An adaptive piecewise filtering method based on relative log transformation

Abstract

This invention relates to the field of electromagnetic nondestructive testing (NDT) technology, specifically disclosing an adaptive piecewise filtering method based on relative logarithmic transformation. The method includes establishing an analytical model for pulsed eddy current testing, equating the pipe structure to a multi-layered flat plate structure and constructing a testing platform. Pulse excitation is applied to the pipe under test through the testing platform, and induced voltage signals are acquired to obtain a detection signal and a reference signal. The detection and reference signals are then discretely sampled, normalized, and subjected to relative logarithmic transformation to obtain a preprocessed signal. The signal is then segmented according to its time-domain variation characteristics, and a filtering strategy is adaptively selected based on the signal characteristics of each segment interval for filtering. This invention effectively amplifies the difference between the detection and reference signals, making the signal response to pipe wall thickness changes more apparent. While suppressing noise, it preserves signal abrupt changes and local detail information, providing a high-quality data foundation for subsequent defect identification and quantitative assessment.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic nondestructive testing technology, specifically to an adaptive piecewise filtering method based on relative logarithmic transformation. Background Technology

[0002] Pulsed eddy current testing (PED) technology, as a crucial method for non-destructive testing and defect detection of materials, has been widely applied in structural health monitoring in fields such as aerospace, petrochemicals, energy and power, and municipal infrastructure. This technology utilizes a pulsed excitation source to induce eddy current responses within the tested component. By analyzing the time-domain or frequency-domain characteristics of the induced voltage signal, it achieves non-contact detection of internal defects and corrosion thinning in metal components, playing a key role in ensuring equipment operational safety and extending service life. Among these methods, PED, as an important non-destructive testing approach, has gained widespread application in pipeline wall thickness assessment and defect location due to its high sensitivity to ferromagnetic materials, penetration capability into coated components, and rich time-domain response information.

[0003] Among them, pulsed eddy current testing technology generates a transient electromagnetic response inside the tested metal component by applying a step-type or square-wave pulse signal to the excitation coil. The induced voltage signal acquired by the receiving coil contains rich defect information and structural features. However, in practical engineering applications, the complexity of on-site conditions and the diversity of surface conditions of the tested components inevitably make the acquired signal susceptible to various noise interferences. During online tubular eddy current testing, instrument vibration causes random disturbance noise, and non-defect factors such as deposits, scale layers, and centralizers on the tube surface generate additional interference signals. These noises superimpose with the useful signal in the time and frequency domains, leading to a more complex test curve. Although analog filtering circuits are usually used to preprocess noise during the data acquisition stage, existing analog preprocessing methods are insufficient to completely eliminate noise due to its diverse sources and characteristics. In addition, pulsed eddy current detection signals usually have a wide dynamic range. The signal amplitude is high and changes drastically in the early stage of excitation, and then gradually decays into the late response stage. In this stage, the signal amplitude is weak, and the response characteristics of small defects are often submerged in background noise. Therefore, noise problems seriously restrict the accuracy of subsequent feature extraction and defect identification.

[0004] To improve signal quality and extract effective defect feature information, researchers both domestically and internationally have proposed various filtering methods, mainly including moving average filtering and first-order lag filtering based on time-domain processing, Kalman filtering based on state estimation, and fast Fourier transform filtering based on frequency-domain analysis. Moving average filtering achieves smooth noise reduction by averaging neighborhood data, but the choice of window size makes it difficult to balance noise reduction effectiveness with signal fidelity. First-order lag filtering suppresses high-frequency noise by introducing an inertial element, but this leads to a decrease in signal response speed. While Kalman filtering can perform optimal estimation based on the system model, it struggles to guarantee filtering effectiveness when model parameters are uncertain or noise statistical characteristics are unknown. Frequency-domain filtering converts the signal to the frequency domain, performs bandpass or low-pass processing, and then reconstructs the time-domain signal; however, the wide-spectrum characteristics of pulsed eddy current signals make it difficult for frequency-domain filtering to accurately distinguish noise frequencies from effective signal frequencies. More importantly, while suppressing noise, these traditional filtering methods inevitably weaken or even lose signal abrupt change features, leading to the loss of local detail information or a decrease in curve resolution, which is particularly detrimental to the identification of minute defects. Existing unified filtering strategies are difficult to adapt to the significant differences in amplitude levels, rates of change, and signal-to-noise ratio distributions of pulsed eddy current signals in different time intervals, resulting in both over-filtering and under-filtering problems. This makes it difficult to meet the urgent need for detailed analysis of complex detection signals. There is a pressing need for a new filtering method that can balance noise suppression and feature preservation. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide an adaptive piecewise filtering method based on relative logarithmic transformation, which can effectively solve the technical problems of existing traditional filtering methods in suppressing noise in pulse eddy current detection signals, such as weakening of signal abrupt change characteristics, loss of local detail information, and decreased curve resolution.

[0006] To achieve the above objectives, the present invention provides the following technical solution: an adaptive piecewise filtering method based on relative logarithmic transform, comprising the following steps: Step 1: Establish an analytical model for pulsed eddy current detection. The pipe structure with the coating layer is equivalent to a multi-layer flat plate structure and a detection platform is constructed. Pulse excitation is applied to the pipe under test through the detection platform and the induced voltage signal is collected to obtain the detection signal and the reference signal. Step 2: Obtain the preprocessed signal. Discretely sample and normalize the detection signal and the reference signal, and introduce a relative logarithmic transformation to obtain the preprocessed signal. Step 3: Perform adaptive segmented filtering. The signal is segmented according to the time-domain variation characteristics of the preprocessed signal, and a filtering strategy is adaptively selected based on the signal characteristics of each segment interval for filtering.

[0007] Preferably, in step 1, the specific process of establishing the analytical model for pulsed eddy current detection includes: A pulsed eddy current analytical model of a three-layer flat plate structure is established, consisting of an air layer, a pipe wall layer, and a lift-off layer from bottom to top. The pulsed eddy current probe is located above the three-layer flat plate structure. Based on the axisymmetry of the model, a cylindrical coordinate system is adopted. A current-mode time-domain signal in the form of a square wave is used as the excitation signal; Perform a Fourier transform on the excitation signal and decompose it into multiple harmonic components. Calculate the expression for the induced voltage signal of each harmonic. ; ; In the formula, The imaginary unit; For the first The angular frequency of the harmonic; The amplitude of the harmonic current; The vacuum permeability; for The number of and It is a constant. Assign a number to each constant; This refers to the lift-off distance between the pulsed eddy current probe and the pipe surface. The lift-off coefficient is used to characterize the effect of probe lift-off on the induced voltage; For the first The coil coefficient of each characteristic quantity; The generalized reflection coefficient for the third to fourth layers; The time-domain induced voltage signal is obtained by performing a discrete inverse Fourier transform on the induced voltage signal of each harmonic. ; In the formula, Indicates a square wave excitation signal. Indicates the amplitude of the excitation signal. The frequency of the excitation signal is represented. After Fourier transform, the square wave signal can be equivalently represented as a superposition of multiple sinusoidal harmonic components. The harmonic index is denoted as , and any harmonic component is denoted as . ; The induced voltage of the receiving coil The time-domain expression is: ; Determine the expression for the coil coefficients and derive the characteristic quantities; Coil coefficient The expression is: ; In the formula, ; Indicates the coil height; and These represent the inner and outer radii of the coil, respectively. Number of coil turns; subscript and These represent the excitation coil and the receiving coil, respectively. The expression for calculating the generalized reflection coefficient is: ; ; In the above formula, ; Number of floors; , These represent the thicknesses of the pipe wall and the cladding layer, respectively. For the first Layer and first Reflection coefficient between layers; For the 1st to the 1st The generalized reflectance coefficient of the layer, ; and These are the first and second type Bessel functions, respectively; The longitudinal wave number of the electromagnetic wave; and The first The magnetic permeability and electrical conductivity of the layer.

[0008] Preferably, in the three-layer flat plate structure, the first layer represents the air in the pipe, the second layer represents the pipe wall, and the third layer represents the lift-off layer; large-area corrosion defects in the pipe wall are simplified into an equivalent region with uniform thinning; a pulse eddy current probe composed of a hollow excitation coil and a receiving coil arranged coaxially is arranged in the space above the structure.

[0009] Preferably, in step 2, the specific process of obtaining the preprocessed signal includes: Select the reference area and the detection area of ​​the specimen, and obtain the reference signal and the detection signal respectively; The reference signal and the detection signal are sampled at equal time intervals and converted into a discrete sequence with a preset number of points; The discrete sequence is normalized to obtain the normalized signal sequence; The signal is processed by introducing a relative logarithmic transform, calculating the logarithmic ratio and performing weighted modulation to obtain a preprocessed signal.

[0010] Preferably, the discrete sequence is normalized to eliminate the influence of amplitude scale differences. The normalization process employs a mathematical transformation method that maps the signal amplitude to a uniform interval. The normalized signal sequence... and It can eliminate the absolute amplitude difference between the detected signal and the reference signal; it introduces a relative logarithmic transform to process the signal, first calculating the logarithmic ratio of the two signals at each sampling point to characterize the relative proportional relationship, and then... and The logarithmic term is modulated using weights, and the contributions of the two parts are adjusted by weighting with preset coefficients. Finally, the weighted results are combined to obtain the preprocessed signal. .

[0011] Preferably, in step 3, the specific process of performing adaptive piecewise filtering includes: The signal is segmented into multiple time intervals based on the time-domain variation characteristics of the preprocessed signal. Extract the amplitude level, rate of change, and noise distribution characteristics of the signal within each segment interval; The filtering strategy is classified based on the signal characteristics, and the corresponding filtering method is applied to different types of intervals.

[0012] Preferably, the signal is segmented according to the time-domain variation characteristics of the preprocessed signal, dividing the signal into multiple time intervals. Each segment interval corresponds to a different stage of signal evolution. The segment threshold is determined based on the calculation result of the preset derivative of the signal amplitude. The selection of segment points should ensure that the signal in each segment interval has relatively consistent statistical characteristics.

[0013] Preferably, for each segmented interval, the amplitude level, rate of change, and noise distribution characteristics of the signal within that interval are extracted to characterize the signal characteristics of that interval. The amplitude level is characterized by calculating the mean of the absolute value of the signal within the interval, the rate of change is characterized by calculating the standard deviation of the first-order difference of the signal within the interval, and the noise distribution characteristics are characterized by calculating the energy proportion of the high-frequency components of the signal within the interval.

[0014] Preferably, the filtering strategy is classified and selected according to the signal characteristics of each segment interval. When the signal is in an interval with high amplitude and stable change, it is determined as the first type interval and weak filtering or no filtering is performed to retain signal details. When the signal is in a transitional interval, it is determined as the second type interval and mean filtering or smoothing filtering is used to reduce random fluctuations. When the signal is in an interval with low amplitude and high noise ratio, it is determined as the third type interval and threshold filtering is used to suppress high-frequency noise interference.

[0015] Preferably, for each sampling point, the corresponding filtering strategy is adaptively selected according to the signal characteristics of its segment interval, thereby realizing the synergistic effect of multiple filtering methods. Through the segmented adaptive filtering mechanism, different signal intervals are matched with different filtering intensities and processing methods, effectively suppressing noise while preserving the effective feature information of the original signal to the greatest extent. At the boundary of each segment interval, a weighted transition method is used for processing. The transition weight is determined according to the distance between the sampling point and the boundary center to ensure the continuity of the overall filtered signal. After the filtering processing of each segment interval is completed, the filtered output is spliced ​​into a complete filtered signal sequence in chronological order.

[0016] Compared with existing technologies, this invention provides an adaptive piecewise filtering method based on relative logarithmic transformation, which has the following advantages: 1. This invention preprocesses the detection signal by introducing relative logarithmic transformation and combines it with piecewise adaptive thresholding and multi-strategy filtering methods. This effectively suppresses high-frequency random noise in pulsed eddy current signals, and significantly improves the noise amplification problem in the low amplitude region of the late stage of the signal, thereby improving the overall smoothness and stability of the signal. The relative logarithmic transformation is based on the relative relationship between the detection signal and the reference signal and can automatically cancel some systematic noise interference, thereby improving the signal-to-noise ratio.

[0017] 2. This invention segments the signal according to its time-domain evolution characteristics and adaptively selects threshold filtering, mean filtering, or smoothing filtering for different intervals to match different filtering intensities for different signal stages. While effectively removing noise, it avoids the weakening of effective feature information by traditional uniform filtering methods and improves feature fidelity. The adaptive segmentation mechanism can dynamically adjust the filtering strategy according to the actual characteristics of the signal, overcoming the defect that fixed filtering parameters are difficult to adapt to the time-varying characteristics of the signal.

[0018] 3. This invention effectively amplifies the difference between the detection signal and the reference signal by constructing a signal enhancement mechanism based on relative logarithmic transformation, making the signal response to changes in pipe wall thickness more obvious. The multi-strategy collaborative filtering framework fully preserves the signal's abrupt change characteristics and local detail information while ensuring noise suppression, providing a high-quality data foundation for subsequent defect identification and quantitative assessment. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the pulsed eddy current analytical model in this invention; Figure 2 This is a schematic diagram of the preprocessing and filtering processes based on relative logarithmic transformation in this invention; Figure 3 (a) in the figure is a schematic diagram of the preprocessed signal based on relative logarithmic transformation simulated in this invention; Figure 3(b) in the figure is a schematic diagram of the adaptive piecewise filtering based on relative logarithmic transformation simulated in this invention; Figure 4 (a) in the figure is a schematic diagram of the original signal of the experimental pulsed eddy current in this invention; Figure 4 (b) in the figure is a schematic diagram of the preprocessed signal based on relative logarithmic transformation in the experiment of this invention; Figure 4 (c) in the figure is a schematic diagram of the adaptive piecewise filtering based on relative logarithmic transformation in the experiment of this invention. Detailed Implementation

[0020] 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.

[0021] This invention discloses an adaptive piecewise filtering method based on relative logarithmic transform, which specifically includes the following process: The model employs a three-layer structure: an air layer, a pipe wall layer, and a lift-off layer, to represent the equivalent cladding pipe. A cylindrical coordinate system is established based on axisymmetry, where z=0 coincides with the upper surface of the third layer, and the z-axis is aligned with the coil's axis of symmetry. This model simplifies large-area corrosion defects into uniformly thinned regions, facilitating subsequent analysis and calculations.

[0022] The pulsed eddy current probe consists of a coaxially arranged hollow excitation coil and a receiving coil, located in the space above a multi-layered structure. It is responsible for generating electromagnetic excitation and acquiring induced voltage signals. The detection platform includes a detection module that generates pulse excitation signals and acquires induced voltage responses, and an analysis module that processes the acquired signals, extracts features, and performs parameter inversion calculations. The two modules are connected via signal transmission lines to achieve data interaction.

[0023] Next, an analytical model of pulsed eddy current needs to be established. The model uses a three-layer flat plate structure, an air layer, a pipe wall layer, and a lift-off layer to represent the pipe structure. The probe is placed on top of the structure, and a cylindrical coordinate system is established based on axisymmetry.

[0024] Then, based on the probe's geometry, material properties, and operating frequency, the inductance, resistance, and mutual inductance parameters of the coil are determined, and the electromagnetic coupling equation between the probe and the flat plate structure is established.

[0025] The excitation signal is a square wave current-type time-domain signal generated by the signal generator module of the pulse eddy current detection platform. The amplitude of the square wave signal is determined by the output voltage amplitude of the signal generator, and the frequency is determined by the pulse repetition frequency. At the rising and falling edges of the square wave signal, due to the abundance of high-frequency components, rich harmonic responses are excited, which contain information about pipeline defects.

[0026] The detection module of the pulsed eddy current detection platform amplifies the square wave excitation signal through a power amplifier and applies it to the excitation coil. Simultaneously, it acquires the induced voltage signal from the receiving coil through a high-speed analog-to-digital converter. The detection module includes components such as a signal generator, power amplifier, receiving amplifier, and analog-to-digital converter, realizing the generation and amplification of the excitation signal, as well as the acquisition and digitization of the response signal.

[0027] The analysis module performs digital filtering, feature extraction, and parameter inversion on the acquired induced voltage signal, and outputs the processing results through a display or communication interface.

[0028] The excitation signal is in the form of a square wave, and its specific parameters include amplitude, frequency, and duty cycle. The amplitude determines the strength of the excitation magnetic field and is usually set to a fixed value in the range of 5-20A; the frequency is determined by the pulse repetition frequency and is usually between 10-100Hz; the duty cycle affects the signal-to-noise ratio and detection depth and is usually set to 50%.

[0029] Please refer to Figures 1-4 This embodiment proposes an adaptive piecewise filtering method based on relative logarithmic transform. By performing piecewise feature analysis on the preprocessed signal and comprehensively considering information such as amplitude level, rate of change, and noise distribution within each interval, an adaptive filtering strategy selection mechanism is constructed to achieve differentiated processing for different signal intervals. While effectively suppressing noise, it preserves the signal's abrupt change characteristics and local detail information as much as possible, thereby improving the overall signal-to-noise ratio and signal reconstruction accuracy. The method includes the following steps: S1. Establishing an analytical model for pulsed eddy current detection: In this model, the pipe structure with a coating layer is equivalent to a multi-layered flat plate structure, consisting of an air layer, a pipe wall layer, and a lift-off layer from bottom to top. Large-area corrosion defects in the pipe wall are simplified into uniformly thinned equivalent regions to facilitate model analysis and calculation. A pulsed eddy current probe, composed of a coaxially arranged hollow excitation coil and a receiving coil, is positioned in the space above the structure to acquire electromagnetic excitation and signal response. Based on this, a pulsed eddy current detection platform is constructed, and an experimental and signal processing system is built according to the analytical model. The platform mainly includes a detection module and an analysis module. The detection module generates pulse excitation signals and acquires the corresponding induced voltage response; the analysis module processes the acquired signals, extracts features, and performs parameter inversion calculations. The detection module and the analysis module are connected and interact with each other via a signal transmission line. S11. The pulsed eddy current analytical model has three layers. Specifically, the first layer represents the air in the pipe, the second layer represents the pipe wall, and the third layer represents the lift-off layer. The pulsed eddy current probe is located above the three-layer flat plate structure. Based on the axisymmetry of the model, a cylindrical coordinate system is adopted. ,in =0 coincides with the upper surface of the third layer. The axis coincides with the axis of symmetry of the coil; S12. The excitation signal is a current-type time-domain signal, and its waveform is in the form of a square wave. S13. Perform a Fourier transform on the excitation signal to decompose it into multiple harmonic components, where any one harmonic is denoted as . , Indicates the harmonic sequence number. Given time, and each harmonic component corresponding to a unique number; the expression for the induced voltage signal of each harmonic is: : (1) In the formula, The imaginary unit; For the first The angular frequency of the harmonic; The amplitude of the harmonic current; The vacuum permeability; for The number of and It is a constant. Assign a number to each constant; This refers to the lift-off distance between the pulsed eddy current probe and the pipe surface. The lift-off coefficient is used to characterize the effect of probe lift-off on the induced voltage; For the first The coil coefficient of each characteristic quantity; For the generalized reflection coefficient of the second to third layers, in actual calculations, the number of harmonic components is determined according to the calculation accuracy requirements and computational cost. Usually, taking the fundamental wave plus the first 10 to 20 odd harmonics can obtain an approximate result with sufficient accuracy. S14, Induced voltage signal for all harmonics Perform inverse discrete Fourier transform to obtain the time-domain induced voltage signal. The Fourier transform expression for the square wave excitation signal is as follows: (2) In the formula, Indicates a square wave excitation signal. Indicates the amplitude of the excitation signal. This represents the frequency of the excitation signal. After Fourier transform, the square wave signal can be equivalently represented as a superposition of multiple sinusoidal harmonic components. Let... For harmonic sequence numbers, when =1 corresponds to the fundamental frequency (first harmonic). =2 corresponds to the third harmonic. =3 corresponds to the fifth harmonic. =4 corresponds to the seventh harmonic, and so on for the others. In actual calculations, the number of harmonics involved in the decomposition can be determined based on the required accuracy and computational cost. The more harmonics, the closer the reconstructed waveform is to the original square wave signal. Any harmonic component is denoted as . .

[0030] The induced voltage of the receiving coil The time-domain expression is: (3) In the formula, The expression represents the total number of harmonics, indicating that the time-domain induced voltage signal is the result of a weighted superposition of each harmonic component, with the weighting coefficients determined by the Fourier expansion coefficients of the square wave signal.

[0031] S15. Further, the side of the two radial end faces of the coil closer to the cladding layer is called the proximal end face, and the side farther from the cladding layer is called the distal end face, and the distance between the proximal end faces of the two coils and the outer surface of the cladding layer is kept consistent; the coil coefficient in S13 The expression is: (4) In the formula, ; Indicates the coil height; and These represent the inner and outer radii of the coil, respectively. Number of coil turns; subscript and These represent the excitation coil and the receiving coil, respectively.

[0032] in, It can be derived from the following expression: (5) In the formula, It is a first-order Bessel function of the first kind. For calculation The radius of the required cutoff region, h, needs to be chosen with a trade-off between computational accuracy and efficiency, and is typically set to 2 to 5 times the outer radius of the coil. The distance from the near-end face of the excitation coil to the outer surface of the cladding layer is set to the same value to ensure that both coils receive the same electromagnetic field distribution. The far-end face of the coil is exposed to air, and the boundary conditions of this end face are treated as free space.

[0033] S16. Further, the generalized reflection coefficient The expression is obtained through the following equations (6)-(7); (6) (7) In the above formula, ; Number of floors; , These represent the thicknesses of the pipe wall and the cladding layer, respectively. For the first Layer and first Reflection coefficient between layers; For the 1st to the 1st The generalized reflectance coefficient of the layer, ; and These are the first and second type Bessel functions, respectively; The longitudinal wave number of the electromagnetic wave; and The first The magnetic permeability and electrical conductivity of the layer.

[0034] When electromagnetic waves propagate from the third layer to the fourth layer, reflection and transmission occur at the interface between the two layers. This reflection coefficient depends on the electromagnetic parameters of each layer, including permeability, conductivity, and layer thickness. By establishing a recursive relationship, the generalized reflection coefficient from any layer to the layers below it can be calculated layer by layer. [The last part, "conductivity," appears to be an incomplete sentence or a fragment and is left untranslated.]

[0035] The electromagnetic parameters of each layer determine the propagation characteristics of electromagnetic waves in different media: the air layer has high permeability and zero conductivity; the permeability and conductivity of the pipe wall layer are determined by the material; the cladding layer, as an insulating material, has a conductivity close to zero.

[0036] S2. Obtaining Preprocessed Signals: Perform pulsed eddy current testing on the test specimen and obtain its detection signals. Simultaneously, the reference signal corresponding to the defect-free specimen is obtained. For the detection signal and reference signal After sampling at equal time intervals, it is converted into an M-point discrete sequence. and For the discrete sequence and Normalization is performed to eliminate the influence of amplitude scale differences, resulting in a normalized signal sequence. and Based on this, a relative logarithmic transform is introduced to process the signal: at each sampling point n, the logarithmic ratio of the two signals is first calculated. ( / The normalized signal is used to characterize the relative change relationship between the detected signal and the reference signal; subsequently, the normalized signal is used to characterize the relative change relationship between the detected signal and the reference signal. and The logarithmic ratio is weighted and modulated, and the contributions of different parts are adjusted by weighting coefficients a and b. Finally, the weighted results are combined to obtain the transformation sequence. This serves as the preprocessed signal. The specific process includes the following steps: S21. Select a reference area and a test area for the specimen, and acquire reference signals and test signals respectively. Mark a certain area of ​​the specimen as the reference area. This area should be a defect-free area, and its material, structure, and size should be consistent with the area to be tested. When selecting the reference area, avoid structural discontinuities such as welds, elbows, and branch pipe connections to ensure the purity of the reference signal. Perform pulsed eddy current testing on the reference area to acquire the signal, which will be used as the reference signal. Other areas of the specimen are marked as inspection areas, which may contain corrosion defects, wall thickness variations, or other anomalies. Pulsed eddy current testing is performed on these inspection areas to acquire signals, which are then used as the detection signals. ; S22, The reference signal obtained in step S21 The detection signal obtained in step S21 After sampling a continuous signal at equal time intervals, it is converted into an M-point discrete sequence. and As shown in equations (8) and (9): (8) (9) The sampling interval should be chosen to ensure that the discrete sequence can fully reflect the time-domain characteristics of the original continuous signal, and the sampling frequency should meet the requirements of the Nyquist sampling theorem. The sampling interval Δt is determined as follows: First, estimate the highest frequency component fmax of the pulsed eddy current signal, usually determined based on the rise time of the excitation signal, typically 50kHz to 100kHz; then set the sampling frequency fs ≥ 2fmax, in practical applications often fs = (3 to 5) × 2fmax to obtain sufficient bandwidth margin; finally, calculate the sampling interval Δt = 1 / fs. The total sampling time T should cover the entire process from the start of excitation to the completion of signal attenuation, typically set to 1ms to 10ms depending on the pipe wall thickness and material. The total number of sampling points M is determined by the sampling frequency and the total sampling time, i.e., M = fs × T, typically ranging from 500 to 5000 sampling points.

[0037] S23, Discrete sequence and Normalization is performed to obtain the normalized signal sequence. and Its expression is: (10) (11) Where, q n The normalized detection signal sequence; p n The normalized reference signal sequence is used; after normalization, the amplitudes of both sequences are mapped to the [0,1] interval, eliminating the absolute amplitude difference between the detection signal and the reference signal, and only retaining their relative change relationship, providing a dimensionally consistent input sequence for subsequent relative logarithmic transformation.

[0038] S24. Introduce relative logarithmic transform to process the signal. Its expression is: at each sampling point, first calculate the logarithmic ratio of the two signals. ( / ), used to depict relative proportions; then respectively with and The logarithmic term is modulated as a weight, and the contributions of the two parts are adjusted by coefficients a and b; finally, the weighted results are combined to obtain the preprocessed signal. The expression is shown in equation (12): (12) The relative logarithmic transform effectively amplifies the difference between the detected signal and the reference signal, making the signal's response to changes in pipe wall thickness more pronounced. The weighting coefficients a and b are both positive real numbers, i.e., a>0, b>0, typically a=1, b=1, where the two components contribute equally. When a>b, the detected signal... contributes more to the transformation result; when a < b, the reference signal contributes more to the transformation result. In practical applications, a and b can be adjusted according to the noise level of the detected signal and the wall thickness change range to obtain the optimal differential amplification effect. When there is a wall thickness reduction in the detection area, the absolute value of will be less than , the logarithmic ratio is negative, and after weighted combination shows a negative shift; when there is a wall thickness increase in the detection area, shows a positive shift. This transformation is based on the relative relationship between the detected signal and the reference signal, which can effectively eliminate the common system error between the two signals and highlight the differential characteristics caused by the pipeline wall thickness change, so as to provide a preprocessed signal with higher signal-to-noise ratio and more significant characteristics for subsequent adaptive segmented filtering processing, and improve the accuracy and stability of defect identification and wall thickness quantitative evaluation.

[0039] S3. Perform adaptive segmented filtering on the preprocessed signal: After obtaining the preprocessed signal , the signal is segmented according to its time-domain change characteristics, and corresponding filtering methods are selected for adaptive processing according to the signal characteristics in different segmented intervals. Specifically, according to the amplitude level, change rate and noise distribution characteristics of the signal in each segmented interval, the filtering strategy is classified and selected: when the signal is in the interval with high amplitude and stable change, weak filtering or no filtering is used to retain the signal detail information; when the signal is in the transition change interval, mean filtering or smoothing filtering method is used to reduce random fluctuations; when the signal is in the interval with low amplitude and high noise proportion, threshold filtering method is used to suppress high-frequency noise interference. Further, for each sampling point, the corresponding filtering strategy is adaptively selected according to the signal characteristics of the segmented interval it belongs to, so as to realize the synergistic effect of multiple filtering methods. Through the above segmented adaptive filtering mechanism, different signal intervals are matched with different filtering intensities and processing methods, which can effectively suppress noise while retaining the effective characteristic information of the original signal to the greatest extent, and improve the accuracy and stability of signal processing.

[0040] S31. According to the time-domain change characteristics of the preprocessed signal , the signal is segmented, and the signal is divided into multiple time intervals. Each segmented interval corresponds to a different signal evolution stage, and the determination of the segmentation threshold is based on the calculation result of the signal amplitude itself. Let the signal sequence be , n = 0, 1,..., M - 1. First, calculate the first-order difference of the signal , n = 0, 1,..., M - 2; then calculate the absolute value of the difference sequence ; then set the amplitude thresholds and (usually​​​​ < ), dividing the signal into low-amplitude ranges ( ), medium amplitude range ( ) and high amplitude range ( The selection of segmentation points should ensure that the signals within each segment interval have relatively consistent statistical characteristics, and that there are obvious characteristic differences between adjacent segment intervals. The segmentation process may generate 3 to 7 different signal intervals, the exact number depending on the complexity of the signal itself.

[0041] S32. For each segmented interval, extract the amplitude level, rate of change, and noise distribution characteristics of the signal within that interval to characterize the signal features of that interval.

[0042] S33. Filtering Strategy Determination. Based on the signal characteristics of each segment interval, filtering strategies are classified and selected: when the signal is in an interval with high amplitude and stable changes, it is identified as the first type of interval, and weak filtering or no filtering is used; when the signal is in an interval with transitional changes, it is identified as the second type of interval, and mean filtering or smoothing filtering methods are used; when the signal is in an interval with low amplitude and high noise content, it is identified as the third type of interval, and threshold filtering is used to suppress high-frequency noise interference. For each sampling point, the corresponding filtering strategy is adaptively selected according to the signal characteristics of its segment interval, thereby realizing the synergistic effect of multiple filtering methods. Through the segmented adaptive filtering mechanism, different filtering intensities and processing methods are matched to different signal intervals, effectively suppressing noise while preserving the effective feature information of the original signal to the greatest extent, improving the accuracy and stability of signal processing.

[0043] The filtering strategy for the first type of interval employs a weak filtering method, with a filter window length set to 3 to 5 sampling points. Only slight smoothing is applied to the signal to remove obvious abnormal spikes. The calculation method for weak filtering is as follows: for the center point of the window... Calculate the mean μ and standard deviation σ of all sampling points within the window; if (k is usually taken as 2 to 3), then the mean μ is used to replace the current value; otherwise, the original value is kept unchanged. This strategy can effectively remove abnormal noise points while preserving the rapid change characteristics of the signal.

[0044] The filtering strategy for the second type of interval employs either mean filtering or smoothing filtering. Mean filtering uses a window length of 5 to 10 sampling points, and the output is the arithmetic mean of all sampling points within the window. Smoothing filtering uses a weighted approach, with the center sampling point having a weight of 2, neighboring sampling points having a weight of 1.5, and edge sampling points having a weight of 1. The total weights are normalized before calculating the weighted average. The smoothing filtering window length is set to 7 to 15 sampling points, with the specific value determined based on the signal noise level.

[0045] The filtering strategy for the third type of interval uses a threshold filtering method. The steps of threshold filtering include: first, calculating the standard deviation σ and mean μ of the signal within the interval; setting the amplitude threshold T = kσ (k is typically taken as 1.5 to 2.5); and then applying the threshold for each sampling point... ,like If the value is not found to be noise, the point is identified as a noise point and replaced with the interpolated result. Linear interpolation or cubic spline interpolation can be used, calculated based on 3 to 5 valid sampling points before and after the interpolation point. Threshold filtering can effectively suppress high-frequency noise while preserving the overall trend characteristics of the signal.

[0046] To verify the effectiveness of the method of this invention, a ferromagnetic pipe with a cladding layer was used as the test object for simulation verification. The basic parameters of the pipe were set as follows: pipe outer diameter... The pipe has a wall thickness of 8mm and a cladding thickness of 15mm. The pipe material is No. 20 carbon steel, and the cladding material is polyurethane foam. The pulsed eddy current probe parameters are set as follows: excitation coil inner radius 8mm, outer radius 12mm, number of turns 200, coil height 10mm; receiving coil inner radius 14mm, outer radius 18mm, number of turns 100, coil height 10mm; probe lift-off distance 2mm. The excitation signal is a square wave current with an amplitude of 10A, frequency of 50Hz, and duty cycle of 50%.

[0047] The original detection signal obtained from the simulation was superimposed with Gaussian white noise with a standard deviation of 0.05 to simulate the noise environment at the site. The reference signal was taken from a defect-free area of ​​the pipeline. The method of this invention was applied for processing: first, the detection signal and the reference signal were normalized, with the normalization coefficient being the maximum of the absolute values ​​of the two signals; then, the relative logarithmic transform was calculated to obtain the preprocessed signal. Next, based on the signal amplitude and rate of change, the signal is divided into a high amplitude range (sampling point 0 to 400), a transition range (sampling point 401 to 1200), and a low amplitude range (sampling point 1201 to 2000). Finally, each range is processed using weak filtering, mean filtering, and threshold filtering methods respectively.

[0048] The processing results show that, using a ferromagnetic pipe with a cladding layer as the simulation object, and setting the pipe wall thickness to 8mm to 18mm for six working conditions, Gaussian white noise with a standard deviation of 0.05 was superimposed on the simulation signal to simulate the on-site noise environment, and the reference signal was taken from a defect-free area. Figure 3 As shown, after normalizing and performing relative logarithmic transformation on the detection signals of each thickness, the preprocessed signals significantly amplified the differences between different wall thicknesses, the separation between the thickness curves was significantly improved, and the signal response to changes in wall thickness became more sensitive. However, due to... Figure 3As can be seen in (a), the original simulated signal is significantly affected by Gaussian white noise in the late decay stage when t>0.1, and there are significant random fluctuations in each thickness curve, with the difference features being submerged by noise. Figure 3 Although the preprocessed signal shown in (b) effectively amplifies the differences between different wall thicknesses, noise interference in the late low amplitude range still exists and needs to be further suppressed by adaptive segmented filtering.

[0049] After adaptive segmented filtering of the preprocessed signal, a weak filtering strategy was used in the early high-amplitude range (t<0.05s), which completely preserved the peak characteristics of each thickness curve, with a peak deviation of less than 5% before and after filtering. A threshold filtering strategy was used in the late low-amplitude range (t>0.1s), which significantly suppressed high-frequency random noise, smoothed the thickness curves, and significantly improved the signal-to-noise ratio. A mean filtering strategy was used in the transition range, resulting in good overall signal continuity. After filtering, the curves corresponding to each wall thickness had clear outlines, and the differences between adjacent thicknesses were completely preserved. The overall signal quality was significantly better than before filtering, providing a high-quality data foundation for subsequent defect identification and quantitative wall thickness assessment.

[0050] To further verify the effectiveness of this method under actual working conditions, pipe specimens with wall thicknesses of 4.00 mm and 14.80 mm were selected for experimental verification. Figure 4 As shown in (a), the original pulsed eddy current induced voltage signal has a high overall amplitude, and the curves for the two wall thicknesses highly overlap. However, in the late decay stage (t>0.1s), the signal amplitude drops sharply, high-frequency noise interference is severe, and the differences between the two wall thicknesses are almost impossible to identify. Figure 4 As shown in (b), after normalization and relative logarithmic transformation, the preprocessed signal effectively highlighted the differences between the two wall thicknesses, with a clear separation between the curves for 4.00 mm and 14.80 mm, and a significant enhancement in the wall thickness response characteristics. However, in the late low-amplitude range of t > 0.1 s, high-frequency noise interference remained severe, and both curves exhibited large random fluctuations, requiring further filtering. Figure 4 As shown in (c), after adaptive segmented filtering, the filtered curves corresponding to 4.00mm and 14.80mm (labeled "after filtering" in the figure) are effectively smoothed. Compared with the preprocessed signal, the peak characteristics of the early high-amplitude range (t<0.05s) are completely preserved; the high-frequency random noise in the late low-amplitude range (t>0.1s) is significantly suppressed, the curves tend to be stable, and the signal-to-noise ratio is significantly improved; the two filtered curves have clear outlines, the difference characteristics between 4.00mm and 14.80mm are completely preserved, and the overall signal quality is significantly better than before filtering, verifying the effectiveness of this method under actual working conditions.

[0051] 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 of adaptive piecewise filtering based on relative log transformation, characterized by, Includes the following steps: Step 1: Establish an analytical model for pulsed eddy current detection. The pipe structure with the coating layer is equivalent to a multi-layer flat plate structure and a detection platform is constructed. Pulse excitation is applied to the pipe under test through the detection platform and the induced voltage signal is collected to obtain the detection signal and the reference signal. Step 2: Obtain the preprocessed signal. Discretely sample and normalize the detection signal and the reference signal, and introduce a relative logarithmic transformation to obtain the preprocessed signal. Step 3: Perform adaptive segmented filtering. The signal is segmented according to the time-domain variation characteristics of the preprocessed signal, and a filtering strategy is adaptively selected based on the signal characteristics of each segment interval for filtering.

2. The adaptive piecewise filtering method based on relative log transformation according to claim 1, characterized in that, In step 1, the specific process of establishing the analytical model for pulsed eddy current detection includes: A pulsed eddy current analytical model of a three-layer flat plate structure is established, consisting of an air layer, a pipe wall layer, and a lift-off layer from bottom to top. The pulsed eddy current probe is located above the three-layer flat plate structure. Based on the axisymmetry of the model, a cylindrical coordinate system is adopted. A current-mode time-domain signal in the form of a square wave is used as the excitation signal; Perform a Fourier transform on the excitation signal and decompose it into multiple harmonic components. Calculate the expression for the induced voltage signal of each harmonic. ; ； In the formula, The imaginary unit; For the first The angular frequency of the harmonic; The amplitude of the harmonic current; The vacuum permeability; for The number of and It is a constant. Assign a number to each constant; This refers to the lift-off distance between the pulsed eddy current probe and the pipe surface. The lift-off coefficient is used to characterize the effect of probe lift-off on the induced voltage; For the first The coil coefficient of each characteristic quantity; The generalized reflection coefficient for the third to fourth layers; The time-domain induced voltage signal is obtained by performing a discrete inverse Fourier transform on the induced voltage signal of each harmonic. ； In the formula, Indicates a square wave excitation signal. Indicates the amplitude of the excitation signal. The excitation signal frequency, after Fourier transform, can be equivalently represented as a superposition of multiple sinusoidal harmonic components. The harmonic index is denoted as , and any harmonic component is denoted as . ; The induced voltage of the receiving coil The time-domain expression is: ； Determine the expression for the coil coefficients and derive the characteristic quantities; Coil coefficient The expression is: ； In the formula, ; Indicates the coil height; and These represent the inner and outer radii of the coil, respectively. Number of coil turns; subscript and These represent the excitation coil and the receiving coil, respectively. ； ； In the above formula, ; Number of floors; , These represent the thicknesses of the pipe wall and the cladding layer, respectively. For the first Layer and first Reflection coefficient between layers; For the 1st to the 1st The generalized reflectance coefficient of the layer, ; and These are the first and second type Bessel functions, respectively; The longitudinal wave number of the electromagnetic wave; and The first The magnetic permeability and electrical conductivity of the layer.

3. The adaptive piecewise filtering method based on relative logarithmic transform according to claim 2, characterized in that, In the three-layer flat plate structure, the first layer represents the air in the pipe, the second layer represents the pipe wall, and the third layer represents the lift-off layer; large-area corrosion defects in the pipe wall are simplified into an equivalent region with uniform thinning; a pulse eddy current probe composed of a hollow excitation coil and a receiving coil arranged coaxially is arranged in the space above the structure.

4. The adaptive piecewise filtering method based on relative logarithmic transform according to claim 1, characterized in that, In step 2, the specific process of obtaining the preprocessed signal includes: Select the reference area and the detection area of ​​the specimen, and obtain the reference signal and the detection signal respectively; The reference signal and the detection signal are sampled at equal time intervals and converted into a discrete sequence with a preset number of points; The discrete sequence is normalized to obtain the normalized signal sequence; The signal is processed by introducing a relative logarithmic transform, calculating the logarithmic ratio and performing weighted modulation to obtain a preprocessed signal.

5. The adaptive piecewise filtering method based on relative logarithmic transform according to claim 4, characterized in that, To eliminate the influence of amplitude scale differences, discrete sequences are normalized. This normalization process employs a mathematical transformation method that maps signal amplitudes to a uniform interval. The normalized signal sequence... and It can eliminate the absolute amplitude difference between the detected signal and the reference signal; it introduces a relative logarithmic transform to process the signal, first calculating the logarithmic ratio of the two signals at each sampling point to characterize the relative proportional relationship, and then... and The logarithmic term is modulated using weights, and the contributions of the two parts are adjusted by weighting with preset coefficients. Finally, the weighted results are combined to obtain the preprocessed signal. .

6. The adaptive piecewise filtering method based on relative logarithmic transform according to claim 1, characterized in that, In step 3, the specific process of adaptive piecewise filtering includes: The signal is segmented into multiple time intervals based on the time-domain variation characteristics of the preprocessed signal. Extract the amplitude level, rate of change, and noise distribution characteristics of the signal within each segment interval; The filtering strategy is classified based on the signal characteristics, and the corresponding filtering method is applied to different types of intervals.

7. The adaptive piecewise filtering method based on relative logarithmic transform according to claim 6, characterized in that, The signal is segmented based on its time-domain variation characteristics, dividing it into multiple time intervals. Each segment interval corresponds to a different stage of signal evolution. The segment threshold is determined based on the calculation result of the preset derivative of the signal amplitude. The selection of segment points should ensure that the signal in each segment interval has relatively consistent statistical characteristics.

8. The adaptive piecewise filtering method based on relative logarithmic transform according to claim 6, characterized in that, For each segmented interval, the amplitude level, rate of change, and noise distribution characteristics of the signal within that interval are extracted to characterize the signal features of that interval. The amplitude level is characterized by calculating the mean of the absolute values ​​of the signal within the interval, the rate of change is characterized by calculating the standard deviation of the first-order difference of the signal within the interval, and the noise distribution characteristics are characterized by calculating the energy proportion of the high-frequency components of the signal within the interval.

9. The adaptive piecewise filtering method based on relative logarithmic transform according to claim 6, characterized in that, The filtering strategy is classified and selected according to the signal characteristics of each segment interval. When the signal is in the interval with high amplitude and stable change, it is identified as the first type interval and weak filtering or no filtering is performed to preserve the signal details. When the signal is in the interval with transitional change, it is identified as the second type interval and mean filtering or smoothing filtering is used to reduce random fluctuations. When the signal is in the interval with low amplitude and high noise ratio, it is identified as the third type interval and threshold filtering is used to suppress high-frequency noise interference.

10. The adaptive piecewise filtering method based on relative logarithmic transform according to claim 9, characterized in that, For each sampling point, the corresponding filtering strategy is adaptively selected based on the signal characteristics of its segment interval, thereby achieving the synergistic effect of multiple filtering methods. Through the segmented adaptive filtering mechanism, different signal intervals are matched with different filtering intensities and processing methods, effectively suppressing noise while preserving the effective feature information of the original signal to the greatest extent. At the boundaries of each segment interval, a weighted transition method is used for processing. The transition weight is determined according to the distance between the sampling point and the boundary center to ensure the continuity of the overall filtered signal. After the filtering processing of each segment interval is completed, the filtered outputs are spliced ​​together in time sequence to form a complete filtered signal sequence.

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