisition of high-resolution temperature data, improve the accuracy of crack detection and imaging quality, and are particularly sensitive to shallow cracks.

[0010] Preferably, an equivalent acceleration method is used to simplify the electromagnetic field and heat conduction problems into an equivalent mathematical model, wherein the equivalent mathematical model is based on the skin effect and describes the exponential decay distribution of eddy current density and the approximate distribution of Joule heat. The electromagnetic field and heat conduction problems are simplified by using the equivalent acceleration method, so that the complex physical problems are converted into an equivalent mathematical model that is easy to solve. The equivalent model is based on the skin effect and describes the exponential decay of eddy current density and the Joule heat distribution, which significantly reduces the calculation complexity and time, improves the real-time performance, and enables the detection results to be output in a short time.

[0011] Preferably, the equivalent mathematical model formula is as follows: in, represents the internal Joule thermal power density, z represents the depth, Used to control the attenuation of the heat source in the depth z direction. Inversely proportional to the depth z and directly proportional to the skin depth, represents the temperature increment distribution on the upper surface, is the surface temperature of the test block at 0ms, K represents the local curvature of the grid discrete points, and K(S) is the discrete curvature of the test block surface S. This preferred solution further clarifies the formula of the equivalent mathematical model, refines the expression of the internal Joule heat power density, controls the heat source attenuation through the exponential attenuation in the depth direction, and can better reflect the impact of cracks on eddy current distribution and temperature field at different depths, thereby improving the quantification accuracy of crack parameters.

[0012] Preferably, the process of solving the inverse problem of heat conduction uses an optimization algorithm to iteratively solve crack parameters, and the crack parameters include crack depth and angle. By iteratively solving parameters such as crack depth and angle through the optimization algorithm, the accuracy of crack quantification is improved. The iterative solution method ensures that the optimization results of crack parameters are close to the true value, reduces calculation errors, and improves the adaptability of crack detection at different depths and angles.

[0013] Preferably, the optimization algorithm adopts a genetic algorithm, comprising the following steps: S61. Initializing the initial population of crack parameters; S62. Calculating the error between the estimated value and the actual value of the crack parameter; S63. Iteratively update the crack parameters based on the error until a preset accuracy is reached.

[0014] Using genetic algorithms as an optimization method can globally search for the optimal solution, avoid falling into local optimality, and improve the accuracy and stability of crack parameter solution. At the same time, multiple iterations of genetic algorithms can automatically adapt to different crack characteristics, improve the generalization ability of the algorithm, and are suitable for quantitative solution of complex cracks.

[0015] Preferably, step S62 includes constructing an objective function; the objective function is based on the spatial distribution characteristics of the temperature field data at a specific time point and is used to optimize the quantitative solution of the crack parameters, and the formula is: in, represents the objective function, represents the characteristic line, i Represents feature lines A specific point on Indicates twice the heating time; Indicates that point i passes The actual temperature distribution after Indicates that point i passes After the simulation temperature distribution. i By summing up the differences, the overall difference on the entire characteristic line can be obtained. In the iterative step of the genetic algorithm, by constructing an objective function based on the spatial distribution of the temperature field, the optimization result is ensured to be more consistent with the actual crack characteristics. The introduction of the objective function provides a metric for the crack parameters, prompting the iterative update to converge to the accurate crack parameters, thereby improving the reliability and accuracy of the crack depth and angle quantification.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a rail defect quantification method based on pulsed eddy current thermal imaging, which includes applying an alternating magnetic field to the rail, measuring temperature field data, and solving the inverse problem of thermal conductivity to determine the crack distribution. Eddy currents are generated by pulsed eddy current excitation, temperature field changes are formed in the crack area, and the inverse problem of thermal conductivity is used to solve the quantification of crack parameters, thereby improving the accuracy and calculation efficiency of crack detection. Specifically, by applying a high-frequency alternating magnetic field to the rail to excite internal eddy currents, Joule heat inside the material can be generated, causing the temperature of the defect area to rise. This step makes the defect area such as cracks appear as an abnormal temperature area in thermal imaging, which helps to quickly identify the defect location. By measuring the surface temperature field data and solving the spatial distribution and characteristics (such as depth and shape) of the crack using the inverse problem of thermal conductivity, accurate quantification of defects can be achieved. This method provides more accurate defect information than traditional detection methods, especially in terms of parameters such as crack depth and angle, and can achieve high-resolution quantitative detection. The method of the present invention does not require cutting or destructive treatment of the rails, and realizes non-contact non-destructive testing through eddy current thermal imaging, thereby reducing physical damage to the rails and is suitable for real-time testing of in-service rails. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a flow chart of a rail defect quantification method based on pulsed eddy current thermal imaging according to Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of an induction thermal imaging nondestructive testing system according to Embodiment 2 of the present invention; Figure 3 This is a flow chart of an algorithm for solving the crack reconstruction problem according to Embodiment 2 of the present invention; Figure 4 Schematic diagram of an L-shaped hidden crack in Example 3 of the present invention; Markings in the figure: 1-L-shaped hidden crack; 2-crack surface S1; 3-external boundary surface S; 4-crack internal surface S2; 5-vertical section; Figure 5 This is a simulated temperature distribution diagram of Example 3 of the present invention; Markings in the figure: (a) 200ms simulation temperature distribution, (b) 400ms simulation temperature distribution; Figure 6 It is the temperature distribution diagram of line lc of Example 3 of the present invention; Markings in the figure: (a) temperature distribution of line lc at 200ms, (b) temperature distribution of line lc at 400ms; Figure 7 Schematic diagram of eddy current distribution characteristics of Example 3 of the present invention; Markings in the figure: (a) schematic diagram of vortex distribution on the inner surface, (b) schematic diagram of vortex distribution on the upper surface; Figure 8 A comparative analysis diagram of the solution results of the direct method and the simplified method of Example 3 of the present invention; Fig. 9 Schematic diagram of an L-shaped hidden crack of a rail test block according to Example 3 of the present invention; Fig.10 This is a schematic diagram of thermal imaging of an L-shaped hidden crack in Example 3 of the present invention; Fig.11 This is a scatter point distribution diagram of crack reconstruction in Example 3 of the present invention; Fig.12 A distribution diagram of the number of angle reconstruction solutions of Example 3 of the present invention; Fig.13 This is a quantitative distribution diagram of the deep reconstruction solutions of Example 3 of the present invention. DETAILED DESCRIPTION

[0018] The following is a further detailed description of a rail defect quantification method based on pulsed eddy current thermal imaging provided by the present invention in conjunction with the accompanying drawings and specific embodiments. However, this should not be understood as the scope of the above-mentioned subject matter of the present invention being limited to the following embodiments, and all technologies implemented based on the content of the present invention belong to the scope of the present invention. Combined with the following description, the advantages and features of the present invention will become clearer. It should be noted that the drawings are all in a very simplified form and use non-precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention.

[0019] Example 1 This embodiment provides a rail defect quantification method based on pulsed eddy current thermal imaging, the method steps are as follows: Figure 1 As shown, the following steps are included: S1. Apply an alternating magnetic field to the rail to be tested to generate eddy currents inside it; S2. Measuring the temperature field data of the rail surface; S3. Solving the inverse heat conduction problem according to the temperature field data to determine the crack distribution of the rail.

[0020] Preferably, the alternating magnetic field is a high-frequency pulse alternating magnetic field, and its frequency range is 10kHz to 1MHz; the alternating magnetic field is generated by an excitation coil; and the temperature field distribution data is measured by an infrared thermal imager. This preferred solution provides the frequency range of the alternating magnetic field and the type of excitation source, excites eddy currents by a high-frequency pulse alternating magnetic field (10kHz to 1MHz), and measures the temperature field by an infrared thermal imager. This frequency range and infrared measurement method can ensure the acquisition of high-resolution temperature data, improve the accuracy of crack detection and imaging quality, and are particularly sensitive to shallow cracks.

[0021] Preferably, an equivalent acceleration method is used to simplify the electromagnetic field and heat conduction problems into an equivalent mathematical model, wherein the equivalent mathematical model is based on the skin effect and describes the exponential decay distribution of eddy current density and the approximate distribution of Joule heat. The electromagnetic field and heat conduction problems are simplified by using the equivalent acceleration method, so that the complex physical problems are converted into an equivalent mathematical model that is easy to solve. The equivalent model is based on the skin effect and describes the exponential decay of eddy current density and the Joule heat distribution, which significantly reduces the calculation complexity and time, improves the real-time performance, and enables the detection results to be output in a short time.

[0022] Preferably, the equivalent mathematical model formula is as follows: in, represents the internal Joule thermal power density, z represents the depth, Used to control the attenuation of the heat source in the depth z direction. Inversely proportional to the depth z and directly proportional to the skin depth, represents the temperature increment distribution on the upper surface, is the surface temperature of the test block at 0ms, K represents the local curvature of the grid discrete points, and K(S) is the discrete curvature of the test block surface S. This preferred solution further clarifies the formula of the equivalent mathematical model, refines the expression of the internal Joule heat power density, controls the heat source attenuation through the exponential attenuation in the depth direction, and can better reflect the impact of cracks on eddy current distribution and temperature field at different depths, thereby improving the quantification accuracy of crack parameters.

[0023] Preferably, the process of solving the inverse problem of heat conduction uses an optimization algorithm to iteratively solve crack parameters, and the crack parameters include crack depth and angle. By iteratively solving parameters such as crack depth and angle through the optimization algorithm, the accuracy of crack quantification is improved. The iterative solution method ensures that the optimization results of crack parameters are close to the true value, reduces calculation errors, and improves the adaptability of crack detection at different depths and angles.

[0024] Preferably, the optimization algorithm adopts a genetic algorithm, comprising the following steps: S61. Initializing the initial population of crack parameters; S62. Calculating the error between the estimated value and the actual value of the crack parameter; S63. Iteratively update the crack parameters based on the error until a preset accuracy is reached.

[0025] Using genetic algorithms as an optimization method can globally search for the optimal solution, avoid falling into local optimality, and improve the accuracy and stability of crack parameter solution. At the same time, multiple iterations of genetic algorithms can automatically adapt to different crack characteristics, improve the generalization ability of the algorithm, and are suitable for quantitative solution of complex cracks.

[0026] Preferably, step S62 includes constructing an objective function; the objective function is based on the spatial distribution characteristics of the temperature field data at a specific time point and is used to optimize the quantitative solution of the crack parameters, and the formula is: in, represents the objective function, represents the characteristic line, i Represents feature lines A specific point on Indicates twice the heating time; Indicates that point i passes The actual temperature distribution after Indicates that point i passes After the simulation temperature distribution. i By summing up the differences, the overall difference on the entire characteristic line can be obtained. In the iterative step of the genetic algorithm, by constructing an objective function based on the spatial distribution of the temperature field, the optimization result is ensured to be more consistent with the actual crack characteristics. The introduction of the objective function provides a metric for the crack parameters, prompting the iterative update to converge to the accurate crack parameters, thereby improving the reliability and accuracy of the crack depth and angle quantification.

[0027] Example 2 This embodiment 2, as a preferred embodiment of embodiment 1, provides a specific implementation of a rail defect quantification method based on pulsed eddy current thermal imaging.

[0028] S1. Generation of eddy current excitation The excitation source signal is used to generate a high-frequency pulse alternating magnetic field through the excitation coil. The alternating magnetic field enters the rail material and excites eddy currents. The eddy currents are disturbed in the defect area, causing the current density to change, which in turn causes the Joule heat distribution inside the material to change. These changes will form a temperature field distribution on the surface of the material.

[0029] S2. Acquisition and quantification of temperature field data Pulsed eddy current thermography has the advantages of high precision and high efficiency. First, by loading the excitation coil with a high-frequency pulse drive current, an eddy current field is generated in the test piece. When there is a crack in the test piece, the eddy current field near the crack is disturbed, so that the corresponding temperature field is disturbed and changes. As the heat diffusion process, the degree of influence of the crack on the temperature field is different. The geometric information of the crack can be obtained by analyzing the heat distribution and its changing characteristics of the heat dissipation process. To this end, it is necessary to establish a simulation model and experiment of the temperature response process, analyze the physical process of the actual heat diffusion process and the specific influence of different cracks on the temperature distribution, and further analyze the algorithm strategy of crack reconstruction.

[0030] like Figure 2 As shown in the figure, the excitation source signal generates an alternating magnetic field through the excitation coil, propagates into the test piece, and excites the eddy current electric field. The defect in the test block disturbs the eddy current, and its current density changes, which causes the Joule heat change caused by the current density, resulting in a distribution change in the temperature field around the defect. The infrared thermal imager is used to collect the temperature field change data on the surface of the rail in real time. When the heating device is working, the thermal imager records the response characteristics of the temperature change over time. The temperature data is input into the computer for further processing to quantify the depth and angle of the crack.

[0031] When the induction heating device starts working, the coil connected to the heating device generates a high-frequency pulse signal. According to Faraday's law of electromagnetic induction, if the coil is close to the conductor, there will be induced eddy currents on the surface of the conductor, and its spatial manifestation is as follows: (1) Where I is the surface induced eddy current, the unit is ; is the surface induced eddy current density, in units of ; is the source current density, which represents the externally applied current density; is the conductivity, in units of , is the magnetic permeability of the material being tested, is the circuit potential, is the loop radius, Is the dielectric constant of the material being measured. Symbol Represents a vector differential operator, which is used to describe gradient, divergence, and curl operations in space. In electromagnetic field theory, It has the following important uses: gradient( f): For a scalar field f, f represents the rate of change in each direction.

[0032] Divergence ( ): For a vector field I, I represents the source intensity of the vector field.

[0033] Curl ( ): For a vector field I, ×I represents the rotational property of the vector field and is used to describe the rotational properties of, for example, electric current or magnetic field.

[0034] According to Joule's law, the thermal power density generated by eddy current in the material being tested is for: (2) Where E is the induced electric field strength.

[0035] According to Fourier's law of heat conduction, for uniform and isotropic materials, ignoring surface radiation and convection, and assuming that the internal heat source is zero, the heat conduction equation of eddy current distribution can be expressed as: (3) in, , , They are the density, specific heat capacity and thermal conductivity of the material being tested; Indicates temperature, including surface temperature ; Express Take the first-order derivative in time; is the Joule thermal power density, which can be expressed as the thermal power density The product of time t, .

[0036] In the rail test block, due to the interaction between the AC magnetic field and the eddy current, the current density distribution is concentrated on the surface, and the eddy current density decreases exponentially with depth. The depth at which , can be used as an important parameter for crack detection, the formula is: (4) Crack quantification refers to the establishment of a mapping relationship and quantitative estimation between data and crack information after obtaining the temperature response data of the specimen, so as to achieve the purpose of estimating and detecting cracks. Quantifying cracks requires solving the inverse problem of heat conduction. After obtaining the difference between the estimated eigenvalue and the observed eigenvalue returned by the real-time forward problem solution, the optimization algorithm is repeatedly iterated until certain target conditions are met, achieving the purpose of approximating the true value of the parameter to be determined.

[0037] S3. Simplification of the solution to the direct problem The complex electromagnetic field and heat conduction problems are simplified by using the equivalent acceleration method. Specifically, the eddy current density distribution is approximated as exponential decay on the surface by using the skin effect, avoiding the direct solution of Maxwell's equations, thus significantly reducing the computational complexity. The calculated temperature field is used for subsequent crack quantification analysis.

[0038] S4. Algorithm implementation of crack parameter quantification process The algorithm implementation of the crack parameter quantification process is as follows Figure 3 As shown, the following steps are included: S401. Initialize crack parameters: Randomly set initial crack parameters , including the crack depth and angle ; S402. Network building: Based on initial crack parameters Establishing computational networks for numerical simulation; S403. Solve the direct problem: Use the established network to solve the numerical heat transfer direct problem and obtain the estimated value of the material surface temperature This step can use an equivalent acceleration method to simplify the solution process and improve computational efficiency; S404. Data collection through pulsed eddy current thermal imaging: Pulsed eddy current thermal imaging technology is used to obtain the true value of the surface temperature of the actual cracks in the rail material , which is used for comparison with the surface temperature estimate; S405. Constructing the objective function: Using surface temperature estimates The actual value of surface temperature Constructing the objective function , calculate the error between the two, whether the error is less than the preset error threshold , expressed as ; S406. Determine whether the accuracy requirement is met: compare the value of the objective function with the error threshold. If the error is less than or equal to , then the estimated value of the crack parameter is considered to be sufficiently accurate, and the crack parameter is output ; S407. Iteratively update crack parameters: If the error does not meet the accuracy requirement, the crack parameters are updated according to an optimization algorithm (such as a genetic algorithm) and the iterative solution continues.

[0039] Among many optimization algorithms with different properties, the genetic algorithm is a bionic algorithm in a macro sense. Its main steps are to initially form a population composed of a certain number of individuals (Population Size), select better individuals (Elite Count) according to certain indicators in each iteration, eliminate inferior individuals, and use genetic operators (including inheritance, crossover, mutation, etc.) to recombine these individuals to generate a new generation of population. Repeating iterations in this way allows the population to evolve to a higher fitness until a certain convergence indicator is met, such as stopping iteration when the objective function reaches the ideal value (Fitness Limit). Compared with other optimization algorithms, the genetic algorithm is a global optimization algorithm. This is because the mutation operation in the iterative process makes it possible for the updated solution to jump out of the local optimum. Therefore, as long as a reasonable optimization objective equation and population size are set, the genetic algorithm solution has good robustness.

[0040] Example 3 Based on the above embodiments, this embodiment provides a specific implementation of a rail defect quantification method based on pulsed eddy current thermal imaging.

[0041] The size of the rail test block used in this embodiment is 80mm*40mm*20mm, and the test material is #45 steel. The specific parameters are shown in Table 1: Then, COMSOL was used to simulate the L-shaped hidden crack of the test block. Figure 4 As shown in the figure, the L-shaped hidden crack is divided into a plane crack and an oblique crack, wherein the oblique crack is located on the crack surface S1 and the plane crack is located on the inner surface S2 of the crack. The angle between the crack surface S1 and the test block surface S of the test block is , the angle between the crack surface S1 and the crack internal surface S2 is , the internal surface S2 of the crack is parallel to the surface S of the specimen, and The depth distance between the internal surface S2 of the crack and the surface S of the test block is d.

[0042] The excitation coil is a straight wire, the lift-off height is 3mm, and the central characteristic line of the test block surface parallel to the straight wire is recorded as lc. The crack runs through the test block in the thickness direction of the test block, and its surface opening width is 1mm. The angles with the test block surface are set to 10°, 15°, and 20°, respectively. The corresponding depths are set to 1.47mm, 2.25mm, and 3.00mm, respectively. The frequency of the excitation current is 190KHz, the intensity is 350A, the excitation pulse width is a Gaussian pulse of 200ms, the initial temperature is 293K, and the recording time is 1000ms. The surface temperature distribution of the 20-degree crack can be obtained as follows Figure 5 As shown, the temperature distribution of the three crack lines lc is as follows Figure 6 shown.

[0043] As attached Figure 5 As shown in (a), after the heat source generates an excitation signal, the heat will diffuse downward from the surface to the crack. Due to the existence of the crack, the downward diffusion of heat is blocked. A high amount of heat is accumulated at the crack tip within 200ms, and the temperature distribution shows a uniform decrease as the distance from the crack tip increases. Figure 5 In (b), after a certain diffusion, the heat of 400ms has diffused downward to the plane crack, so in the area corresponding to the plane crack The surface temperature of the Figure 6 (a) and the attached Figure 6 As can be seen in (b), different crack sizes have different effects on eddy currents, and thus different temperatures transmitted back to the surface. Characteristics such as the time it takes for heat to be transmitted back to the surface under oblique cracks and planar cracks will also change due to the crack size.

[0044] Since the magnetic permeability of the rail material is very large, the skin depth is very shallow. The skin depth of the rail test block used in this embodiment is 0.06 mm. In this case, the eddy current distribution generated by the excitation source Can be decomposed into two parts, such as Figure 7 As shown, when the eddy current density is In case of: Figure 7 (a) is a schematic diagram of the vortex distribution on the inner surface. This part only has a turning point with the test block, and the sharper the turning point, the higher the vortex temperature. Figure 7 (b) is a schematic diagram of the eddy current distribution on the upper surface. The other part of the eddy current generated by the excitation source exists on the upper surface of the specimen and decays exponentially with increasing depth.

[0045] Using this temperature distribution characteristic, equation (3) can be rewritten into an equivalent mathematical model as follows: (5) In formula (5), is the Joule heat power density, z represents the depth, , is the surface temperature of the test block at 0ms, the coefficient , It is related to the magnetic field strength and skin depth. Among them, , used to control the attenuation of the heat source in the depth direction; Inversely proportional to the depth z and directly proportional to the skin depth, .

[0046] In formula (5), The distribution of the approximate temperature increment of the crack on the surface of the test block at the time of 0ms, the positive and negative of which depends on the normal direction of the surface, and the temperature increment distribution of the upper surface K(S) is the discrete curvature of the test block surface S, and the sharper the position, the larger the parameter. The above process uses the skin effect and the known upper surface temperature increment. Get the approximate eddy current distribution and further get the internal Joule heat After verification, it was found that the direct method and the simplified normal Lc temperature distribution forward problem solution results are as follows Figure 8 As shown in the 400ms temperature response curve of a 20°, 3mm deep crack, the simplified expression The two simulation results of the original temperature increment Q are almost the same, with the maximum relative error being about 0.1%, indicating that the simplified method is effective.

[0047] The time taken by the direct method and the simplified method for solving the direct problem is shown in Table 2. It can be seen that the simplified method greatly reduces the calculation time when solving the direct problem. The direct method uses 69,240 grid points for calculation, and the total time is 676 seconds; while the simplified method uses 58,261 grid points and only takes 12 seconds. In contrast, the simplified method simplifies the process of solving the eddy current distribution in solving the direct problem, omitting the process of solving the magnetic field distribution of the Maxwell equations, that is, using formula (5) to equivalently calculate Q, avoiding the process of formulas (1) and (2), greatly reducing the calculation time of the numerical solution of induction heating, and providing a fast solution strategy for the optimization algorithm to solve the three-dimensional reconstruction of cracks.

[0048] S4. The specific steps of the algorithm implementation of the crack parameter quantification process are as follows: S401. Eddy current excitation and temperature field distribution changes Use straight wires to generate alternating magnetic fields and excite eddy current electric fields. Through pulse heating, defects in the rails cause changes in the temperature field distribution. Set the heating time of the excitation coil , ensuring that the eddy current excitation is sufficient to cause detectable changes in surface temperature.

[0049] S402. Temperature field data acquisition Use infrared thermal imagers to monitor the temperature field of the rail surface in real time and collect data to obtain the true value of the surface temperature in the cracked area. These data will be used for subsequent quantitative analysis of crack parameters.

[0050] S403. Initialize crack parameters and set optimization algorithm Randomly generate initial crack parameters within the solution range, that is, the depth of the crack and angle These parameters are used as the initial population of the genetic algorithm, and the number of iterations N is set to 1.

[0051] S404. Meshing for Numerical Simulation According to the initial crack parameters and , establish the simulation grid for the numerical heat transfer forward problem. Set the grid spacing to 0.2mm to ensure the balance between calculation accuracy and calculation efficiency.

[0052] S405. Calculate local curvature Using the initial crack depth and angle parameters, the local curvature K of the mesh discrete points is calculated, which will be used in the subsequent calculation of the equivalent heat source.

[0053] S406. Calculation of equivalent Joule heat According to the local curvature K and the true value of the surface temperature obtained in step S5 , through the equivalent formula Calculating internal Joule heating .

[0054] S407. Calculation of surface temperature estimate in Indicates temperature, including surface temperature , and then solve the heat conduction equation to estimate the surface temperature .

[0055] S408. Constructing the objective function Select the characteristic line below the wire where the eddy current distribution is high Temperature distribution, calculate twice the heating time Simulation temperature distribution at time The actual value of surface temperature The Euclidean distance of constitutes the objective function, and the formula is: In the formula, represents the objective function, represents the characteristic line, i Represents feature lines A specific point on is the heating time of the excitation coil, indicating the length of time the material is heated; It means twice the heating time. The purpose of choosing twice the heating time is to ensure that the heat has enough time to diffuse in the material, so as to more accurately reflect the temperature distribution inside the material. Indicates that point i passes The actual temperature distribution after Indicates that point i passes After the simulation temperature distribution. i By summing up the differences, we can get the overall difference on the entire characteristic line.

[0056] S409. Iterative update using genetic algorithm Set the population size to 100 and retain 30 elite individuals in each iteration; Maximum allowable error = 0.28, the mutation probability is set to 30%; Set the computational boundary: Crack depth Between 1mm and 5mm, angle Between 15° and 90°; Perform a crossover operation on the population: randomly select pairs of individuals and exchange some of their codes to generate new individuals; Perform mutation operations: change certain encoding values ​​according to the mutation probability to increase the diversity of the algorithm.

[0057] S410. Determine the convergence conditions Check whether the objective function value is less than the preset error tolerance value , and whether the number of iteration steps N is less than the maximum number of steps 1000. If the conditions are met, the final reconstruction result of the crack parameters is output: depth and angle If the condition is not met, the crack parameters are updated according to the genetic algorithm, and the process returns to step S3 to continue the iteration, with the number of iteration steps N = N + 1.

[0058] The above parameters are set for the genetic algorithm to perform quantitative crack reconstruction. The L-shaped hidden crack of the rail test block is as follows: Fig. 9 As shown in Figure 2, the captured thermal image of the L-shaped hidden crack is as follows: Fig.10 As shown, the crack angle and depth reconstruction results of the five sets of experimental data are shown in Table 3.

[0059] It can be seen that the increase in temperature has an amplifying effect on the error, and the rest of the results are good.

[0060] Due to the randomness of the initial value and mutation operator of the genetic algorithm, the error presents a certain random distribution. In order to further study the robustness of the genetic algorithm for crack reconstruction, the actual crack was reconstructed 200 times to study the distribution of its reconstruction solution. The results are plotted on the x / y / z axis with the reconstruction angle, reconstruction depth and error value returned by the objective function as shown in the figure. Fig.11 Scatter distribution diagram, where the light grey point (15.5°, 2.1mm) is the average value of all reconstruction results, and the errors relative to the true value (15°, 2mm) are 3.33% and 5% respectively. The statistical distribution of the reconstruction angle and reconstruction depth are shown in Figure 2. Fig.11 shown.

[0061] It can be seen from the reconstruction results that the reconstruction results are consistent with the maximum allowable error value set by the optimization algorithm. The smaller the maximum allowable error, the more concentrated the reconstruction solution will be in a small range, which will require a longer iteration process. Here, all errors are distributed below the maximum allowable error of 0.28, such as Fig.12 As shown in the figure, the angle reconstruction results show a concentrated distribution with 15.5° as the center and a range of [14°, 18.5°]. As the distance from the center increases, the number of solutions decreases. Among the 200 reconstructions, only one point with a large error appeared at 18.5°, that is, the maximum error was 23%; Fig.13 As shown in the figure, the depth reconstruction solution is distributed more evenly. This is because the minimum grid step size is set to a fixed value of 0.2 mm, so the crack depth reconstruction resolution is within this range. Further reducing this error requires a denser grid setting, which will have higher requirements on the computer's computing power.

[0062] Those skilled in the art will appreciate that the embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware.

[0063] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0064] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A rail defect quantification method based on pulsed eddy current thermal imaging, characterized in that: The following steps are involved: S1. Apply an alternating magnetic field to the rail to be tested to generate eddy currents inside it; S2. Measuring the temperature field data of the rail surface; S3. Solving the inverse heat conduction problem according to the temperature field data to determine the crack distribution of the rail.

2. A rail defect quantification method based on pulsed eddy current thermal imaging according to claim 1, characterized in that: The alternating magnetic field is a high-frequency pulse alternating magnetic field, and its frequency range is 10kHz to 1MHz; the alternating magnetic field is generated by an excitation coil; and the temperature field distribution data is measured by an infrared thermal imager.

3. A rail defect quantification method based on pulsed eddy current thermal imaging according to any one of claims 1 to 2, characterized in that: The electromagnetic field and heat conduction problems are simplified into an equivalent mathematical model by using an equivalent acceleration method, wherein the equivalent mathematical model is based on the skin effect and describes the exponential decay distribution of eddy current density and the approximate distribution of Joule heat.

4. The rail defect quantification method based on pulsed eddy current thermal imaging according to claim 3 is characterized in that: The equivalent mathematical model formula is as follows: in, represents the internal Joule thermal power density, z represents the depth, Used to control the attenuation of the heat source in the depth z direction. Inversely proportional to the depth z and directly proportional to the skin depth, represents the temperature increment distribution on the upper surface, is the surface temperature of the test block at 0 ms, K represents the local curvature of the grid discrete points, and K(S) is the discrete curvature of the test block surface S.

5. The rail defect quantification method based on pulsed eddy current thermal imaging according to claim 4, characterized in that: The process of solving the inverse heat conduction problem utilizes an optimization algorithm to iteratively solve crack parameters, where the crack parameters include crack depth and angle.

6. A rail defect quantification method based on pulsed eddy current thermal imaging according to claim 5, characterized in that: The optimization algorithm adopts a genetic algorithm and includes the following steps: S61. Initializing the initial population of crack parameters; S62. Calculating the error between the estimated value and the actual value of the crack parameter; S63. Iteratively update the crack parameters based on the error until a preset accuracy is reached.

7. A rail defect quantification method based on pulsed eddy current thermal imaging according to claim 6, characterized in that: Wherein step S62 includes constructing an objective function; the objective function is based on the spatial distribution characteristics of the temperature field data at a specific time point and is used to optimize the quantitative solution of crack parameters, and the formula is: ， in, represents the objective function, represents the characteristic line, i Represents feature lines A specific point on Indicates twice the heating time; Indicates that point i passes The actual temperature distribution after Indicates that point i passes The simulated temperature distribution after .

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