Pipeline anticorrosion layer resistivity calculation method and system

Abstract

The application discloses a pipeline anticorrosion layer resistivity calculation method and system, obtains the multi-frequency variable-frequency impedance data of the pipeline anticorrosion layer in a preset low-frequency range; carries out signal-to-noise ratio evaluation on the multi-frequency variable-frequency impedance data to obtain initial impedance spectrum data; carries out Kramers-Kronig relationship validity verification on the initial impedance spectrum data to generate a set of available frequency points; carries out relaxation time distribution analysis on the impedance data corresponding to the set of available frequency points to identify the relaxation time constant; generates a set of candidate equivalent circuit models and model parameter initial values according to the relaxation time constant; carries out complex nonlinear least square fitting on the candidate equivalent circuit models to obtain an optimal equivalent circuit model; extracts an anticorrosion layer ohmic resistance term from the parameters of the optimal equivalent circuit model, and calculates the real value of the anticorrosion layer surface resistivity according to a geometric conversion coefficient. Through the establishment of a multi-frequency joint fitting and resistivity calculation framework, the real value of the output resistivity has consistency and repeatability.

Description

Technical Field

[0001] This invention relates to the field of pipeline corrosion protection and detection technology, and in particular to a method and system for calculating the resistivity of pipeline anti-corrosion coating. Background Technology

[0002] The integrity of the anti-corrosion coating of buried pipelines is directly related to the pipeline's operational safety and service life. Currently, methods such as close-interval pipe-to-ground potential measurement (CIPS) or DC voltage gradient (DCVG) are used to evaluate the effectiveness of cathodic protection and locate coating defects.

[0003] However, for in-service pipelines, especially deeply buried sections and directional drilling crossings, potential measurements are affected by ohmic voltage drops. Furthermore, the power-off response is influenced by system parameters such as soil resistivity, pipeline length, coating defects, and the number of decouplers. Instantaneous power-off readings may deviate from the true polarization potential, leading to misjudgments. Polarization effects caused by DC testing can cause measured values ​​to deviate from reality; AC signals are significantly affected by interference, and improper frequency selection can exacerbate data deviations; the limitations of testing at both ends make it difficult to capture local risks in the intermediate area, placing higher demands on sampling speed and the measurement link.

[0004] These methods have the following problems: 1. Potential measurement is easily affected by factors such as soil resistivity, pipe length, coating defect distribution and stray current. Especially when there is AC interference, the instantaneous power failure potential may not accurately reflect the true polarization potential, leading to misjudgment or omission of underprotected areas. 2. It relies heavily on manual labor for densely deploying testing points along the route, resulting in low operational efficiency and high costs. It also lacks representativeness for deeply buried or inaccessible crossing sections. The large amount of manual labor required and the high requirements for point deployment mean that polarization test pieces are time-consuming and their representativeness is affected by location, making it difficult to meet the needs of efficient and accurate on-site testing.

[0005] 3. It can locate the defect, but it is difficult to provide reproducible electrical parameters of the defect, and it cannot directly quantify the corrosion risk; it has poor applicability and lacks a fitting framework that can be implemented, verified and quantified, and cannot support engineering decisions and subsequent verification. Summary of the Invention

[0006] This invention aims to solve at least one of the technical problems existing in the prior art. To this end, this invention proposes a method and system for calculating the resistivity of pipeline anti-corrosion layers. By establishing a multi-frequency joint fitting and resistivity calculation framework, the output resistivity values ​​of the anti-corrosion layer are made consistent and verifiable, thereby improving pipeline inspection efficiency and reducing cost.

[0007] On one hand, embodiments of the present invention provide a method for calculating the resistivity of a pipeline anti-corrosion layer, including: Obtain multi-frequency impedance data of the pipeline anti-corrosion layer within a preset low-frequency range, wherein the preset low-frequency range is 0.1Hz to 80Hz; The signal-to-noise ratio of the multi-frequency impedance data is evaluated to obtain the initial impedance spectrum data; The initial impedance spectrum data is subjected to Kramers-Kronig relationship validity verification to generate a set of usable frequency points; The relaxation time distribution of the impedance data corresponding to the set of available frequency points is analyzed to identify the relaxation time constant. Based on the relaxation time constant, a set of candidate equivalent circuit models and initial values ​​of model parameters are generated. The candidate equivalent circuit model is fitted with complex nonlinear least squares to obtain the optimal equivalent circuit model; The ohmic resistance term of the anti-corrosion layer is extracted from the parameters of the optimal equivalent circuit model, and the true value of the resistivity of the anti-corrosion layer is calculated based on the geometric conversion factor.

[0008] According to some embodiments of the present invention, the validity of the Kramers-Kronig relationship in the initial impedance spectrum data is verified, including: Calculate the residual between the measured impedance data and the theoretical KK impedance data; Frequency points where the residual exceeds a preset threshold are marked as abnormal frequency points; Perform elimination, weight reduction, or trigger retesting operations on abnormal frequency points to generate the set of available frequency points.

[0009] According to some embodiments of the present invention, relaxation time distribution analysis is performed on the impedance data corresponding to the available frequency point set to identify the relaxation time constant, including: The impedance data of the available frequency point set is subjected to regularized inversion to obtain the relaxation time distribution function; Identify the peak characteristics of the relaxation time distribution function to determine the number and range of relaxation time constants; The corresponding physical process is automatically matched based on the peak characteristics.

[0010] According to some embodiments of the present invention, the complex nonlinear least squares fitting employs a modulus reciprocal square weighted strategy, and the objective function is: In the formula, S(θ) is the objective cost function, representing the weighted sum of squared fitting errors; θ is the set of model parameters, such as resistance and capacitance; N valid W represents the number of available frequency points. k For frequency f k The weighting factor Z′ is as follows: meas,k For frequency f k The real part of the measured complex impedance; Z′ model,k(θ) represents the frequency f k The real part of the theoretical complex impedance is calculated from the model parameter set θ; Z′′ meas,k For frequency f k The imaginary part of the measured complex impedance; Z′′ model,k (θ) represents the frequency f k The imaginary part of the theoretical complex impedance is calculated from the model parameter set θ.

[0011] According to some embodiments of the present invention, prior to the step of performing complex nonlinear least squares fitting on the candidate equivalent circuit model, the method includes: Perform measurement and verification on standard analog circuits; If the parameter deviation exceeds the preset tolerance, the output of the true resistivity value of the pipeline anti-corrosion layer will be stopped.

[0012] According to some embodiments of the present invention, the step of extracting the ohmic resistance term of the anti-corrosion layer from the parameters of the optimal equivalent circuit model and calculating the true value of the resistivity of the anti-corrosion layer based on the geometric conversion factor includes: The pure anti-corrosion layer ohmic resistance term is extracted from the optimal model parameter set, and polarization resistance and diffusion impedance are eliminated. The true resistivity of the anti-corrosion layer is calculated based on the geometric conversion factor. The formula for converting the true resistivity is as follows: R true = R coat ·K geom ; In the formula, R true This is the actual resistivity value of the anti-corrosion layer, in Ω·m. 2 R coat For the pure anti-corrosion layer ohmic resistance term, K geom The effective geometric conversion area is calculated based on the pipe diameter and the test section length. Output the fitted variance-covariance matrix, and combine it with the KK population residuals to generate a confidence level with a confidence interval of 95%.

[0013] According to some embodiments of the present invention, after the step of calculating the true resistivity value of the anti-corrosion layer based on the geometric conversion factor, the method further includes: In addition to the actual value, each output also synchronously outputs the KK residual index, confidence level, and frequency point list; Among them, the KK residual index serves as a data quality indicator, a retest consistency indicator, and a noise and interference indicator; the confidence level provides a confidence interval based on the CNLS parameter covariance and residual level; the frequency point list includes the original Z(fi), elimination rules, the final model and parameters, ensuring traceability and recalculation.

[0014] According to some embodiments of the present invention, the confidence level includes at least one of the following: The data include fitting residual index, confidence intervals derived from the parameter covariance matrix, KK consistency score, and data quality indicators.

[0015] According to some embodiments of the present invention, the preset low-frequency range uses a segmented encryption strategy to generate frequency points, and automatically performs frequency point avoidance or frequency hopping when power frequency interference is detected.

[0016] In another aspect, embodiments of the present invention provide a pipeline anti-corrosion coating resistivity calculation system for implementing the aforementioned pipeline anti-corrosion coating resistivity calculation method. The system includes: The data acquisition and preprocessing module is used to acquire the multi-frequency variable impedance data of the pipeline anti-corrosion layer and to evaluate the signal-to-noise ratio of the raw impedance data. The KK test module is used to perform validity verification of the Kramers-Kronig relationship and generate a set of available frequency points; The DRT parsing module is used to identify relaxation time constants through relaxation time distribution analysis. The model generation and fitting module is used to construct candidate equivalent circuit models based on the output of the DRT analysis module; and to perform complex nonlinear least squares fitting to obtain the optimal equivalent circuit model. The data calculation module is used to calculate the true resistivity of the anti-corrosion layer and generate confidence information.

[0017] The pipeline anti-corrosion coating resistivity calculation method and system of the present invention have at least the following beneficial effects: After acquiring multi-frequency impedance data of the pipeline corrosion protection layer, the effectiveness of the Kramers-Kronig relationship is verified. Distorted impedance spectra caused by electromagnetic interference and potential drift are identified and eliminated, ensuring that the data input to the core algorithm meets the prerequisites of linearity, causality, and steady-state operation, resulting in an output resistivity of the corrosion protection layer that more closely approximates real-world DC operating conditions. Through multiple strategies, including real-time signal-to-noise ratio evaluation, repeated measurement consistency screening, and modulus reciprocal square weighted fitting, robustness and anti-interference capabilities under harsh field conditions are enhanced. Noise is automatically suppressed, and the contributions of high- and low-frequency data are balanced, resulting in stable and reliable outputs, expanding the applicability of the technology. Relaxation time distribution analysis is introduced to automatically identify the inherent physical processes in the data (such as coating response and interface polarization), and candidate models are objectively generated accordingly. Combined with the Akaike Information Criterion, automatic model selection is performed, effectively solving the problem of inconsistent results due to differences in manual model selection in traditional methods, ensuring consistency of results. This achieves objectivity and automation in model selection and parameter fitting, reducing reliance on subjective human experience. It provides quantifiable and verifiable decision-making basis, forming a complete engineering closed loop; it provides a complete data chain for subsequent auditing, review, and trend comparison, elevating empirical judgment to scientific decision-making based on quantitative confidence. By combining multi-frequency testing with automated algorithm analysis, it effectively solves the core pain points of current pipeline corrosion protection layer detection data being unreliable, models being highly subjective, and results being unverifiable, enabling rapid quantitative assessment at key nodes and reducing on-site manual operation time and costs.

[0018] In another aspect, embodiments of the present invention provide a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program, the processor executes the above-described method for calculating the resistivity of the pipeline anti-corrosion layer.

[0019] On the other hand, an embodiment of the present invention provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method for calculating the resistivity of the pipeline anti-corrosion layer.

[0020] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0021] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart of the pipeline anti-corrosion coating resistivity calculation method according to an embodiment of the present invention; Figure 2 This is a current and voltage diagram illustrating the pipeline anti-corrosion layer resistivity calculation method according to an embodiment of the present invention. Figure 3This is a schematic diagram of the frequency and modulus of the pipeline anti-corrosion layer resistivity calculation method according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the frequency and phase of the pipeline anti-corrosion layer resistivity calculation method according to an embodiment of the present invention; Figure 5 This is an impedance diagram illustrating the pipeline anti-corrosion layer resistivity calculation method according to an embodiment of the present invention. Figure 6 This is a functional block diagram of the pipeline anti-corrosion coating resistivity calculation system according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the structure of a computer device according to an embodiment of the present invention. Detailed Implementation

[0022] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0023] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, left, right, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0024] In the description of this invention, "several" means one or more, "multiple" means two or more, "greater than," "less than," "exceeding," etc. are understood to exclude the stated number, and "above," "below," "within," etc. are understood to include the stated number. If "first," "second," etc. are used in the description, they are only for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance or implicitly indicating the number of indicated technical features or the order of the indicated technical features.

[0025] Current cathodic protection assessments generally rely on potential-based indicators, such as cathodic protection de-energization potential and close-interval potential. In in-service pipelines, especially those crossing directional drilling sections, potential measurements are affected by ohmic voltage drops, requiring simultaneous power outages to collect instantaneous de-energization potentials to minimize errors. Furthermore, the de-energization response is influenced by system parameters such as soil resistivity, pipeline length, coating defects, and the number of decouplers. If the characteristics of the de-energization response are not fully identified, the instantaneous de-energization reading may deviate from the true polarization potential, leading to misjudgments. In addition, under AC interference conditions, potential assessment places higher demands on sampling speed and measurement links; even when the instantaneous de-energization potential can approximate the true zero-voltage-drop potential, the absence of a balanced current may occur. In deeply buried pipeline scenarios, the applicability of fine measurement methods based on potential gradient extrapolation also decreases. The close-interval potential method requires significant manual labor and precise point placement; polarization specimens are time-consuming and their representativeness is affected by location, making it difficult to meet the efficient and accurate on-site testing needs of pipeline crossing sections.

[0026] The DC voltage gradient (DCVG) method can locate coating damage and provide a relative severity index, and is often used in engineering to select priority excavation points. However, its results are sensitive to factors such as low soil resistivity areas, external interference, defect orientation, and shielding, requiring detailed data analysis and empirical interpretation. More importantly, there is no simple and direct correlation between the voltage gradient index of the DCVG method and the corrosion depth. Therefore, it is difficult to quantitatively predict the corrosion depth or provide reproducible electrical parameters using the DCVG method alone, which can easily lead to the problem of "finding defects, but struggling to explain the electrical properties of the defects and the strength of the risk."

[0027] Electrochemical impedance spectroscopy (EIS) is highly sensitive to instrument configuration, connection methods, measurement range, and data validity checks in high-resistivity coated systems. Acquiring impedance data for high-resistivity systems requires careful attention to instrument configuration requirements and potential pitfalls, and data validity verification is essential. However, this section does not provide a methodology for data interpretation, meaning there is still a significant gap between "correct acquisition" and "accurate calculation and consistent interpretation." Under field conditions, nonlinearity and unsteady-state conditions can lead to impedance spectrum distortion; and the validity of impedance data is often underestimated. The key to impedance data validity lies in satisfying and verifying the assumptions of linearity and steady-state conditions. Methods such as the Kramers-Kronig consistency test are proposed to test the self-consistency of impedance data. Polarization effects caused by DC testing can cause measured values ​​to deviate from reality; AC signals are significantly affected by interference, and improper frequency selection can exacerbate data deviations; the limitations of testing at both ends make it difficult to capture local risks in the intermediate region. Existing impedance methods suffer from common pain points in field multi-frequency testing: "difficulty in guaranteeing data validity, subjective model interpretation, and unverifiable results."

[0028] Common practices involve selecting a few frequency points or a single equivalent formula for conversion, or relying on manually selecting an equivalent circuit model and then fitting it using CNLS (Complex Nonlinear Least Squares) to obtain the parameters. However, under conditions of noise, interference, and unsteady state in the field, the following problems easily arise: First, the fitting is sensitive to initial values ​​and model structure, and the parameters have multiple solutions, leading to different "true values" given by different personnel or different batches of data. Second, there is a lack of integrated constraints on fitting residuals, frequency anomalies, and data validity, making it difficult to "automatically remove abnormal frequencies and provide reasons." Third, there is a lack of true values ​​and confidence level outputs, which cannot support engineering decisions and subsequent verification, and it is difficult to form a scalable and software-based calculation process. Existing methods lack a fitting framework that can be implemented, verified, and has quantifiable confidence levels.

[0029] The Kramers-Kronig (KK) relation can be used to verify whether impedance data satisfies the presuppositions of causality, linearity, and time invariance. However, in current technologies, the KK relation is mostly used for post-hoc academic analysis in laboratories and has not been deeply embedded into the real-time control and decision-making closed loop of field testing. The Distribution of Relaxation Times (DRT) is an analytical method that does not require pre-specified equivalent circuits. By deconvolution, it maps the impedance spectrum to the time constant domain, clearly distinguishing different physical processes in the system (such as coating dielectric response and interface charge transfer). However, the DRT method is currently mainly at the theoretical research level and has not yet been combined with the automatic generation of models and the estimation of initial parameter values ​​for field corrosion protection layer testing.

[0030] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0031] This embodiment provides a method for calculating the resistivity of pipeline anti-corrosion coating. Please refer to [link to relevant documentation]. Figure 1 The method for calculating the resistivity of the pipeline anti-corrosion layer mainly includes steps S101~S107: S101. Obtain the multi-frequency impedance data of the pipeline anti-corrosion layer within a preset low-frequency range, where the preset low-frequency range is 0.1Hz to 80Hz.

[0032] S102. Evaluate the signal-to-noise ratio of the multi-frequency impedance data to obtain the initial impedance spectrum data.

[0033] S103. Verify the validity of the Kramers-Kronig relationship on the initial impedance spectrum data and generate a set of usable frequency points.

[0034] S104. Perform relaxation time distribution analysis on the impedance data corresponding to the available frequency point set to identify the relaxation time constant.

[0035] S105. Based on the relaxation time constant, generate a set of candidate equivalent circuit models and initial values ​​of model parameters.

[0036] S106. Perform complex nonlinear least squares fitting on the candidate equivalent circuit model to obtain the optimal equivalent circuit model.

[0037] S107. Extract the ohmic resistance term of the anti-corrosion layer from the parameters of the optimal equivalent circuit model, and calculate the true value of the resistivity of the anti-corrosion layer based on the geometric conversion factor.

[0038] The above step S103, which verifies the validity of the Kramers-Kronig relationship in the initial impedance spectrum data, includes: Calculate the residual between the measured impedance data and the theoretical KK impedance data; Frequency points where the residual exceeds a preset threshold are marked as abnormal frequency points; Perform removal, weight reduction, or trigger retesting operations on abnormal frequency points to generate a set of usable frequency points.

[0039] The relaxation time distribution analysis of the impedance data corresponding to the available frequency point set in step S104 above, and the identification of the relaxation time constant, includes: The impedance data of the available frequency point set is regularized and inverted to obtain the relaxation time distribution function; Identify the peak characteristics of the relaxation time distribution function and determine the number and range of relaxation time constants; Automatic matching of the corresponding physical process based on peak characteristics.

[0040] The complex nonlinear least squares fitting in step S106 above adopts a modulus reciprocal square weighted strategy, and the objective function is: In the formula, S(θ) is the objective cost function, representing the weighted sum of squared fitting errors; θ is the set of model parameters, such as resistance and capacitance; N valid W represents the number of available frequency points. k For frequency f k The weighting factor Z′ is as follows: meas,k For frequency f k The real part of the measured complex impedance; Z′ model,k (θ) represents the frequency f k The real part of the theoretical complex impedance is calculated from the model parameter set θ; Z′′ meas,k For frequency f k The imaginary part of the measured complex impedance; Z′′ model,k (θ) represents the frequency f k The imaginary part of the theoretical complex impedance is calculated from the model parameter set θ.

[0041] Before the step of performing complex nonlinear least squares fitting on the candidate equivalent circuit model in step S106 above, the following steps are included: Perform measurement and verification on standard analog circuits; If the parameter deviation exceeds the preset tolerance, the output of the true resistivity value of the pipeline anti-corrosion layer will be stopped.

[0042] The step S107 above, which involves extracting the ohmic resistance term of the anti-corrosion layer from the parameters of the optimal equivalent circuit model and calculating the true resistivity value of the anti-corrosion layer based on the geometric conversion factor, includes: The pure anti-corrosion layer ohmic resistance term is extracted from the optimal model parameter set, and polarization resistance and diffusion impedance are eliminated. The true resistivity of the anti-corrosion layer is calculated based on the geometric conversion factor. The formula for converting the true resistivity is as follows: R true = R coat ·K geom ; In the formula, R true This is the actual resistivity value of the anti-corrosion layer, in Ω·m. 2 R coat For the pure anti-corrosion layer ohmic resistance term, K geom The effective geometric conversion area is calculated based on the pipe diameter and the test section length. Output the fitted variance-covariance matrix, and combine it with the KK population residuals to generate a confidence level with a confidence interval of 95%.

[0043] Following the step of calculating the true resistivity of the anti-corrosion layer based on the geometric conversion factor in step S107 above, the method further includes: In addition to the actual value, each output also synchronously outputs the KK residual index, confidence level, and frequency point list; Among them, the KK residual index serves as a data quality indicator, a retest consistency indicator, and a noise and interference indicator; the confidence level provides a confidence interval based on the CNLS parameter covariance and residual level; the frequency point list includes the original Z(fi), elimination rules, the final model and parameters, ensuring traceability and recalculation.

[0044] It should be noted that confidence level includes at least one of the following: The data include fitting residual index, confidence intervals derived from the parameter covariance matrix, KK consistency score, and data quality indicators.

[0045] It should be noted that the preset low-frequency range uses a segmented encryption strategy to generate frequency points, and automatically performs frequency avoidance or frequency hopping when power frequency interference is detected.

[0046] Please see Figure 6This embodiment also provides a pipeline anti-corrosion coating resistivity calculation system for implementing the above-described pipeline anti-corrosion coating resistivity calculation method. The system includes: The data acquisition and preprocessing module 100 is used to acquire multi-frequency variable impedance data of the pipeline anti-corrosion layer and evaluate the signal-to-noise ratio of the original impedance data. This module includes a variable impedance testing device, which can output multi-frequency voltage, current and phase information. The frequency range can be set from 0.1Hz to 80Hz according to the site requirements, and supports continuous acquisition and automated testing under dynamic potential or variable frequency scanning conditions. KK test module 200 is used to perform validity verification of the Kramers-Kronig relationship and generate a set of available frequency points; DRT parsing module 300 is used to identify relaxation time constants through relaxation time distribution analysis; The model generation and fitting module 400 is used to construct candidate equivalent circuit models based on the output of the DRT analysis module; and to perform complex nonlinear least squares fitting to obtain the optimal equivalent circuit model. The data calculation module 500 is used to calculate the true value of the resistivity of the anti-corrosion layer and generate confidence information.

[0047] The following is a detailed description of the pipeline anti-corrosion layer resistivity calculation method provided in the embodiments of the present invention: 1. Acquisition and Refined Preprocessing of Multi-Frequency Variable Frequency Impedance Data (1) Test condition setting and frequency planning: Based on the on-site task requirements, the frequency range of the frequency converter signal is set, preferably the low frequency band from 0.1Hz to 80Hz. A frequency point set F={f1, f2, ..., f} is generated using a logarithmic interval or segmented encryption strategy. N}, where N takes values ​​between 30 and 50.

[0048] For frequency bands known to have severe interference, such as the 50Hz power frequency and its harmonics, a preset avoidance strategy can be implemented, or the number of retests can be increased within the interference frequency band to distinguish between genuine and false signals.

[0049] (2) Synchronous acquisition and phase-sensitive demodulation: Using a frequency converter impedance testing device with synchronous time synchronization function, at each frequency point f k Simultaneously, the time-domain signal v(t) of the voltage applied to the pipeline and the time-domain signal i(t) of the current flowing through the anti-corrosion layer are acquired. The amplitude and phase of the fundamental component are accurately extracted using Fast Fourier Transform or digital phase-locked loop technology, while higher harmonics and random noise are filtered out.

[0050] The complex form of the voltage phasor is calculated as follows: V(f k )=∣V k |e jθvk ; In the formula, V(f) k ) is at a specific test frequency f k The voltage phasor V k For frequency f k The fundamental amplitude of the voltage signal, θ vk For frequency f k The phase angle of the voltage signal relative to the reference time base; j is the imaginary unit, satisfying j 2 =-1, used to represent the orthogonal component that is 90 degrees out of phase with the real part.

[0051] The complex form of the current phasor is calculated as follows: I(f k )=∣I k |e jθik ; In the formula, I(f) k ) is at a specific test frequency f k Current phasor under V k For frequency f k The fundamental amplitude of the current signal, θ ik For frequency f k The phase angle of the current signal relative to the reference time base; j is the imaginary unit, satisfying j 2 =-1, used to represent the orthogonal component that is 90 degrees out of phase with the real part.

[0052] The complex impedance is calculated as follows: Z(f k ) = V(f k ) / I(f k ) = Z k ′ + jZ k ′′ ; In the formula, Z(f k V(f) is the complex impedance at frequency fk. k ) is at a specific test frequency f k The voltage phasor under the following conditions, I(f k ) is at a specific test frequency f k The current phasor Z k ′ is at frequency f k The real part of the complex impedance Z k ′′ is at frequency f k The imaginary part of the complex impedance.

[0053] (3) Perform signal-to-noise ratio and stability evaluation: Calculate the signal-to-noise ratio for the impedance magnitude at each frequency point using the following formula: SNR = 20log10(∣V signal ∣ / ∣V noise |); In the formula, SNR is the signal-to-noise ratio, measured in decibels (dB); V signal V represents the voltage amplitude of the fundamental signal. noise This represents the noise floor voltage amplitude in the adjacent frequency band.

[0054] If the signal-to-noise ratio (SNR) is below 15dB, the point is marked as a low-confidence point. At the same time, short-term rapid repeated measurements are performed on key frequency points, and the relative standard deviation is calculated. If the standard deviation exceeds the threshold (e.g., 5%), it is determined to be an unstable contact or a time-varying state, triggering a retest or elimination mechanism.

[0055] 2. Final verification of data validity and intelligent frequency band clipping based on KK consistency test (1) Verification of KK linearity: The complex impedance data Z retained after preprocessing meas (fk) Input KK fitting framework. Using the integral transform of the KK relationship, the theoretical real part is calculated from the imaginary part of the impedance, or the theoretical imaginary part is calculated from the real part, to obtain the ideal KK compliant impedance ZKK(f k ).

[0056] (2) Residual calculation and cause diagnosis: The relative residual ΔKK at each frequency point is calculated as follows: ΔKK(f k =∣Z meas (f k ) ZKK(f k )∣ / ∣Z meas (f k |×100%; In the formula, Z meas (fk) represents the complex impedance data retained after preprocessing, ZKK(f k () is the ideal KK compliant impedance.

[0057] (3) Intelligent cropping decision The preset threshold is 5%. If the residual ΔKK at a certain frequency point is greater than 5%, it is determined that it violates the linearity or time-invariance assumptions, and is directly removed from the usable dataset F. valid .

[0058] If the residual shows a systematic increasing trend in the low-frequency range, the cause is attributed to the drift of the pipeline polarization potential during the test. In this case, the single scan time should be shortened or dynamic segmented fitting should be used.

[0059] If the residual suddenly increases in a specific narrow frequency band, it is attributed to fixed-frequency electromagnetic interference. This bandwidth is automatically marked, and frequency hopping is performed in subsequent measurements.

[0060] Output a rigorously verified set of available frequency points F validThis ensures that subsequent fitting is based solely on physically consistent and reliable data.

[0061] 3. DRT-assisted adaptive model selection and initial parameter generation This step replaces the traditional manual model selection, objectively determining the model structure through a data-driven approach.

[0062] (1) DRT inversion analysis: in the available frequency band F valid The Tikhonov regularized inversion is performed on the complex impedance data Z(fi) to solve for the relaxation time distribution function γ(lnτ). This function reveals multiple relaxation processes inherent in the system.

[0063] (2) Peak identification and physical mapping: Extract the number of peaks, peak position (i.e. relaxation time constant τ) and peak area of ​​the relaxation time distribution function γ(lnτ) curve. For example, in the anti-corrosion coating system, the peaks at the high frequency end (small τ) usually correspond to the polarization of the coating medium, while the peaks at the low frequency end (large τ) correspond to the charge transfer process at the metal / electrolyte interface.

[0064] (3) Candidate model library construction: Based on the number of peaks n identified, candidate equivalent circuits are automatically matched from the pre-set model library. For example, if two main peaks are detected, a dual time constant equivalent circuit model is automatically matched, and the integral area is used as the initial resistance value. The area of ​​the DRT peak is used to estimate the initial range of resistance values ​​for each branch, providing a scientific initial guess for subsequent fitting and avoiding blind searching.

[0065] 4. CNLS Fitting and Model Optimization with Physical Constraints and Robust Weights This step ensures the numerical stability and physical accuracy of the fitting process.

[0066] (1) Weighted objective function design: For the high resistance characteristics of the coating, a weighted strategy based on the inverse square of the modulus is adopted, i.e., W k =1 / |Z meas,k | 2 .

[0067] This strategy effectively balances the contributions of low-frequency high-impedance points and high-frequency low-impedance points to the objective function, preventing the fitting process from being interfered with by a few extremely high impedance points.

[0068] (2) Complex Nonlinear Least Squares (CNLS) Fitting: For each candidate equivalent circuit model, the real and imaginary parts of the impedance are fitted simultaneously in its parameter space. The objective function is: In the formula, S(θ) is the objective cost function, representing the weighted sum of squared fitting errors; θ is the set of model parameters, such as resistance and capacitance; N valid W represents the number of available frequency points. kFor frequency f k The weighting factor Z′ is as follows: meas,k For frequency f k The real part of the measured complex impedance; Z′ model,k (θ) represents the frequency f k The real part of the theoretical complex impedance is calculated from the model parameter set θ; Z′′ meas,k For frequency f k The imaginary part of the measured complex impedance; Z′′ model,k (θ) represents the frequency f k The imaginary part of the theoretical complex impedance is calculated from the model parameter set θ.

[0069] (3) Physical hard constraints and convergence criteria: During the fitting process, physical feasibility constraints are enforced, such as all resistances R>0 and capacitance values ​​within the reasonable dielectric constant range of the material. Convergence is not only determined by minimizing the residuals, but also by checking the random distribution of the residuals and verifying whether the fitted spectrum still satisfies the KK relationship.

[0070] (4) Model optimization: The Akaike Information Criterion (AIC) is used for model optimization. AIC = 2p + N valid ·ln(S min / N valid ) ; In the formula, p is the number of parameters to be fitted in the equivalent circuit model, and S min To fit the minimum objective function that converges, N valid This represents the number of available frequency points for fitting.

[0071] Choosing the model with the lowest AIC value as the optimal solution achieves the best trade-off between fitting accuracy and model complexity, effectively preventing overfitting.

[0072] 5. Definition, extrapolation, and calculation of the true resistivity of the anti-corrosion layer This step defines the transformation path from the fitted parameters to the required engineering metrics.

[0073] (1) Parameter stripping: from the parameter set θ of the optimal model opt In the process, the resistance term R, which represents the pure ohmic leakage path of the anti-corrosion layer, is clearly distinguished and extracted. coat That is, resistance that is independent of polarization and diffusion processes.

[0074] (2) Geometric conversion: Determine the geometric conversion factor K based on the electrode configuration of the system, such as pipe diameter, test clamp spacing or exposed area. geom .

[0075] The actual resistivity of the anti-corrosion layer is calculated as follows: Rtrue = R coat ·K geom ; In the formula, R true This is the actual resistivity value of the anti-corrosion layer, in Ω·m. 2 ;R coat The resistance parameter, representing the pure ohmic leakage path of the anti-corrosion layer, is extracted from the optimal equivalent circuit model and is expressed in Ω; K. geom These are geometric conversion factors used to convert point or local resistance values ​​to surface resistivity, measured in meters (m). 2 .

[0076] It should be noted that, from a physical perspective, a simple ohmic resistance value only represents the absolute resistance over a specific area at the test point and lacks universality. The resistivity of the corrosion-resistant layer obtained by multiplying by an area factor, however, is the true insulation resistivity that reflects the material's inherent characteristics. This accurately represents the objective health level of the corrosion-resistant layer at that location, thus eliminating the influence of specific test dimensions and enabling lateral comparisons between different pipe sections.

[0077] (3) Compliance extrapolation: When the test frequency band is insufficient to directly cover DC, the parameterized form of the optimal fitting function is used to perform mathematical extrapolation towards zero frequency within the range allowed by the KK relationship, and the limiting resistance is obtained as the DC steady-state equivalent value.

[0078] 6. Full-process confidence assessment and traceability (1) Confidence quantification: Based on the covariance matrix fitted by CNLS, calculate key parameters (such as resistance parameter R). coat The standard uncertainty of KK is used to derive the 95% confidence interval for surface resistivity. A comprehensive confidence level is generated by combining the overall KK residual and the retest consistency index, such as A (high confidence), B (medium confidence), or C (low confidence).

[0079] (2) Complete record keeping: The system automatically saves and outputs a complete data package including the original frequency point list, removed frequency points and reasons, available frequency bands, the final model topology, fitting parameters, and residual spectrum. This allows any calculation of the true resistivity value of the corrosion protection layer to be completely reproduced and verified.

[0080] The following example illustrates the inspection of a DN800 natural gas pipeline. This pipeline crosses a large river using directional drilling, with a crossing length of approximately 1.2 km and a burial depth of 15-20 meters. To ensure the safe operation of this concealed structure, the insulation resistivity of its outer anti-corrosion layer (3PE structure) needs to be quantitatively tested. Traditional testing methods suffer from severe signal attenuation at this depth, making it impossible to obtain effective data.

[0081] 1. Site setup and data collection At the pipeline test pile near the entry point of the crossing section, the testing personnel connected the variable frequency impedance testing device to the pipeline via a polarized test piece or directly via a circuit breaker, with the other end connected to a copper sulfate reference electrode. The scanning frequency range was set to 0.1Hz to 80Hz, generating 50 frequency points at logarithmic intervals. The excitation signal used a small-amplitude AC constant voltage mode, with an amplitude set to 20mV to avoid damaging the linear response range of the coating. After system startup, it automatically outputs the frequency signals sequentially and simultaneously acquires the voltage and current responses. Please refer to [link to relevant documentation]. Figure 2 During the data acquisition process, the system monitored the background noise at 50Hz in real time and found that the power frequency interference was strong. The 50Hz frequency point was automatically removed, and the adjacent frequency points were retested with higher density. Finally, the original data of 49 valid frequency points were retained.

[0082] 2. Data preprocessing and impedance calculation Please see Figure 3 and Figure 4 The acquired time-domain signal was analyzed using Fast Fourier Transform (FFT) to extract the fundamental component. Taking 0.1Hz as an example, the measured voltage amplitude |V| = 20.0mV, the current amplitude |I| = 0.81μA, and the voltage-current phase difference Δθ = 12.5°.

[0083] The impedance magnitude is calculated as follows: |Z| = |V| / |I| = 20.0 × 10 -3 / (0.81×10 -6 )≈24.69kΩ.

[0084] Convert to complex impedance form: The real part Z′ = 24.69cos( 12.5°)≈24.11kΩ, The imaginary part Z′′ = 24.69sin( 12.5°)≈ 5.34kΩ.

[0085] Perform the same calculations at all frequencies to obtain the complete complex impedance spectrum.

[0086] 3. KK validity test The system imports the complex impedance data from these 49 frequency points into the KK verification module. Through integration calculations, the residuals between the measured real part and the theoretical real part of KK at each frequency point are obtained.

[0087] At low frequency point f m The maximum deviation across the entire frequency band occurs at 0.05Hz, at which point the measured modulus value |Z| is... meas | = 26.31kΩ, while the theoretically calculated modulus |ZKK| = 25.76kΩ.

[0088] The maximum residual ΔKK across the entire frequency band is calculated as follows: ΔKK =∣Z meas ZKK∣ / ∣Z meas |×100% =∣26.31 25.76∣ / 26.31×100%≈2.1%.

[0089] Since the residual value is far below the specified 5% threshold, this result physically proves that the tested corrosion protection system meets the three steady-state prerequisites of causality, linearity, and stability. This indicates that throughout the test, the pipeline corrosion protection system maintained essentially linear and time-invariant characteristics, without significant potential drift or nonlinear distortion. The system determined that the data set was valid overall and included all 49 frequency points in the usable set F. valid .

[0090] 4. Analysis of the DRT (Distributed Relaxation Time) Process The impedance data in the available frequency band is solved by inverse Fourier transform and Tikhonov regularization, with the regularization parameter set to λ = 1 × 10⁻⁶. 3 Please see. Figure 5 Two well-separated extreme peaks appeared. The high-frequency main peak frequency f1≈10.61Hz, with a corresponding relaxation time constant τ1=1 / (2π×10.61)≈0.015s; the low-frequency secondary peak frequency f2≈0.132Hz, with a corresponding relaxation time constant τ2=1 / (2π×0.132)≈1.2s. According to the physical mechanism, the high-frequency fast process (i.e., the smaller relaxation time constant) represents the high-frequency response process of current passing through the coating insulating medium, while the low-frequency slow process (i.e., the larger relaxation time constant) represents the charge transfer polarization process occurring at the metal substrate interface at the bottom of the coating micropores. This indicates that micro-corrosion has begun to take shape.

[0091] 5. CNLS (Complex Nonlinear Least Squares) Fitting Based on the bimodal characteristics detected by DRT, an equivalent circuit model with two time constants is automatically matched during the CNLS fitting stage. This model is an equivalent circuit containing two parallel RC branches, with the following topology: R s + (R coat || C coat ) + (R ct ||C dl ), where R s R is the resistance of the solution. coat For the coating resistor, C coat For coated capacitors, R ctFor the interface polarization resistance, C dl It is a double-layer capacitor.

[0092] The model includes five parameters: solution resistance, coating resistance, coating capacitance, polarization resistance, and double-layer capacitance, i.e., p=5; and uses the reciprocal square of the modulus as the weighting function, i.e., W. k = 1 / |Z meas,k | 2 .

[0093] After multiple iterations of optimization, the weighted sum of squared residuals reached its minimum value S. min = 2.062, at which point the optimal coating resistance R of the engine output is... coat = 15.2kΩ, coated capacitor C coat = 120nF, polarization resistance R ct =8.5kΩ, solution resistance R s =102Ω, double-layer capacitance C dl = 220μF.

[0094] The calculated information for Akaike is as follows: AIC = 2p + N valid ·ln(S min / N valid = 2×5+49ln(2.062 / 49)≈ 145.2A; This process precisely separates the total resistance into two parts, successfully extracting the true resistance value of the pure anti-corrosion layer. Simultaneously, the extremely low AIC value proves that the selected model is neither underfitting nor overfitting due to excessive use of complex parameters. This indicates that the model selection is appropriate, both explaining the main characteristics of the data and avoiding over-parameterization.

[0095] 6. Calculation of the true resistivity value and confidence level output of the anti-corrosion layer The absolute ohmic resistance R of the peeled coating was fitted. coat =15.2kΩ is converted into a physical quantity that can be compared laterally between different pipe sections. Based on the calibration of the test fixture and the exposed area of ​​the tested pipe, the conversion factor K is... geom = 0.8m 2 .

[0096] The actual resistivity of the anti-corrosion layer was calculated as follows: R true = R coat × K geom = 15.2 × 0.8 = 12.16 kΩ·m 2 .

[0097] In a physical sense, the simple ohmic resistance value only represents the absolute resistance of a specific area at the test point and lacks universality; however, the true value of the resistivity of the anti-corrosion layer obtained by multiplying it by the area factor is the true insulation resistivity that reflects the characteristics of the material itself and accurately represents the objective health level of the anti-corrosion layer at that location.

[0098] Based on the parameter covariance matrix generated by CNLS fitting, the joint standard uncertainty of the surface resistivity is extracted to be approximately σ = 0.16 kΩ·m. 2 .

[0099] To provide a sufficient margin of safety for decision-making, a coverage factor k=1.96 is used to calculate the 95% confidence interval, yielding a lower limit of 12.16. 1.96 × 0.16 ≈ 11.85 kΩ·m 2 The upper limit of the interval is: 12.16 + 1.96 × 0.16 ≈ 12.48 kΩ·m², that is, the final confidence interval is [11.85, 12.48] kΩ·m. 2 .

[0100] The optimal solution for the true resistivity of the corrosion-resistant layer is 12.16 kΩ·m. 2 Due to the slight influence of ambient noise, the true value has a 95% probability of falling within the confidence interval. Since the lower limit of this interval is still far higher than the general standard for scrapping anti-corrosion layers, and the previous fitting error and KK residual are extremely low, the overall reliability rating of this measurement is determined to be A (high reliability). This provides solid decision support for whether subsequent excavation or repair work is necessary; compared to the previous reliance on vague judgments based on experience, it provides a clear quantitative basis for decision-making.

[0101] The embodiments of the present invention have the following beneficial effects: 1. Improve the accuracy and consistency of the resistivity of the anti-corrosion layer. By validating the multi-frequency impedance data, adaptively selecting the model, and fitting the constraints, the multi-frequency response measured on-site is transformed into "the true value of the resistivity of the anti-corrosion layer that is closer to the DC operating condition," and the fluctuation of results caused by differences in frequency point selection and manual modeling is significantly reduced, thereby improving the comparability and consistency between tests conducted by different personnel and in different batches.

[0102] 2. Enhance on-site anti-interference and anti-noise capabilities To address the practical problems of high-impedance coating systems being susceptible to electromagnetic noise in the field and having high requirements for shielding and grounding, this invention uses algorithm-based noise assessment, abnormal frequency point identification, and frequency band clipping to enable stable output results even in imperfect shielding and complex electromagnetic environments, reducing dependence on "ideal laboratory conditions."

[0103] 3. Transform the reliability of impedance spectroscopy into a quantifiable, automatic criterion. A self-consistency verification mechanism for the Kramers-Kronig consistency test relationship is introduced to identify and intercept impedance spectra that do not meet the linearity, causality and stability conditions, thus avoiding the forced fitting of distorted spectral data and the generation of seemingly reasonable but actually erroneous outputs.

[0104] 4. Reduce reliance on manual experience in model selection and improve engineering interpretability. Using relaxation time distribution analysis as the basis for model selection and parameter initial value generation, the main time constant process is identified without pre-specifying a single equivalent circuit, thereby reducing the risk of underfitting / overfitting, making the output parameters more consistent with physical meaning and easier to interpret in engineering.

[0105] 5. Output confidence level and traceability information to facilitate review and decision-making closure. In addition to outputting the resistivity of the anti-corrosion layer, it also outputs data quality indicators, fitting residual indices and confidence intervals, and retains information such as frequency points, elimination rules and model parameters throughout the entire process, thereby supporting engineering review, subsequent auditing and trend comparison, and enhancing the usability of the results in acceptance, promotion and large-scale application.

[0106] 6. Improve on-site operation efficiency and reduce cost input in crossing sections. Compared to conventional methods such as densely spaced potential measurements that require extensive data points along the route and high manual labor intensity, standardizing and automating the calculation process from multi-frequency measurement results to actual values ​​reduces the probability of manual interpretation and rework, thereby improving on-site efficiency and delivery speed.

[0107] Please see Figure 7 This application also provides a computer device 600, which includes a memory 601 and a processor 602. The processor 602 is used to run computer program instructions stored in the memory 601 to implement a method for calculating the resistivity of a pipeline anti-corrosion layer. The memory 601 includes at least one type of storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 601 can be an internal storage unit of a computer device, such as a hard disk. In other embodiments, the memory 601 can be an external storage device of a computer device, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, Flash Card, etc. The memory 601 can also include both internal and external storage units of a computer device. The memory 601 can be used not only to store application software and various types of data installed on the computer device, but also to temporarily store data that has been output or will be output. Computer device 600 also includes bus 603. Bus 603 can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, it is represented by only one thick line in the figure, but this does not mean that there is only one bus or one type of bus. Computer device 600 may also include a display component 604. The display component 604 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen, etc. The display component 604 may also be appropriately referred to as a display device or display unit, used to display information processed in computer device 600 and to display a visual user interface.

[0108] Computer device 600 may also include communication component 605. Communication component 605 may optionally include wired communication component and / or wireless communication component (such as Wi-Fi communication component, Bluetooth communication component, etc.), and is typically used to establish communication connections between computer device 600 and other computer devices.

[0109] The figure only shows a computer device 600 with some components. Those skilled in the art will understand that the structure shown in the figure does not constitute a limitation on the computer device 600, and may include fewer or more components than shown, or combine certain components, or have different component arrangements.

[0110] This application also provides a storage medium that, when executed by a computer's processor, enables the computer to perform the pipeline corrosion protection layer resistivity calculation method provided in the above embodiments. For example, the storage medium can be a ROM, RAM, CD-ROM, magnetic tape, floppy disk, USB flash drive, or optical data storage device. It is worth noting that the storage medium mentioned in this application can be a non-volatile storage medium or a non-transient storage medium. It should be understood that all or part of the steps of the above embodiments can be implemented by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part as a computer program product. A computer program product includes one or more computer instructions; the computer instructions can be stored in the aforementioned storage medium. That is, in some embodiments, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to execute the pipeline corrosion protection layer resistivity calculation method provided in the above embodiments. The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for calculating the resistivity of a pipeline anti-corrosion coating, characterized in that, include: Obtain multi-frequency impedance data of the pipeline anti-corrosion layer within a preset low-frequency range, wherein the preset low-frequency range is 0.1Hz to 80Hz; The signal-to-noise ratio of the multi-frequency impedance data is evaluated to obtain the initial impedance spectrum data; The initial impedance spectrum data is subjected to Kramers-Kronig relationship validity verification to generate a set of usable frequency points; The relaxation time distribution of the impedance data corresponding to the set of available frequency points is analyzed to identify the relaxation time constant. Based on the relaxation time constant, a set of candidate equivalent circuit models and initial values ​​of model parameters are generated. The candidate equivalent circuit model is fitted with complex nonlinear least squares to obtain the optimal equivalent circuit model; The ohmic resistance term of the anti-corrosion layer is extracted from the parameters of the optimal equivalent circuit model, and the true value of the resistivity of the anti-corrosion layer is calculated based on the geometric conversion factor.

2. The method for calculating the resistivity of the pipeline anti-corrosion layer according to claim 1, characterized in that, The validity of the Kramers-Kronig relationship was verified on the initial impedance spectrum data, including: Calculate the residual between the measured impedance data and the theoretical KK impedance data; Frequency points where the residual exceeds a preset threshold are marked as abnormal frequency points; Perform elimination, weight reduction, or trigger retesting operations on abnormal frequency points to generate the set of available frequency points.

3. The method for calculating the resistivity of the pipeline anti-corrosion layer according to claim 2, characterized in that, The relaxation time distribution of the impedance data corresponding to the available frequency point set is analyzed to identify the relaxation time constant, including: The impedance data of the available frequency point set is subjected to regularized inversion to obtain the relaxation time distribution function; Identify the peak characteristics of the relaxation time distribution function to determine the number and range of relaxation time constants; The corresponding physical process is automatically matched based on the peak characteristics.

4. The method for calculating the resistivity of the pipeline anti-corrosion layer according to claim 3, characterized in that, The complex nonlinear least squares fitting adopts a modulus reciprocal square weighted strategy, and the objective function is: In the formula, S(θ) is the objective cost function, representing the weighted sum of squared fitting errors; θ is the set of model parameters, such as resistance and capacitance; N valid W represents the number of available frequency points. k For frequency f k The weighting factor Z′ is as follows: meas,k For frequency f k The real part of the measured complex impedance; Z′ model,k (θ) represents the frequency f k The real part of the theoretical complex impedance is calculated from the model parameter set θ; Z′′ meas,k For frequency f k The imaginary part of the measured complex impedance; Z′′ model,k (θ) represents the frequency f k The imaginary part of the theoretical complex impedance is calculated from the model parameter set θ.

5. The method for calculating the resistivity of the pipeline anti-corrosion layer according to claim 4, characterized in that, Before the step of performing complex nonlinear least squares fitting on the candidate equivalent circuit model, the following steps are included: Perform measurement and verification on standard analog circuits; If the parameter deviation exceeds the preset tolerance, the output of the true resistivity value of the pipeline anti-corrosion layer will be stopped.

6. The method for calculating the resistivity of pipeline anti-corrosion coating according to claim 1, characterized in that, Extract the ohmic resistance term of the anti-corrosion layer from the parameters of the optimal equivalent circuit model, and calculate the true resistivity value of the anti-corrosion layer based on the geometric conversion factor, including: The pure anti-corrosion layer ohmic resistance term is extracted from the optimal model parameter set, and polarization resistance and diffusion impedance are eliminated. The true resistivity of the anti-corrosion layer is calculated based on the geometric conversion factor. The formula for converting the true resistivity is as follows: R true = R coat ·K geom ; In the formula, R true This is the actual resistivity value of the anti-corrosion layer, in Ω·m. 2 R coat For the pure anti-corrosion layer ohmic resistance term, K geom The effective geometric conversion area is calculated based on the pipe diameter and the test section length. Output the fitted variance-covariance matrix, and combine it with the KK population residuals to generate a confidence level with a confidence interval of 95%.

7. The method for calculating the resistivity of pipeline anti-corrosion coating according to claim 1, characterized in that, Following the step of calculating the true resistivity value of the anti-corrosion layer based on the geometric conversion factor, the method further includes: In addition to the actual value, each output also synchronously outputs the KK residual index, confidence level, and frequency point list; Among them, the KK residual index serves as a data quality indicator, a retest consistency indicator, and a noise and interference indicator; the confidence level provides a confidence interval based on the CNLS parameter covariance and residual level; the frequency point list includes the original Z(fi), elimination rules, the final model and parameters, ensuring traceability and recalculation.

8. The method for calculating the resistivity of pipeline anti-corrosion coating according to claim 7, characterized in that, The confidence level includes at least one of the following: The data include fitting residual index, confidence intervals derived from the parameter covariance matrix, KK consistency score, and data quality indicators.

9. The method for calculating the resistivity of pipeline anti-corrosion coating according to claim 1, characterized in that, The preset low-frequency range uses a segmented encryption strategy to generate frequency points, and automatically performs frequency avoidance or frequency hopping when power frequency interference is detected.

10. A system for calculating the resistivity of a pipeline anti-corrosion coating, characterized in that, The method for calculating the resistivity of the pipeline anti-corrosion layer according to any one of claims 1 to 9 includes: The data acquisition and preprocessing module is used to acquire the multi-frequency variable impedance data of the pipeline anti-corrosion layer and to evaluate the signal-to-noise ratio of the raw impedance data. The KK test module is used to perform validity verification of the Kramers-Kronig relationship and generate a set of available frequency points; The DRT parsing module is used to identify relaxation time constants through relaxation time distribution analysis. The model generation and fitting module is used to construct candidate equivalent circuit models based on the output of the DRT analysis module; and to perform complex nonlinear least squares fitting to obtain the optimal equivalent circuit model. The data calculation module is used to calculate the true resistivity of the anti-corrosion layer and generate confidence information.

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