A Method for Quantifying Rail Defects Based on Pulse Eddy Current Thermography

Abstract

The present invention relates to the field of non-destructive testing technology, and particularly relates to a method for quantifying rail defects based on pulsed eddy current thermography, comprising the following steps: S1. Applying an alternating magnetic field to the rail to be tested to generate eddy currents inside it; S2. Measuring the temperature field data on the surface of the rail; S3. Solving the inverse heat conduction problem according to the temperature field data to determine the crack distribution of the rail. This method generates eddy currents through pulsed eddy current excitation, forms temperature field changes in the crack area, and realizes the quantification of crack parameters by solving the inverse heat conduction problem, thereby improving the accuracy and calculation efficiency of crack detection. The present invention is applicable to various detection conditions, especially suitable for in-service detection of rails, and solves the problems of insufficient detection accuracy and poor real-time performance in the prior art.

Description

Technical Field

[0001] The present invention relates to the technical field of non-destructive testing, and particularly to a method for quantifying rail defects based on pulsed eddy current thermography. Background Art

[0002] During the operation of trains, rails are subjected to huge pressure and impact forces from wheels, resulting in wavy wear and plastic deformation on their surfaces. These conditions often trigger rolling contact fatigue (RCF) cracks in the rails. The horizontal length of these cracks can exceed 10 millimeters and gradually expand over time, ultimately leading to crack spalling or even rail fracture. Therefore, timely prediction and quantitative analysis of these cracks are crucial for ensuring the safe operation of railways.

[0003] Currently, common rail crack detection methods include ultrasonic testing, magnetic particle testing, and conventional eddy current testing, etc. However, these techniques all have their limitations: Although ultrasonic testing is suitable for detecting internal defects, its sensitivity is relatively low when identifying surface micro-cracks. Magnetic particle testing is mainly used for detecting surface defects, but its ability to identify deep or subtle 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 suffer from the deficiencies of low detection accuracy, poor real-time performance, and inability to achieve crack quantification. With the continuous development of rail materials and the increasing complexity of their structures, the existing detection methods face more severe challenges.

[0004] Pulsed eddy current thermography (ECPT) is a non-destructive testing method that combines electromagnetic induction and infrared thermography techniques. 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 defects. However, due to the ill-posedness of the heat conduction inverse problem, current pulsed eddy current thermography is mostly limited to two-dimensional analysis in crack quantitative reconstruction, or can only achieve the reconstruction of a single parameter. Existing quantification methods are mainly divided into two categories: black box methods and model methods. 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 interpretability. Once the detection conditions change, the model may fail and must be retrained. Model methods solve the forward problem through optimization algorithms (such as Newton's method, conjugate gradient method, genetic algorithm). Although model methods have strong physical interpretability, each iteration requires solving complex computational problems, resulting in a long calculation time.

[0005] Patent CN201910019827 introduces a method for identifying defect features in infrared thermal images based on dynamic multi-objective optimization. It extracts defect features through multi-objective optimization and pulse-coupled neural networks. Although the detection accuracy is improved, it relies on a large amount of thermal image data for training, and in a dynamic environment, it requires a complex multi-objective optimization process, resulting in a high computational cost.

[0006] "Liang Yuanyuan, Yang Shengsheng, Wen Xuan, et al. Research on Defect Quantification Technology in Pulse Eddy Current Nondestructive Testing [J]. Chinese Journal of Scientific Instrument, 2018, 39(11):9" proposed a pulse eddy current detection method based on tunnel magnetoresistive sensors, and used the BP neural network algorithm to quantitatively evaluate the defect depth. However, this method needs to train the network separately for different shapes of defects, with poor generalization ability, and the model needs to be retrained when the detection conditions change, resulting in a high application cost. Summary of the Invention

[0007] The present invention aims to overcome the deficiencies of the prior art, such as low detection accuracy, slow calculation speed, poor system adaptability and stability, and provides a method for quantifying rail defects based on pulse eddy current thermography, specifically including: improving the accuracy of detection by realizing the multi-parameter precise quantification of crack depth and angle; significantly reducing the calculation time by simplifying the solution process through an equivalent acceleration method; being applicable to different detection conditions without retraining the model by using an algorithm with good generalization ability, improving the adaptability of the system; and improving the detection stability in a dynamic environment by combining an optimized algorithm with multi-parameter analysis.

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

[0009] A method for quantifying rail defects based on pulse eddy current thermography, comprising the following steps:

[0010] S1. Apply an alternating magnetic field to the rail to be measured to generate eddy currents inside it;

[0011] S2. Measure the temperature field data on the surface of the rail;

[0012] S3. Solve the heat conduction inverse problem according to the temperature field data to determine the crack distribution of the rail.

[0013] Preferably, the alternating magnetic field is a high-frequency pulsed alternating magnetic field with a frequency range of 10 kHz to 1 MHz; the alternating magnetic field is generated by an excitation coil; the temperature field distribution data is measured by an infrared thermal imager. This preferred solution gives the frequency range of the alternating magnetic field and the type of excitation source. Eddy currents are excited by a high-frequency pulsed alternating magnetic field (10 kHz to 1 MHz), and the temperature field is measured by an infrared thermal imager. This frequency range and infrared measurement method can ensure high-resolution temperature data, improve the accuracy of crack detection and imaging quality, and are particularly sensitive to superficial cracks.

[0014] Preferably, an equivalent acceleration method is used to simplify the electromagnetic field and heat conduction problems into an equivalent mathematical model, where 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. By using the equivalent acceleration method, the electromagnetic field and heat conduction problems are simplified, and complex physical problems are transformed 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, significantly reducing the computational complexity and time, improving the real-time performance, and enabling the detection results to be output in a short time.

[0015] Preferably, the formula of the equivalent mathematical model is as follows:

[0016]

[0017] Where, represents the internal Joule heat power density, z represents the depth, is used to control the attenuation degree of the heat source in the depth z direction, is inversely proportional to the depth z and directly proportional to the skin depth, represents the upper surface temperature increment distribution, is the surface temperature of the test block at 0 ms, K represents the local curvature of the grid discrete point, 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 exponential decay in the depth direction, can better reflect the influence of cracks at different depths on the eddy current distribution and temperature field, and improves the quantization accuracy of crack parameters.

[0018] Preferably, the process of solving the inverse heat conduction problem uses an optimization algorithm to iteratively solve the crack parameters, and the crack parameters include the depth and angle of the crack. By using an optimization algorithm to iteratively solve parameters such as the depth and angle of the crack, the accuracy of crack quantification is improved. The iterative solution method ensures that the optimization result of the crack parameters is close to the true value, reduces the calculation error, and improves the adaptability of crack detection at different depths and angles.

[0019] Preferably, the optimization algorithm uses a genetic algorithm, including the following steps:

[0020] S61. Initialize the initial population of crack parameters;

[0021] S62. Calculate the error between the estimated value and the actual value of the crack parameters;

[0022] S63. Iteratively update the crack parameters based on the error until a preset accuracy is reached.

[0023] Using the genetic algorithm as an optimization means can globally search for the optimal solution, avoid falling into local optima, and improve the accuracy and stability of crack parameter solving. At the same time, multiple iterations of the genetic algorithm can automatically adapt to different crack characteristics, enhance the generalization ability of the algorithm, and are suitable for the quantitative solution of complex cracks.

[0024] 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 crack parameters. The formula is:

[0025]

[0026] Where, represents the objective function, represents the characteristic line, i represents the characteristic line a specific point on, represents twice the heating time; represents the true temperature distribution at point i after ; represents the simulated temperature distribution at point i after . By summing the differences of all points i , 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, it is ensured that the optimization result is more consistent with the true crack characteristics. The introduction of the objective function provides a measurement standard for crack parameters, promotes the iterative update to converge to accurate crack parameters, and thus improves the reliability and accuracy of crack depth and angle quantification.

[0027] Compared with the prior art, the beneficial effects of the present invention:

[0028] The present invention provides a method for quantifying rail defects based on pulsed eddy current thermography, which includes applying an alternating magnetic field to the rail, measuring temperature field data, and solving the inverse heat conduction problem to determine the crack distribution. By generating eddy currents through pulsed eddy current excitation, a temperature field change is formed in the crack area, and the inverse heat conduction problem is solved to achieve 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, internal eddy currents are excited, which can generate Joule heat inside the material, causing the temperature in the defect area to rise. This step makes defect areas such as cracks appear as temperature anomaly areas in thermography, helping to quickly identify the defect locations. By measuring the surface temperature field data and using the inverse heat conduction problem to solve for the spatial distribution and characteristics (such as depth and shape) of the cracks, the precise quantification of the 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 described in the present invention does not require cutting or destructive treatment of the rail, realizes non-contact non-destructive detection through eddy current thermography, reduces physical damage to the rail, and is suitable for real-time detection of in-service rails. Description of the Drawings

[0029] Figure 1 It is a flowchart of a method for quantifying rail defects based on pulsed eddy current thermography according to Embodiment 1 of the present invention;

[0030] Figure 2 It is a schematic diagram of an induction thermography non-destructive detection system according to Embodiment 2 of the present invention;

[0031] Figure 3 It is a flowchart of an algorithm for solving the crack reconstruction problem according to Embodiment 2 of the present invention;

[0032] Figure 4 It is a schematic diagram of an L-shaped hidden crack according to Embodiment 3 of the present invention;

[0033] Markings in the figure: 1 - L-shaped hidden crack; 2 - crack surface S1; 3 - external boundary surface S; 4 - internal crack surface S2; 5 - vertical section;

[0034] Figure 5 It is a simulated temperature distribution diagram according to Embodiment 3 of the present invention;

[0035] Markings in the figure: (a) Simulated temperature distribution at 200 ms, (b) Simulated temperature distribution at 400 ms;

[0036] Figure 6 It is a temperature distribution diagram of line lc according to Embodiment 3 of the present invention;

[0037] Markings in the figure: (a) Temperature distribution of line lc at 200 ms, (b) Temperature distribution of line lc at 400 ms;

[0038] Figure 7 Schematic diagram of the eddy current distribution characteristics in Embodiment 3 of the present invention;

[0039] Markings in the figure: (a) Schematic diagram of the eddy current distribution on the inner surface, (b) Schematic diagram of the eddy current distribution on the upper surface;

[0040] Figure 8 Comparative analysis diagram of the solution results of the direct method and the simplified method in Embodiment 3 of the present invention;

[0041] Figure 9 Schematic diagram of the L-shaped hidden crack in the rail test block in Embodiment 3 of the present invention;

[0042] Figure 10 Thermal imaging schematic diagram of the L-shaped hidden crack in Embodiment 3 of the present invention;

[0043] Figure 11 Scatter distribution diagram of crack reconstruction in Embodiment 3 of the present invention;

[0044] Figure 12 Quantity distribution diagram of the angular reconstruction solutions in Embodiment 3 of the present invention;

[0045] Figure 13 Quantity distribution diagram of the depth reconstruction solutions in Embodiment 3 of the present invention. Specific embodiments

[0046] The following further elaborates in detail a method for quantifying rail defects based on pulsed eddy current thermography provided by the present invention in combination with the accompanying drawings and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments. All technologies implemented based on the content of the present invention fall within the scope of the present invention. In combination with the following description, the advantages and features of the present invention will be clearer. It should be noted that the accompanying drawings are all in a very simplified form and use non-precise scales, only for conveniently and clearly assisting in explaining the purpose of the embodiments of the present invention.

[0047] Embodiment 1

[0048] This embodiment provides a method for quantifying rail defects based on pulsed eddy current thermography, and the method steps are as Figure 1 shown, including the following steps:

[0049] S1. Apply an alternating magnetic field to the rail to be measured to generate eddy currents inside it;

[0050] S2. Measure the temperature field data on the surface of the rail;

[0051] S3. Solve the heat conduction inverse problem based on the temperature field data to determine the crack distribution of the rail.

[0052] Preferably, the alternating magnetic field is a high-frequency pulsed alternating magnetic field with a frequency range of 10 kHz to 1 MHz; the alternating magnetic field is generated by an excitation coil; the temperature field distribution data is measured by an infrared thermal imager. This preferred solution gives the frequency range of the alternating magnetic field and the type of excitation source. Eddy currents are excited by the high-frequency pulsed alternating magnetic field (10 kHz to 1 MHz), and the temperature field is measured by an infrared thermal imager. This frequency range and infrared measurement method can ensure high-resolution temperature data, improve the accuracy of crack detection and imaging quality, and are particularly sensitive to superficial cracks.

[0053] Preferably, the equivalent acceleration method is used to simplify the electromagnetic field and heat conduction problems into an equivalent mathematical model, where 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. By using the equivalent acceleration method, the electromagnetic field and heat conduction problems are simplified, and the complex physical problems are transformed 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 Joule heat distribution, significantly reducing the computational complexity and time, improving the real-time performance, and enabling the detection results to be output in a short time.

[0054] Preferably, the formula of the equivalent mathematical model is as follows:

[0055]

[0056] where, represents the internal Joule heat power density, z represents the depth, is used to control the attenuation degree of the heat source in the depth z direction, is inversely proportional to the depth z and directly proportional to the skin depth, represents the upper surface temperature increment distribution, is the surface temperature of the test block at 0 ms, K represents the local curvature of the grid discrete point, and K(S) is the discrete curvature of the surface S of the test block. 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 exponential decay in the depth direction, can better reflect the influence of cracks at different depths on the eddy current distribution and temperature field, and improves the quantization accuracy of crack parameters.

[0057] Preferably, the process of solving the inverse heat conduction problem uses an optimization algorithm to iteratively solve the crack parameters, and the crack parameters include the depth and angle of the crack. By using an optimization algorithm to iteratively solve parameters such as the depth and angle of the crack, the accuracy of crack quantification is improved. The iterative solution method ensures that the optimization result of the crack parameters is close to the true value, reduces the calculation error, and improves the adaptability of crack detection at different depths and angles.

[0058] Preferably, the optimization algorithm uses a genetic algorithm, including the following steps:

[0059] S61. Initialize the initial population of crack parameters;

[0060] S62. Calculate the error between the estimated value and the actual value of the crack parameters;

[0061] S63. Iteratively update the crack parameters based on the error until the preset accuracy is reached.

[0062] Using the genetic algorithm as an optimization means can globally search for the optimal solution, avoid falling into local optima, and improve the accuracy and stability of solving crack parameters. At the same time, multiple iterations of the genetic algorithm can automatically adapt to different crack characteristics, enhancing the generalization ability of the algorithm and making it suitable for the quantitative solution of complex cracks.

[0063] 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 crack parameters. The formula is:

[0064]

[0065] Where, represents the objective function, represents the characteristic line, i represents the characteristic line at a specific point on it, represents twice the heating time; represents the true temperature distribution at point i after ; represents the simulated temperature distribution at point i after . By summing the differences of all points i , the overall difference on the entire characteristic line can be obtained. In the iterative steps of the genetic algorithm, by constructing an objective function based on the spatial distribution of the temperature field, it is ensured that the optimization result is more consistent with the true crack characteristics. The introduction of the objective function provides a measurement standard for crack parameters, prompting the iterative update to converge to accurate crack parameters, thereby improving the reliability and accuracy of crack depth and angle quantification.

[0066] Embodiment 2

[0067] As a preferred embodiment of Embodiment 1, this Embodiment 2 provides a specific implementation manner of a method for quantifying rail defects based on pulsed eddy current thermography.

[0068] S1. Generation of eddy current excitation

[0069] A high-frequency pulsed alternating magnetic field is generated by an excitation source signal through an excitation coil. The alternating magnetic field enters the rail material and induces eddy currents. The eddy currents are disturbed in the defect area, resulting in a change in the current density, which in turn causes a change in the Joule heat distribution inside the material. These changes form a temperature field distribution on the material surface.

[0070] S2. Acquisition and Quantification of Temperature Field Data

[0071] The pulsed eddy current thermography method has the advantages of high precision and high efficiency. First, by applying a high-frequency pulsed driving current to the excitation coil, 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, causing the corresponding temperature field to be disturbed and change. During the heat diffusion process, the influence degree of the crack on the temperature field is different. By analyzing the heat distribution and its change characteristics during the heat dissipation process, the geometric information of the crack can be obtained. For this purpose, a simulation model and experiment of the temperature response process need to be established to analyze the physical process of the actual heat diffusion process and the specific influence of different cracks on the temperature distribution. Further, the algorithm strategy for crack reconstruction is analyzed.

[0072] As Figure 2 shown, the excitation source signal generates an alternating magnetic field through the excitation coil, which propagates into the test piece and induces an eddy current electric field. The defect in the test block disturbs the formation of eddy currents, causing a change in its current density, thereby resulting in a change in the Joule heat caused by the current density and generating a change in the temperature field distribution around the defect. An 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 changing with time. The temperature data is input into a computer for further processing to quantitatively analyze the depth and angle of the crack.

[0073] When the induction heating device starts to work, the coil connected to the heating device generates a high-frequency pulsed signal. According to Faraday's law of electromagnetic induction, if the coil is close to the conductor, there is an induced eddy current on the surface of the conductor, and its spatial manifestation is:

[0074] (1)

[0075] where I is the surface induced eddy current, with the unit of ; is the surface induced eddy current density, with the unit of ; is the source current density, representing the externally applied current density; is the conductivity, with the unit of , is the magnetic permeability of the material to be measured, is the loop electromotive force, is the loop radius, is the dielectric constant of the material to be measured. The symbol denotes the vector differential operator, which is used to describe the gradient, divergence, and curl operations in space. In the theory of electromagnetic fields, it has the following several important applications:

[0076] Gradient ( f): For a scalar field f, f represents the rate of change in all directions.

[0077] Divergence ( ): For a vector field I, ·I represents the source strength of the vector field.

[0078] Curl ( ): For a vector field I, ×I represents the rotational property of the vector field and is used to describe, for example, the rotational properties of an electric current or a magnetic field.

[0079] According to Joule's law, the thermal power density generated by eddy currents in the measured material is:

[0080] (2)

[0081] where E is the induced electric field strength.

[0082] According to Fourier's law of heat conduction, for a homogeneous and isotropic material, neglecting its surface radiation and convection and assuming the internal heat source is zero, the heat conduction equation for the eddy current distribution can be expressed as:

[0083] (3)

[0084] where , , are the density, specific heat capacity, and thermal conductivity of the measured material, respectively; represents the temperature, including the surface temperature ; represents the first-order derivative of with respect to time; is the Joule heat power density and can be expressed as the product of the heat power density and the time t, .

[0085] In a rail specimen, due to the interaction between the alternating magnetic field and the eddy current, the current density distribution is concentrated on the surface, and its eddy current density decreases exponentially with depth. When defining the depth at which the eddy current density decays to of the surface as the skin depth , it can be used as an important parameter for crack detection, and the formula is:

[0086] (4)

[0087] Quantification of cracks refers to establishing the 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 heat conduction problem. After obtaining the difference between the estimated eigenvalue and the observed eigenvalue returned by solving the real-time forward problem, iterative optimization algorithms are used until certain target conditions are met to approximate the true value of the parameter to be solved.

[0088] S3. Simplification of forward problem solution

[0089] The complex electromagnetic field and heat conduction problems are simplified by the equivalent acceleration method. Specifically, using the skin effect, the eddy current density distribution is approximated as an exponentially decaying form on the surface, avoiding directly solving the Maxwell equations, thus significantly reducing the computational complexity. The calculated temperature field is used for subsequent crack quantification analysis.

[0090] S4. Algorithm implementation of crack parameter quantification process

[0091] The algorithm implementation of the crack parameter quantification process is as Figure 3 shown, including the following steps:

[0092] S401. Initialize crack parameters: Randomly set the initial crack parameters , including the depth and angle ;

[0093] S402. Establish a network: Establish a computational network for numerical simulation according to the initial crack parameters ;

[0094] S403. Solve the forward problem: Use the established network to solve the numerical heat transfer forward problem to obtain the estimated value of the material surface temperature . This step can adopt the equivalent acceleration method to simplify the solution process and improve the computational efficiency;

[0095] S404. Data acquisition by pulsed eddy current thermography: Use pulsed eddy current thermography technology for the actual cracks in the rail material to obtain the true value of the surface temperature on the surface, which is used to compare with the estimated value of the surface temperature;

[0096] S405. Construct the objective function: Use the estimated value of the surface temperature and the true value of the surface temperature to construct the objective function , calculate the error between the two, and whether the error is less than the preset error threshold , expressed as ;

[0097] 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 , it is considered that the estimated value of the crack parameter is accurate enough, and the crack parameter is output ;

[0098] S407. Iteratively update the crack parameter: If the error does not meet the accuracy requirement, update the crack parameter according to the optimization algorithm (such as the genetic algorithm), and continue the iterative solution.

[0099] Among many optimization algorithms with different properties, the genetic algorithm is a bionic algorithm in a macroscopic sense. Its main steps are as follows: A population composed of a certain number of individuals (Population Size) is initially formed. In each iteration process, relatively excellent individuals (Elite Count) are selected according to a certain index, inferior individuals are eliminated, and these individuals are recombined using genetic operators (including inheritance, crossover, mutation, etc.) to generate a new generation of population. Repeat this iteration so that the population evolves towards higher fitness until a certain convergence index is met, such as stopping the iteration when the objective function reaches the ideal value (Fitness Limit). Compared with other optimization algorithms, the genetic algorithm belongs to a global optimization algorithm because the mutation operation in the iteration 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 has good robustness in solving problems.

[0100] Example 3

[0101] Based on the foregoing embodiments, this embodiment provides a specific implementation manner of a method for quantifying rail defects based on pulsed eddy current thermography.

[0102] 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:

[0103]

[0104] Next, use COMSOL to perform simulation calculations on the L-shaped hidden crack of the test block. As Figure 4 shown, the L-shaped hidden crack is divided into a planar crack and an inclined crack. Among them, the inclined crack is located on the crack surface S1, and the planar crack is located on the inner crack surface S2. The included angle between the crack surface S1 and the test surface S of the test block is , and the included angle between the crack surface S1 and the inner crack surface S2 is , and the inner crack surface S2 is parallel to the test surface S of the test block. and are complementary angles. The depth distance between the inner surface S2 of the crack and the surface S of the test block is d.

[0105] The excitation coil is a straight wire with a lift-off height of 3 mm. The central feature line parallel to the straight wire on the surface of the test block is denoted as lc. The crack penetrates the test block in the thickness direction of the test block, with a surface opening width of 1 mm. The included angles with the surface of the test block are set to 10°, 15°, and 20° respectively, and the corresponding depths are set to 1.47 mm, 2.25 mm, and 3.00 mm. The frequency of the excitation current is 190 KHz, the intensity is 350 A, the excitation pulse width is a Gaussian pulse of 200 ms, the initial temperature is 293 K, and the recording time is 1000 ms. The surface temperature distribution of the 20-degree crack can be obtained as Figure 5 shown, and the line lc temperature distribution of the three cracks is as Figure 6 shown.

[0106] As shown in (a) of the appendix Figure 5 , 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, and a relatively high amount of heat accumulates at the crack tip at 200 ms. The temperature distribution decreases uniformly with the increase in the distance from the crack tip. As shown in Figure 5 the (b) in the appendix, after a certain amount of diffusion, the heat at 400 ms has diffused downward to the planar crack, so a relatively high-temperature distribution appears on the surface corresponding to the planar crack . It can be seen from (a) in the appendix Figure 6 and (b) in the appendix Figure 6 that cracks of different sizes have different degrees of influence on eddy currents, and thus the temperatures transmitted back to the surface are different. Characteristics such as the time for the heat below the inclined crack and the planar crack to be transmitted back to the surface will also change due to the crack size.

[0107] 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. For this case, the eddy current distribution generated by the excitation source can be decomposed into two parts, as Figure 7 shown. In the case where the eddy current density is : (a) in the appendix Figure 7 is a schematic diagram of the eddy current distribution on the inner surface. This part only exists at the turning parts of the test block, and the sharper the turn, the higher the eddy current temperature; (b) in the appendix Figure 7 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 the increase in depth.

[0108] Using this temperature distribution characteristic, Equation (3) can be rewritten into the following equivalent mathematical model:

[0109] (5)

[0110] In Equation (5), is the Joule heat power density, z represents the depth, , is the surface temperature of the specimen at 0 ms, and the coefficients , are related to the magnetic field strength and the skin depth. Among them, is used to control the attenuation degree of the heat source in the depth direction; is inversely proportional to the depth z and directly proportional to the skin depth, .

[0111] In Equation (5), is the distribution of the approximate temperature increment on the surface of the specimen with a crack at 0 ms, and its positive or negative depends on the normal direction of this surface, and is obtained from the upper surface temperature increment distribution . K(S) is the discrete curvature of the surface S of the specimen, and the larger this parameter is at a sharper position. The above process is to use the skin effect and the known upper surface temperature increment to obtain the approximate eddy current distribution, and further obtain the internal Joule heat distribution. After verification, it is found that the direct method and the simplified normal Lc temperature distribution forward problem solution results are as Figure 8 shown. In the temperature response curve of a 400 ms crack with a depth of 3 mm at 20°, the two simulation results using the simplified expression and the original temperature increment Q are almost the same, and the maximum relative error is about 0.1%, indicating the effectiveness of the simplified method.

[0112]

[0113] The time used for the direct method and the simplified method in the forward problem is shown in Table 2. It can be seen that the simplified method greatly reduces the calculation time in solving the forward problem. The direct method uses 69,240 grid points for calculation, and the total time consumption is 676 seconds; while the simplified method uses 58,261 grid points and only requires 12 seconds. In comparison, the simplified method simplifies the process of solving the eddy current distribution in the forward problem, omits the process of solving the magnetic field distribution by the Maxwell equations, that is, equivalently calculates Q through formula (5), avoiding the processes of formulas (1) and (2), and greatly reduces the calculation time of the numerical solution of induction heating, providing a fast solution strategy for optimizing the algorithm to solve the three-dimensional reconstruction of cracks.

[0114] S4. The specific steps of the algorithm implementation for the crack parameter quantification process are as follows:

[0115] S401. Eddy current excitation and temperature field distribution change

[0116] An alternating magnetic field is generated by a straight wire to excite an eddy current electric field. By means of pulse heating, the distribution change of the temperature field is caused by the defects existing in the rail. Set the heating time of the excitation coil , ensuring that the eddy current excitation is sufficient to cause a detectable change in the surface temperature.

[0117] S402. Temperature field data acquisition

[0118] Use an infrared thermal imager to conduct real-time monitoring and data acquisition of the temperature field on the surface of the rail, and obtain the true value of the surface temperature of the crack-containing area . These data will be used for the quantitative analysis of subsequent crack parameters.

[0119] S403. Initialize crack parameters and set optimization algorithm

[0120] Randomly generate initial crack parameters within the solution range, that is, the depth and angle of the crack. Take these parameters as the initial population of the genetic algorithm, and set the number of iteration steps N to 1.

[0121] S404. Numerical simulation grid meshing

[0122] According to the initial crack parameters and , establish a simulation grid for the forward problem of numerical heat transfer. Set the grid spacing to 0.2 mm to ensure the balance between calculation accuracy and calculation efficiency.

[0123] S405. Calculate local curvature

[0124] Use the initial crack depth and angle parameters to calculate the local curvature K of the grid discrete points, which will be used for the calculation of the subsequent equivalent heat source.

[0125] S406. Calculation of equivalent Joule heat

[0126] According to the local curvature K obtained in step S5 and the true value of the surface temperature , through the equivalent formula

[0127]

[0128] calculate the internal Joule heat .

[0129] S407. Calculation of surface temperature estimated value

[0130]

[0131] where represents temperature, including surface temperature , then solve the estimated surface temperature through the heat conduction equation .

[0132] S408. Construct the objective function

[0133] Select the characteristic line below the wire with a higher eddy current distribution of the temperature distribution, and calculate twice the heating time The simulated temperature distribution at the moment and the true value of the surface temperature The Euclidean distance of forms the objective function, and the formula is:

[0134]

[0135] In the formula, represents the objective function, represents the characteristic line, i represents the characteristic line at a specific point on, is the heating time of the excitation coil, indicating the length of time the material is heated; represents twice the heating time. Selecting twice the heating time is to ensure that there is enough time for heat to diffuse in the material, so as to more accurately reflect the temperature distribution inside the material; represents the true temperature distribution at point i after ; represents the simulated temperature distribution at point i after . By summing the differences of all points i , the overall difference on the entire characteristic line can be obtained.

[0136] S409. Use the genetic algorithm for iterative update

[0137] Set the population size to 100, and retain 30 elite individuals in each iteration;

[0138] Allow the maximum error value = 0.28, and set the mutation probability to 30%;

[0139] Set the calculation boundary: the crack depth is between 1 mm and 5 mm, and the angle is between 15° and 90°;

[0140] Perform crossover operation on the population: randomly select paired individuals and exchange their partial codes to generate new individuals;

[0141] Perform mutation operation: change some code values according to the mutation probability to increase the diversity of the algorithm.

[0142] S410. Judge the convergence condition

[0143] 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, output the final reconstruction result of the crack parameters: depth and angle . If the conditions are not met, update the crack parameters according to the genetic algorithm, return to step S3 for continued iteration, and the number of iteration steps N = N + 1.

[0144] Perform the above parameter settings for the genetic algorithm and conduct crack quantitative reconstruction. The L-shaped hidden crack of the rail test block is as Figure 9 shown, and the captured thermal image of the L-shaped hidden crack is as Figure 10 shown. The reconstruction results of the crack angle and depth of five groups of experimental data are shown in Table 3.

[0145]

[0146] It can be seen that the temperature increase amplifies the error, and the other results are good.

[0147] Due to the randomness of the initial value and mutation operator of the genetic algorithm, the error shows a certain random distribution. To further study the robustness of the genetic algorithm for crack reconstruction, the actual crack is reconstructed 200 times to study the distribution of its reconstruction solutions. The results are plotted as scatter distribution diagrams with the reconstructed angle, reconstructed depth, and the error value returned by the objective function as the x / y / z axes respectively. Among them, the light gray point (15.5°, 2.1 mm) is the average value of all reconstruction results, and the errors relative to the true value (15°, 2 mm) are 3.33% and 5% respectively. The statistical distribution quantities of the reconstructed angle and reconstructed depth are as Figure 11 shown. Figure 11 shown.

[0148] It can be seen from the reconstruction results that the reconstruction results are related to the maximum allowable error value set by the optimization algorithm. The smaller the maximum allowable error, the more concentrated the reconstruction solutions will be in a small range nearby, and a longer iteration process will be required. All the errors here are distributed below the maximum allowable error of 0.28, as Figure 12 shown. Among them, the reconstruction results of the angle show a concentrated distribution centered at 15.5° and in the range of [14°, 18.5°]. As the distance from the central value increases, the number of occurrences of the solutions gradually decreases. Only one point with a large error appears in the 200 reconstructions, and the result is 18.5°, that is, the maximum error is 23%; as Figure 13As shown, the depth reconstruction solution is relatively evenly distributed. This is because the minimum grid step size is set to a fixed value of 0.2 mm. Therefore, the crack depth reconstruction resolution is within this range. To further reduce this error, a denser grid setting is required, which places higher demands on the computing power of the computer.

[0149] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects.

[0150] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, 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, it should be considered as the scope described in this specification.

[0151] The above-described embodiments only represent several implementation manners of the present invention. Their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the invention patent should be subject to the appended 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 problem of heat conduction according to the temperature field data to determine the crack distribution of the rail; The 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 the eddy current density and the approximate distribution of Joule heat; the formula of the equivalent mathematical model 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.

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.

3. A rail defect quantification method based on pulsed eddy current thermal imaging according to claim 2, 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.

4. The rail defect quantification method based on pulsed eddy current thermal imaging according to claim 3 is 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.

5. The rail defect quantification method based on pulsed eddy current thermal imaging according to claim 4, 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 the characteristic line 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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