A pulse eddy current signal preprocessing and thickness evaluation method based on relative logarithmic transformation

Abstract

This invention relates to the fields of electromagnetic nondestructive testing and pulsed eddy current signal processing technology, and in particular to a method for pulsed eddy current signal preprocessing and thickness assessment based on relative logarithmic transform. The method includes: establishing an analytical model for pulsed eddy current testing of a coated ferromagnetic pipe; acquiring reference and test signals and performing amplitude normalization preprocessing; constructing a relative logarithmic transform (RLT) algorithm, using logarithmic ratio calculation and weight modulation to enhance weak signals and suppress noise; extracting the peak time of the transformed signal sequence as a feature quantity; and using a linear fitting equation to quantitatively assess the pipe wall thickness. This invention effectively solves the problem of weak and easily interfered induced signals in the testing of coated pipes, significantly improves the signal-to-noise ratio, and the extracted feature quantity is highly robust to the lift-off effect, greatly improving the accuracy and stability of quantitative wall thickness assessment under complex working conditions.

Description

Technical Field

[0001] This invention relates to the fields of electromagnetic nondestructive testing and pulsed eddy current signal processing technology, specifically a pulsed eddy current signal preprocessing and thickness assessment method based on relative logarithmic transformation. Background Technology

[0002] Pipelines are widely used in industries such as petroleum, chemical, and power, undertaking the task of transporting high-temperature and high-pressure media. To reduce heat loss and ensure operational safety, pressure-bearing pipelines typically employ a cladding structure. The main body—the insulation layer—is primarily composed of non-conductive insulation materials such as polyurethane, rock wool, or calcium silicate, effectively reducing heat loss from the medium. However, under high-temperature and high-pressure conditions, pipelines may be affected by corrosion, flow-accelerated corrosion, and droplet impact, leading to thinning of the pipe wall. Once the thinning reaches a critical level, the pipeline may experience sudden rupture and media leakage, causing severe economic losses and safety risks. Existing testing methods usually require removing the cladding layer, which is complex, inefficient, and difficult to implement for high-frequency on-site testing. Therefore, there is an urgent need to develop a non-destructive testing technology that does not require removing the cladding layer while balancing operational accessibility and testing efficiency.

[0003] Pulsed eddy current testing, as an important branch of eddy current testing, is feasible and has been applied to thickness assessment of coated components. Compared to traditional sinusoidal eddy current testing, pulsed eddy current testing uses rectangular pulse excitation, featuring a wide spectrum and high current excitation, significantly improving the electromagnetic field penetration and non-contact remote detection capabilities, thus enabling effective assessment of pipe wall thickness by penetrating the coating. However, in practical applications, the lift-off effect caused by the coating remains a key challenge affecting the accuracy of thickness assessment.

[0004] To mitigate the impact of the lift-off effect, existing research primarily focuses on optimizing probe structure design and extracting insensitive features. In probe design, researchers have developed three-coil probes, U-shaped probes, or semi-circular probes to improve the signal-to-noise ratio and reduce lift-off interference. Regarding feature extraction, features such as differential signal peak time, lift-off crossover point, and derivative-integral ratio have been proposed and, to some extent, established a linear relationship with pipe wall thickness. However, the exact mechanism by which the lift-off effect affects pulsed eddy current signals remains unclear, and feature extraction and lift-off suppression methods require further refinement. Summary of the Invention

[0005] This invention addresses the technical shortcomings of pulsed eddy current testing of coated ferromagnetic pipes, such as low signal-to-noise ratio of induced voltage signal, weak and easily submerged signal in the later stages, poor stability of feature extraction, and limited accuracy of quantitative wall thickness assessment due to the lift-off effect interference caused by the coating thickness. It provides a pulsed eddy current signal preprocessing and thickness assessment method based on relative logarithmic transform (RLT).

[0006] In industries such as petroleum, chemical, and power, ferromagnetic carbon steel pipes are typically covered with a cladding layer. Pulsed eddy current detection technology uses broadband rectangular pulse excitation to allow the electromagnetic field to penetrate the cladding layer and induce eddy currents within the pipe wall. However, the high permeability of ferromagnetic materials causes the skin effect, leading to rapid attenuation of the induced eddy currents as they diffuse deeper into the pipe wall. This results in a very weak voltage signal induced by the receiving coil—the signal reflecting the pipe wall thickness—typically only in the millivolt or microvolt range. Simultaneously, the cladding layer, primarily composed of non-conductive insulating material, generates a lift-off effect that further weakens the electromagnetic field; the greater the lift-off, the smaller the signal amplitude. Furthermore, minute probe jitter during detection introduces additional noise, causing shifts or distortions in the effective features of the original signal. However, traditional differential signaling or logarithmic conversion methods are highly sensitive to changes in lift-off distance, making it difficult to effectively resist these effects.

[0007] To address this, the present invention introduces the Relative Logarithmic Transform (RLT) algorithm, which utilizes the nonlinear correlation mapping between the reference signal and the test signal to enhance weak effective signals and extract a peak time feature that is highly robust to the lift-off effect, thereby enabling accurate assessment of pipe wall thickness under complex operating conditions.

[0008] To achieve the above objectives, this invention provides a method for preprocessing and thickness assessment of pulsed eddy current signals based on relative logarithmic transform, the method comprising the following steps: S1: Establish a physical model for pulsed eddy current detection in a ferromagnetic pipe with a cladding layer. This model includes an internal air region, the ferromagnetic pipe wall, and a non-conductive, non-magnetic cladding layer. A pulsed eddy current probe containing a transmitting coil and a receiving coil is placed above the cladding layer. The selection of probe parameters is crucial for signal quality. The transmitting coil is typically wound with high-strength enameled wire to withstand the thermal effects generated by the large current pulse. The receiving coil is wound with multi-turn fine wire to improve sensitivity. The establishment of the three-layer flat plate model needs to consider the nonlinear magnetization characteristics of the ferromagnetic material; however, in the weak-field detection stage of pulsed eddy currents, its initial permeability is usually used for analytical calculation. S2: Use the pulsed eddy current probe to acquire the reference induced voltage signal U of the reference pipe. r (t) and the test induced voltage signal U of the pipeline under test. m (t), and perform digital sampling to obtain the discrete sequence U. m (n) and U r (n); S3: For the discrete sequence U m (n) and U r (n) Perform maximum value normalization on each signal to obtain the normalized reference signal sequence p.n and normalized test signal sequence q n ; S4: Construct a relative logarithmic transform operator for the normalized reference signal sequence p. n and normalized test signal sequence q n Perform nonlinear transformation to generate the transformed signal sequence z. n The expression for the relative logarithmic transformation operator is: ; Where a and b are preset adjustment coefficients;

[0009] The mathematical logic of relative logarithmic transformation lies in: when the test signal q n With reference signal p n When there are minor differences (i.e., wall thickness reduction), the ratio q n / p n Deviation from 1. Logarithmic term This deviation will be quickly detected. Through the weighting terms... The modulation algorithm assigns a lower gain in the early stage (n) when the signal energy is high to prevent signal saturation; while in the later stage (n is large) when the signal energy is weak, the algorithm uses a logarithmic nonlinear amplification effect to make the wall thickness information form a clear peak feature on the time domain curve. This dynamic gain adjustment mechanism is the key to achieving a high signal-to-noise ratio in this invention.

[0010] S5: For the signal sequence z n Perform feature recognition and extract the signal sequence z n The time corresponding to the peak point of the curve is used as the peak time feature tPeak. To further eliminate the influence of random noise on the peak point location, before extracting tPeak, z can be... n The sequence is subjected to a five-point cubic smoothing filter. Since the RLT transform has already significantly suppressed high-frequency components, a simple smoothing process can obtain an extremely smooth feature curve, ensuring the uniqueness and accuracy of feature extraction; S6: Substitute the peak time characteristic tPeak into the pre-established quantitative evaluation equation to realize the inversion of the pipe wall thickness d.

[0011] Preferably, the transmitting coil and the receiving coil are coaxially arranged. The parameters of the transmitting coil include an inner diameter r1, an outer diameter r2, and a height h1, and the parameters of the receiving coil include an inner diameter r3, an outer diameter r4, and a height h1. 2。

[0012] Preferably, step one further includes solving the analytical model using the truncated region expansion method. By introducing a first-order Bessel function of the first kind in the radial direction to construct the characteristic function expansion, and applying electromagnetic field continuity boundary conditions at the interface of different media, the analytical expression of the induced voltage of the receiving coil in the time domain is derived.

[0013] Preferably, in step two, the sampling frequency fs covers the early, middle, and late response stages of the pulsed eddy current signal, and the discrete sequence U... m (n) and U r The length of (n) is M.

[0014] Preferably, the normalization formula in step three is: ; ; Where k is the index variable of the sampling sequence.

[0015] Preferably, the adjustment coefficients a and b range from 0.5 to 2.0.

[0016] Preferably, the process of extracting the peak time feature tPeak in step five includes: processing the signal sequence z... n Polynomial interpolation fitting is performed, and the peak position is locked by finding the point where the derivative is zero.

[0017] Preferably, the excitation signal of the pulsed eddy current probe in step one is a square wave. Using inverse discrete Fourier transform, the time-domain induced voltage signal of the pulsed eddy current is obtained. The expression for the induced voltage ΔU in the receiving coil under harmonic excitation is: ; ; Where j is the imaginary unit, ω is the angular frequency of the harmonic, I is the amplitude of the harmonic current, μ0 is the free permeability; Ns is the number of summation terms; α i l1 is the i-th eigenvalue of the characteristic equation; l1 is the lift-off. S(α) is the lift-off coefficient; i R' is the coil coefficient. 4,3 (α i () is the generalized reflection coefficient.

[0018] Preferably, the generalized reflectance coefficient R' 4,3 (α i The calculation formula for ) is as follows: ; ; ; ; ; Where (l2-l1) is the coil height, r1 and r2 represent the inner and outer radii of the coil, respectively, n is the number of coil turns, and the subscripts T and R represent the excitation coil and the receiving coil, respectively; d1-d2 and d2-d3 represent the thickness of the pipe wall and the cladding layer, respectively; k is the number of layers, R k+1,k (k=1,2,3) represents the reflection coefficient between the (k+1)th layer and the kth layer, R' k+1,k (k=1,2,3) represents the generalized reflection coefficients from layer 1 to layer k, R' 2,1 =R 2,1 J1(αr) and Y1(αr) are the Bessel functions of the first and second kind, respectively, and β k μ is the longitudinal wave number of the electromagnetic wave. rk and σ k denoted as , respectively, the magnetic permeability and electrical conductivity of the k-th layer.

[0019] Preferably, the quantitative evaluation equation in step six is ​​a linear fitting equation: ; ; ; Where tPeak is the peak time of the preprocessed signal, Peak is the peak value of the preprocessed signal, and e r It is a relative error, (d1-d2) actual d1 represents the actual thickness, and d2 represents the calculated thickness.

[0020] Compared with existing technologies, this invention provides a method for pulsed eddy current signal preprocessing and thickness evaluation based on relative logarithmic transformation, which has the following advantages: 1. This pulsed eddy current signal preprocessing method based on relative logarithmic transform (RLT) achieves efficient enhancement of weak pulsed eddy current signals by introducing the RLT algorithm. Because the RLT transform utilizes the high sensitivity of the logarithmic function in the small numerical region, it highlights the late response components that were originally submerged by noise in the original induced voltage signal. Experimental data shows that, under the same noise environment, the signal-to-noise ratio of the RLT-preprocessed signal is improved by more than 15 dB compared to the original signal, solving the problem of difficult extraction of deep defect signals in ferromagnetic pipeline inspection.

[0021] 2. The peak time feature tPeak extracted by this pulse eddy current signal preprocessing method based on relative logarithmic transform exhibits extremely strong anti-lift-off interference capability. In the inspection of pipes with cladding layers, the unevenness of the cladding layer thickness often leads to severe lift-off effects, rendering traditional amplitude-based features ineffective. This invention eliminates the influence of amplitude fluctuations on the time dimension through the nonlinear mapping of RLT transform, ensuring that the linearity of wall thickness assessment remains above 0.999 as the lift-off distance increases from 0 mm to 40 mm, greatly expanding the applicability of pulse eddy current detection technology.

[0022] 3. Significantly improves the accuracy of quantitative wall thickness assessment. Through RLT transform processing, feature point drift caused by environmental interference is effectively suppressed. Simulation and experimental results verify that the relative error of wall thickness inversion using the method of this invention is controlled within 0.25%, far superior to existing differential signal peak-time method (approximately 2.1%) or double logarithmic coordinate intercept method, providing more reliable data support for pipeline safety evaluation.

[0023] 4. The method described in this invention has low algorithmic complexity and high computational efficiency. The RLT transformation only involves basic arithmetic and logarithmic operations, without involving complex iterative processes or large-scale matrix decomposition. Therefore, it can be integrated into portable embedded detection devices to support real-time online monitoring and rapid evaluation in industrial settings.

[0024] 5. This invention enhances the algorithm's adaptability to pipes of different materials and diameters through normalization and the introduction of weighting coefficients a and b. By adjusting the weighting coefficients, the sensitivity to defects within a specific depth range can be optimized, demonstrating high flexibility and practical engineering value. Attached Figure Description

[0025] Figure 1 The physical model and probe structure diagram for pulsed eddy current detection of ferromagnetic pipes with coating provided by the present invention are shown below. Figure 2 A flowchart of the pulsed eddy current signal preprocessing and thickness evaluation method based on relative logarithmic transform (RLT) provided by the present invention; Figure 3 A comparison diagram of the waveforms of the original induced voltage signal and the preprocessed signal after RLT transformation provided by the present invention; Figure 4 A fitting diagram of the quantitative relationship between pipe wall thickness and RLT signal characteristics provided by the present invention; Figure 5 The stability analysis diagram of RLT signal features at different lift-off distances provided by this invention.

[0026] Figure 3 (a) in the diagram represents the original signal. Figure 3 (b) in the diagram represents the RLT-transformed signal; Figure 4 In the diagram, (a) represents the linear fit at the peak time. Figure 4 (b) in the figure represents the quadratic fitting of the peak amplitude; Figure 5 (a) in the figure represents the robustness verification at peak time. Figure 5 (b) in the figure is the sensitivity verification of the peak amplitude. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] In industrial production and energy transportation, oil, gas, and chemical pipelines are typically exposed to harsh external environments. To reduce heat loss and prevent external corrosion, these pipelines, made of ferromagnetic carbon steel, are usually covered with coatings of varying thicknesses, such as insulation cotton or foam materials. However, the presence of these coatings poses a significant challenge to pipeline wall thickness measurement. Traditional ultrasonic testing methods require peeling off the coating, which is not only costly but also poses a significant safety risk in high-temperature operating environments. Pulsed eddy current testing technology generates a broadband pulsed magnetic field through a transmitting coil. This magnetic field penetrates the coating and induces diffused eddy currents in the ferromagnetic pipe wall. By capturing the induced voltage signal generated by the eddy currents through a receiving coil, non-destructive thickness assessment without removing the coating is achieved. However, the lift-off distance variation caused by the coating can produce severe lift-off interference, and the signal becomes extremely weak in the later stages, easily drowned out by system noise. This embodiment provides a pulsed eddy current signal preprocessing and thickness assessment method based on relative logarithmic transformation, which solves the above-mentioned technical problems from the perspectives of signal enhancement and feature extraction.

[0029] Based on the above analytical model, this application analyzes the performance of the proposed relative logarithmic transform signal processing method and its preprocessed signal's peak value and peak time in wall thickness assessment, and further quantitatively evaluates its robustness to the lift-off effect. In the simulation, the excitation signal is a square wave current with an amplitude of 4A, a duty cycle of 50%, and a frequency of 1Hz. The probe consists of an excitation coil and a receiving coil, and their detailed geometric parameters are summarized in Table 1.

[0030] Table 1 Probe Parameters

[0031] The technical solution of this application will be further described below with reference to specific embodiments.

[0032] Combination Figure 1 As shown, this embodiment first constructs an accurate physical model for pulsed eddy current detection of a coated ferromagnetic pipe. This model simplifies the complex engineering site into a four-layer dielectric structure. The first layer is the internal air region, representing the cavity inside the pipe; the second layer is the ferromagnetic pipe wall, which has a thickness *d*, electrical conductivity, and relative magnetic permeability; thickness reduction defects are equivalent to a uniform reduction in the thickness of this layer; the third layer is the coating layer, whose thickness corresponds to the probe's lift-off distance, and this layer is typically composed of non-conductive and non-magnetic materials; the fourth layer is the air region where the pulsed eddy current probe is located. The pulsed eddy current probe is arranged above the coating layer and includes a transmitting coil and a receiving coil. The geometric parameters of the transmitting coil are defined as inner diameter *r1*, outer diameter *r2*, and height *h1*, and the geometric parameters of the receiving coil are defined as inner diameter *r3*, outer diameter *r4*, and height *h2*. In actual detection, the transmitting and receiving coils are coaxially arranged and aligned at the bottom to ensure the symmetry of the magnetic field distribution.

[0033] To obtain an accurate theoretical benchmark, this embodiment uses the truncated region expansion method to solve for the electromagnetic field distribution of the model in step one. By separating the vector magnetic potential variables in cylindrical coordinates and applying boundary conditions for continuous tangential field components at each layer interface, the harmonic induced voltage in the receiving coil is derived. Since pulse excitation can be regarded as the superposition of countless harmonic components, the frequency domain response is converted into a time domain induced voltage signal U(t) using the inverse discrete Fourier transform. This analytical model provides a noise-free, clean reference for the verification of subsequent signal processing algorithms.

[0034] Combination Figure 2 The illustrated method flow, in step two, involves performing signal acquisition on the actual pipe under test. First, a reference induced voltage signal Ur(t) is acquired by testing a standard reference pipe with a known wall thickness. Then, a test induced voltage signal Um(t) is acquired by testing a pipe with potential wall thinning defects. To capture the rich spectral information contained in the pulsed eddy current signal, the sampling frequency is set to 100kHz, ensuring complete recording from the early response in microseconds to the late response in milliseconds. The acquired continuous signal is converted into discrete sequences Ur(n) and Um(n) of length M by a 16-bit high-resolution A / D converter.

[0035] In step three, signal amplitude normalization is performed. Due to power fluctuations at the detection site, differences in the coupling state between the probe and the pipe surface, and gain drift of the amplifier circuit, the absolute amplitudes of the original signals are often not directly comparable. By finding the maximum absolute value in the sequence, Ur(n) and Um(n) are divided by their respective maximum values ​​to obtain the normalized sequence p. n and q nThis operation maps the signal scale uniformly to a dimensionless range of 0 to 1, ensuring a consistent input reference for subsequent relative logarithmic transformation algorithms and eliminating errors caused by differences in system range.

[0036] In step four, this embodiment executes the core Relative Logarithmic Transform (RLT) algorithm. The physical logic of this algorithm lies in the fact that the attenuation of the pulsed eddy current signal in ferromagnetic materials follows a logarithmic law, and subtle differences in wall thickness information manifest as extremely small amplitude deviations in the later stages of the signal response. This is achieved by constructing a transform sequence. This achieves nonlinear amplification of these minute differences. In the specific application of this embodiment, the adjustment coefficients a=1 and b=1 are set. At this time, when the test signal q n With reference signal p n When completely identical, z n It is always equal to 0; when the pipe wall thickness is reduced, q n Deviation from p n At that time, for several terms It will produce a rapid and significant response. Because the logarithmic function has a very large slope near 0, this transformation effectively extracts the thickness features hidden in the microvolt-level signal. Meanwhile, the front-end weighting term (p...) n -q n It acts as a low-pass filter, automatically attenuating the gain in the very early and very late stages of the signal where noise dominates, thereby enhancing the effective signal while suppressing high-frequency random noise.

[0037] Combination Figure 3 The simulation results shown verify that Figure 3 Figure (a) shows the original pulsed eddy current induced voltage signal. It can be seen that when the pipe wall thickness d changes from 8 mm to 20 mm, the voltage curves corresponding to different thicknesses almost overlap, and in the later stage of the signal (approximately 0.05 s), the signal amplitude approaches zero, making the thickness difference difficult to distinguish visually. However, after the RLT transformation in this embodiment, as shown... Figure 3 As shown in (b) above, the generated preprocessed signal z n The curves exhibit a clear single-peak characteristic. Curves of different thicknesses show significant differentiation in peak amplitude and time to peak, and the curve waveforms are smooth without obvious high-frequency spikes, demonstrating the noise suppression effect of this method.

[0038] In step five, this embodiment extracts two key features from the preprocessed signal: peak time tPeak and peak amplitude Peak. A high-order polynomial fitting algorithm is then used to fit z... n The top of the curve is locally reconstructed to precisely pinpoint the time point where the derivative is zero. Combined with... Figure 4 (a) and Figure 4The fitting analysis in (b) of this embodiment revealed an excellent linear relationship between the peak time tPeak and the pipe thickness, with a linear regression coefficient R² exceeding 0.999. This was achieved by establishing a fitting equation. This enabled a preliminary modeling of the wall thickness. In contrast, the peak amplitude (Peak) exhibits a quadratic function relationship with the thickness, and its fitting accuracy is slightly lower than that of the peak time.

[0039] To further verify the robustness of this feature to the lift-off effect caused by the coating layer, the anti-interference analysis in step six was performed. Combined with... Figure 5 As shown, when the lift-off distance increases from 0 mm to 40 mm (in 10 mm increments), the traditional induced voltage characteristic fluctuates drastically due to the weakened magnetic coupling. However, as... Figure 5 As shown in (a) of this embodiment, the peak time tPeak extracted based on RLT transform exhibits remarkable consistency under different lift-off conditions. For the same wall thickness d, the tPeak data points corresponding to different lift-off distances almost overlap, as shown in (a). Figure 5 As shown in (b) in the figure. This demonstrates that the RLT transform successfully removes the lift-off interference in the amplitude dimension while retaining the time dimension information reflecting the eddy current diffusion process.

[0040] In practical industrial applications, such as monitoring the wall thickness of an oil pipeline in a chemical plant, the inspector places a pulsed eddy current probe on the surface of a pipeline with a 30mm thick insulation layer (coating). First, a reference signal is acquired on a known 20mm thick intact pipe section. Then, the probe is moved to scan the entire pipeline. The processor inside the inspection equipment executes steps two through five in real time. When the probe passes through an area where the wall thickness has been reduced to 16mm due to internal erosion, the z-axis generated by the RLT transform... n The curve has shifted. The extracted peak time is 0.038s. Substitute this value into the pre-stored quantitative evaluation equation. The calculated predicted thickness is 15.96 mm. The relative error between this inversion result and the actual thickness is only 0.25%.

[0041] The signal processing method based on relative logarithmic transformation described in this embodiment achieves nonlinear gain for weak signals through logarithmic ratio calculation, enabling in-depth mining of deep information in ferromagnetic materials. This method not only performs excellently in theoretical analytical models but also exhibits extremely high stability when faced with experimental data containing real noise. By combining relative logarithmic transformation with feature extraction algorithms, this invention achieves accurate and stable quantitative assessment of the wall thickness of coated pipes under conditions of strong interference removal and high background noise, providing a key technical means for preventative maintenance of industrial pipelines. The steps and parameter settings shown in this embodiment are based on the results of extensive simulation and experimental optimization, possessing strong operability and promotional value. For pipes of different materials, such as stainless steel or aluminum pipes, only the fitting coefficients in step six need to be adjusted for rapid application transfer, demonstrating good versatility.

[0042] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for preprocessing and thickness assessment of pulsed eddy current signals based on relative logarithmic transform, characterized in that, The method includes the following steps: Step 1: Establish a physical model for pulsed eddy current detection of a ferromagnetic pipe with a cladding layer. The physical model includes an internal air region, a ferromagnetic pipe wall, and a non-conductive and non-magnetic cladding layer. A pulsed eddy current probe containing a transmitting coil and a receiving coil is set above the cladding layer. Step 2: Use the pulsed eddy current probe to acquire the reference induced voltage signal U of the reference pipe. r (t) and the test induced voltage signal U of the pipeline under test. m (t), and perform digital sampling to obtain the discrete sequence U. m (n) and U r (n); Step 3: For the discrete sequence U m (n) and U r (n) Perform maximum value normalization on each signal to obtain the normalized reference signal sequence p. n and normalized test signal sequence q n ; Step 4: Construct a relative logarithmic transform operator for the normalized reference signal sequence p. n and normalized test signal sequence q n Perform nonlinear transformation to generate the transformed signal sequence z. n The expression for the relative logarithmic transformation operator is: ； Where a and b are preset adjustment coefficients; Step 5: Process the signal sequence z n Perform feature recognition and extract the signal sequence z n The time corresponding to the peak point of the curve is used as the peak time characteristic quantity tPeak; Step 6: Substitute the peak time characteristic tPeak into the pre-established quantitative evaluation equation to realize the inversion of the pipe wall thickness d.

2. The method for pulse eddy current signal preprocessing and thickness evaluation based on relative logarithmic transform according to claim 1, characterized in that, The transmitting coil and the receiving coil are coaxially arranged. The parameters of the transmitting coil include inner diameter r1, outer diameter r2 and height h1, and the parameters of the receiving coil include inner diameter r3, outer diameter r4 and height h2.

3. The method for preprocessing and thickness assessment of pulsed eddy current signals based on relative logarithmic transformation according to claim 1, characterized in that, Step one also includes solving the analytical model using the truncated region expansion method, constructing the characteristic function expression through the first-order Bessel function of the first kind, and applying the electromagnetic field continuity boundary condition at the interface of different media to derive the analytical expression of the induced voltage of the receiving coil in the time domain.

4. The method for pulse eddy current signal preprocessing and thickness evaluation based on relative logarithmic transform according to claim 1, characterized in that, In step two, the sampling frequency fs covers the early, middle, and late response stages of the pulsed eddy current signal, and the discrete sequence U... m (n) and U r The length of (n) is M.

5. The method for pulse eddy current signal preprocessing and thickness evaluation based on relative logarithmic transformation according to claim 1, characterized in that, The normalization formula in step three is: ； ； Where k is the index variable of the sampling sequence.

6. The method for preprocessing and thickness assessment of pulsed eddy current signals based on relative logarithmic transform according to claim 1, characterized in that, The adjustment coefficients a and b range from 0.5 to 2.

0.

7. The method for preprocessing and thickness assessment of pulsed eddy current signals based on relative logarithmic transform according to claim 1, characterized in that, The process of extracting the peak time feature tPeak in step five includes: processing the signal sequence z... n Polynomial interpolation fitting is performed, and the peak position is locked by finding the point where the derivative is zero.

8. The method for preprocessing and thickness assessment of pulsed eddy current signals based on relative logarithmic transformation according to claim 1, characterized in that, In step one, the excitation signal of the pulsed eddy current probe is a square wave. Using the inverse discrete Fourier transform, the time-domain induced voltage signal of the pulsed eddy current is obtained. The expression for the induced voltage ΔU in the receiving coil under harmonic excitation is: ； ； Where j is the imaginary unit, ω is the angular frequency of the harmonic, I is the amplitude of the harmonic current, μ0 is the free permeability; Ns is the number of summation terms; α i l1 is the i-th eigenvalue of the characteristic equation; l1 is the lift-off. S(α) is the lift-off coefficient; i R' is the coil coefficient. 4,3 (α i () is the generalized reflection coefficient.

9. The method for preprocessing and thickness assessment of pulsed eddy current signals based on relative logarithmic transform according to claim 8, characterized in that, Generalized reflection coefficient R' 4,3 (α i The calculation formula for ) is as follows: ； ； ； ； ； Where (l2-l1) is the coil height, r1 and r2 represent the inner and outer radii of the coil, respectively, n is the number of coil turns, and the subscripts T and R represent the excitation coil and the receiving coil, respectively; d1-d2 and d2-d3 represent the thickness of the pipe wall and the cladding layer, respectively; k is the number of layers, R k+1,k (k=1,2,3) represents the reflection coefficient between the (k+1)th layer and the kth layer, R' k+1,k (k=1,2,3) represents the generalized reflection coefficients from layer 1 to layer k, R' 2,1 =R 2,1 J1(αr) and Y1(αr) are the Bessel functions of the first and second kind, respectively, and β k μ is the longitudinal wave number of the electromagnetic wave. rk and σ k denoted as , respectively, the magnetic permeability and electrical conductivity of the k-th layer.

10. The method for preprocessing and thickness assessment of pulsed eddy current signals based on relative logarithmic transformation according to claim 1, characterized in that, The quantitative evaluation equation in step six is ​​a linear fitting equation: ； ； ； Where tPeak is the peak time of the preprocessed signal, Peak is the peak value of the preprocessed signal, and e r It is a relative error, (d1-d2) actual d1 represents the actual thickness, and d2 represents the calculated thickness.

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