A quantitative evaluation method for contact resistance of submersible electric pump power cable joint

CN122839852APending Publication Date: 2026-09-29CHENGDU YUKAIJIA PETROLEUM TECHNOLOGY CO LTD
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Patent Information

Application Number
CN202611193986.8
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-08-07
Publication Date
2026-09-29

AI Technical Summary

Technical Problem

[0002]潜油电泵动力电缆接头是油井电缆连接的关键部件,其接触电阻的稳定性直接影响电缆载流能力和设备安全运行;现有技术中,接触电阻的检测方法多依赖人工调节,精度低且效率不足,同时一些采用单一物理场仿真模型检测的,其模型未综合考虑电磁-热耦合效应,难以反映动态工况下的接触电阻变化,且对复杂工况适应性差,缺乏实时数据驱动的动态修正能力,因此,本发明提出一种潜油电泵动力电缆接头接触电阻定量评价方法以解决现有技术中存在的问题

Benefits of technology

[0012]本发明的有益效果为:本发明通过采集多维动态数据,结合电磁-热耦合模型揭示接触电阻与温升的内在关联,通过离散小波变换降噪与特征融合提升信号可靠性,采用蝙蝠算法优化支持向量机构建反演模型,并引入混合遗传算法动态调整权重矩阵,有效适应复杂工况变化,同时集成环境与电磁干扰修正机制,进一步消除外部因素影响,解决了传统方法静态建模与单一数据驱动的局限,显著提升了接触电阻评价的实时性、准确性与鲁棒性,为潜油电泵电缆接头的状态监测与故障预警提供了科学可靠的技术支撑,保障油井设备长期安全稳定运行。

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Abstract

The application discloses a kind of submersible electric pump power cable joint contact resistance quantitative evaluation method, including step one, multi-source data acquisition, step two, electromagnetic-thermal coupling simulation modeling, step three, feature extraction and data fusion, step four, machine learning model training, step five, dynamic weight distribution and error compensation, step six, quantitative evaluation and output;The application reveals the internal correlation of contact resistance and temperature rise by collecting multi-dimensional dynamic data and combining electromagnetic-thermal coupling model, improves signal reliability through discrete wavelet transform noise reduction and feature fusion, builds inversion model using bat algorithm optimized support vector machine, and introduces hybrid genetic algorithm to dynamically adjust weight matrix, effectively adapts to complex working condition changes, while integrating environmental and electromagnetic interference correction mechanism, further eliminates the influence of external factors, and provides scientific and reliable technical support for submersible electric pump cable joint state monitoring and fault warning.
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Description

Technical Field

[0001] This invention relates to the field of power equipment testing technology, and in particular to a method for quantitatively evaluating the contact resistance of a submersible electric pump power cable joint. Background Technology

[0002] The submersible electric pump power cable joint is a key component of oil well cable connection, and the stability of its contact resistance directly affects the cable's current-carrying capacity and the safe operation of the equipment. In the existing technology, the contact resistance detection methods mostly rely on manual adjustment, which has low accuracy and insufficient efficiency. At the same time, some detection methods using single physical field simulation models do not comprehensively consider the electromagnetic-thermal coupling effect, making it difficult to reflect the changes in contact resistance under dynamic operating conditions. Furthermore, they have poor adaptability to complex operating conditions and lack the ability to dynamically correct based on real-time data. Therefore, this invention proposes a quantitative evaluation method for the contact resistance of submersible electric pump power cable joints to solve the problems existing in the prior art. Summary of the Invention

[0003] To address the aforementioned problems, the present invention aims to propose a quantitative evaluation method for the contact resistance of submersible electric pump power cable joints. This method achieves high-precision quantitative evaluation of the contact resistance of submersible electric pump power cable joints through multi-source data fusion, electromagnetic-thermal coupling simulation, and intelligent algorithm collaborative optimization.

[0004] To achieve the objectives of this invention, the invention is implemented through the following technical solution: a method for quantitatively evaluating the contact resistance of a submersible electric pump power cable connector, comprising the following steps: Step 1: Multi-source data acquisition. Temperature distribution data of the cable joint surface and body are collected using distributed optical fiber temperature measurement technology. At the same time, the magnetic induction intensity at the joint is measured using a Rogowski coil, and the cable operating current, voltage and environmental parameters are recorded to form a multi-dimensional time series dataset. Step 2: Electromagnetic-thermal coupling simulation modeling. An electromagnetic-thermal coupling simulation model is built in COMSOL Multiphysics. Cable structural parameters and material properties are input, and steady-state temperature difference ΔT and contact resistance R under different operating conditions are calculated using finite element analysis. j The mapping relationship; Step 3: Feature extraction and data fusion. The collected magnetic induction intensity signal is subjected to discrete wavelet transform noise reduction processing to extract the steady-state component after high-frequency noise suppression. Combined with the ΔT data output by the simulation model, a multi-dimensional feature vector containing magnetic induction intensity gradient, temperature gradient and current density distribution is constructed. Step 4: Machine learning model training. A contact resistance inversion model is constructed using the support vector machine algorithm. The hyperparameters of the support vector machine are optimized using the bat algorithm, and the bat positions are iteratively updated until convergence. Step 5: Dynamic weight allocation and error compensation. Based on historical data, a dynamic weight matrix for contact resistance, temperature, and current is established. The weight matrix is ​​adaptively adjusted using a hybrid genetic algorithm to compensate for measurement deviations caused by environmental temperature drift and electromagnetic interference. Step Six: Quantitative Evaluation and Output. Input the real-time data into the trained model and output the quantitative value of contact resistance R. j The error analysis report is generated by comparing the value with the actual value measured by the micro-ohmmeter. An error of ≤1.5% is considered qualified; otherwise, an early warning is triggered.

[0005] A further improvement is made in step two, where the contact surface between the first and second cable cores on the inner surface of the crimped copper tube is set as the key calculation area in the simulation model.

[0006] A further improvement lies in the following: The establishment of the electromagnetic-thermal coupling simulation model in step two specifically involves setting up a two-dimensional axisymmetric model in COMSOL, dividing it into hexahedral meshes, and setting boundary conditions including current density J = I / (πr²). 2 ) and thermal convection coefficient h = 10 W / (m 2 ·K), where I is the total current and r is the conductor radius; the current loading process is simulated using a transient solver to solve the Poisson equation ∇·(σ∇V)=0 and the heat conduction equation ∇·(k∇T)=Q, where σ is the electrical conductivity, V is the electric potential, k is the thermal conductivity, T is the temperature distribution of the cable joint and the cable body, and Q is the Joule heat; the output results include the contact resistance R of the contact surface. j1 R j2 R j3 Distribution cloud map and corresponding heat loss power density.

[0007] Further improvements are made in the following steps: In step three, feature extraction includes performing discrete wavelet transform decomposition on the magnetic induction intensity signal, selecting the db4 wavelet basis function, decomposing it into 5 layers, and retaining the low-frequency component a5 as the effective signal; calculating the temperature gradient ∇T=∂T / ∂x, where T is the temperature value collected by the distributed optical fiber temperature measurement technology, x is the axial coordinate along the cable, and combining the current density J=σE from the finite element simulation results for feature fusion, where σ is the conductivity and E is the electric field strength.

[0008] A further improvement is that the fitness function of the bat algorithm in step four is defined as the mean squared error of the support vector machine model on the validation set.

[0009] A further improvement lies in the following: the process of optimizing the support vector machine hyperparameters using the bat algorithm in step four includes: S1. Initialize the bat population N=30, frequency range f min =0-2, pulse emission rate r0=0.5; S2. Calculate the fitness function f = 1 / MSE, where the mean square error MSE = 1 / N∑(y i - i ) 2 N is the sample size, y i For actual measured temperature, i To predict temperature; S3, Update Bat Speed ,Location pulse frequency ,in Let be the speed of the i-th bat in the (t+1)th iteration. Let i be the position of the i-th bat in the (t+1)th iteration. Let be the pulse frequency of the i-th bat in the (t+1)th iteration. Let be the speed of the i-th bat in the t-th iteration. Let i be the position of the i-th bat in the t-th iteration. f is the current globally optimal position. i Let f be the pulse frequency of the i-th bat. min f is the minimum pulse frequency. max This represents the maximum pulse frequency. S4. If the fitness does not improve for 5 consecutive generations, perform a mutation operation to generate a new bat individual.

[0010] A further improvement lies in the following: the construction of the dynamic weight matrix in step five specifically involves establishing a historical database to store data on different ambient temperatures T. env Contact resistance R under operating current I j Correlation data with temperature T; define the weighting function w=exp(-λ·ΔT / ΔT) max ), where λ is the coefficient of thermal expansion of the material, ΔT is the actual temperature rise, and ΔT max To determine the maximum allowable temperature rise, a hybrid genetic algorithm is used to optimize the weight coefficients, with the fitness function being F = α·R. j,pred +β·ΔT pred, Where α and β are the dynamic coefficients generated by the genetic algorithm, and R0 j,pred To predict contact resistance, ΔT pred To predict temperature differences.

[0011] The further improvement lies in the fact that, in step six, the error compensation specifically involves introducing an ambient temperature compensation term ΔR. env =K·(T env -T ref ), where K is a temperature coefficient taken as 0.02 / ℃, T env For ambient temperature, T refThe reference temperature is taken as 25℃; calculate the electromagnetic interference correction factor F. em =1 / (1+ε·B 2 ), where ε is the permeability and B is the effective value of the magnetic flux density; the final output R j,comp =R j,raw ·ΔR env ·F em R j,comp To determine the quantitative value of the contact resistance after compensation, R j,raw This is the original predicted contact resistance.

[0012] The beneficial effects of this invention are as follows: By collecting multi-dimensional dynamic data and combining it with an electromagnetic-thermal coupling model, this invention reveals the intrinsic relationship between contact resistance and temperature rise. It improves signal reliability through discrete wavelet transform noise reduction and feature fusion, uses the bat algorithm to optimize the support vector machine to construct the inversion model, and introduces a hybrid genetic algorithm to dynamically adjust the weight matrix, effectively adapting to complex working conditions. At the same time, it integrates environmental and electromagnetic interference correction mechanisms to further eliminate the influence of external factors. This invention solves the limitations of traditional static modeling and single data-driven methods, significantly improving the real-time performance, accuracy, and robustness of contact resistance evaluation. It provides scientific and reliable technical support for the condition monitoring and fault early warning of submersible pump cable joints, ensuring the long-term safe and stable operation of oil well equipment. Attached Figure Description

[0013] Figure 1 This is a flowchart of the evaluation method of the present invention. Detailed Implementation

[0014] To enhance understanding of the present invention, the present invention will be further described in detail below with reference to embodiments. These embodiments are only used to explain the present invention and do not constitute a limitation on the scope of protection of the present invention.

[0015] according to Figure 1 As shown in the figure, this embodiment provides a method for quantitatively evaluating the contact resistance of a submersible electric pump power cable connector, including the following steps: Step 1: Multi-source data acquisition. Temperature distribution data of the cable joint surface and body are collected using distributed fiber optic temperature measurement technology. At the same time, the magnetic induction intensity at the joint is measured using a Rogowski coil, and the cable operating current, voltage and environmental parameters are recorded to form a multi-dimensional time series dataset, in which the environmental parameters include temperature and humidity.

[0016] The distributed fiber optic temperature measurement system employs the Raman scattering principle, with a spatial resolution of 0.5m and a sampling frequency ≥10Hz; the Rogowski coil has 50 turns and a cross-sectional area ≥20mm². 2 The linearity error is ≤0.5%.

[0017] Step 2: Electromagnetic-thermal coupling simulation modeling. An electromagnetic-thermal coupling simulation model is built in COMSOL Multiphysics. Cable structural parameters and material properties are input, and steady-state temperature difference ΔT and contact resistance R under different operating conditions are calculated using finite element analysis. j The mapping relationship; The structural parameters include conductor cross-sectional area and contact pressure, and the material properties include resistivity and thermal conductivity. In the simulation model, the contact surface between the first cable core and the second cable core on the inner surface of the crimped copper tube is set as the key calculation area; The electromagnetic-thermal coupling simulation model was established by setting up a two-dimensional axisymmetric model in COMSOL, dividing it into hexahedral meshes, and setting boundary conditions including current density J=I / (πr²). 2 ) and thermal convection coefficient h = 10 W / (m 2 ·K), where I is the total current, the rated current passing through the cable during submersible pump operation, and r is the conductor radius, the equivalent radius of the cable core; the current loading process is simulated using a transient solver to solve the Poisson equation ∇·(σ∇V)=0 and the heat conduction equation ∇·(k∇T)=Q, where σ is the conductivity, the electrical conductivity of the cable conductor material, V is the potential, the potential distribution at the cable joint, k is the thermal conductivity, the thermal conductivity of the cable material, T is the temperature distribution of the cable joint and the cable body, and Q is the Joule heat, the heat generated by the current passing through the contact resistance of the joint. In the Poisson equation and the heat conduction equation, the first ∇ is the divergence operator, representing the spatial rate of change of the scalar field, and the second ∇ is the potential gradient operator, representing the direction of the maximum rate of change of the scalar field; the output results include the contact resistance R of the contact surface. j1 R j2 R j3 Distribution cloud map and corresponding heat loss power density.

[0018] Step 3: Feature extraction and data fusion. The collected magnetic induction intensity signal is subjected to discrete wavelet transform noise reduction processing to extract the steady-state component after high-frequency noise suppression. Combined with the ΔT data output by the simulation model, a multi-dimensional feature vector containing magnetic induction intensity gradient, temperature gradient and current density distribution is constructed. Feature extraction includes discrete wavelet transform decomposition of the magnetic induction intensity signal, selecting the db4 wavelet basis function, decomposing it into 5 layers, and retaining the low-frequency component a5 as the effective signal; calculating the temperature gradient ∇T=∂T / ∂x, where T is the temperature value collected by distributed fiber optic temperature measurement technology, and x is the axial coordinate along the cable axis with the center of the joint as the origin; and combining the current density J=σE from the finite element simulation results for feature fusion, where σ is the conductivity, E is the electric field strength, and the electric field distribution at the cable joint is represented.

[0019] ∇T is the temperature gradient, representing the rate of temperature change along the cable axis; ∂T / ∂x describes the temperature change with the cable length.

[0020] Step 4: Machine learning model training. A contact resistance inversion model is constructed using the support vector machine algorithm. The hyperparameters of the support vector machine are optimized using the bat algorithm, and the bat positions are iteratively updated until convergence. The fitness function of the Bat algorithm is defined as the mean squared error of the support vector machine model on the validation set, and the hyperparameters include the penalty factor and kernel function parameters. The process of optimizing the hyperparameters of a support vector machine using the bat algorithm includes: S1. Initialize the bat population N=30, frequency range f min =0-2, pulse emission rate r0=0.5; S2. Calculate the fitness function f = 1 / MSE, where the mean square error MSE = 1 / N∑(y i - i ) 2 N is the number of samples, the total number of measured temperature samples used for training, and y i The measured temperature is the actual value from the distributed fiber optic temperature measurement system. i The output value of the support vector machine model for predicting temperature; f is the fitness function value, which measures the prediction accuracy of the support vector machine model. The larger the value, the higher the accuracy. S3, Update Bat Speed ,Location pulse frequency ,in Let be the speed of the i-th bat in the (t+1)th iteration. Let i be the position of the i-th bat in the (t+1)th iteration. Let be the pulse frequency of the i-th bat in the (t+1)th iteration. Let be the speed of the i-th bat in the t-th iteration. Let i be the position of the i-th bat in the t-th iteration. f represents the current globally optimal position, i.e., the hyperparameter combination that minimizes the current mean square error. i Let f be the pulse frequency of the i-th bat, and let f be the step size that controls the movement of the bat. min f is the minimum pulse frequency. max The maximum pulse frequency is given, and rand is a random number in the interval [0, 1] to simulate the random exploration behavior of bats. S4. If the fitness does not improve for 5 consecutive generations, perform a mutation operation to generate a new bat individual.

[0021] Step 5: Dynamic weight allocation and error compensation. Based on historical data, a dynamic weight matrix for contact resistance, temperature, and current is established. The weight matrix is ​​adaptively adjusted using a hybrid genetic algorithm to compensate for measurement deviations caused by environmental temperature drift and electromagnetic interference. The construction of the dynamic weight matrix specifically involves establishing a historical database to store data on different ambient temperatures T. env Contact resistance R under operating current I j Correlation data with temperature T; define the weighting function w=exp(-λ·ΔT / ΔT) max This represents the degree of influence of temperature on contact resistance. exp is the natural exponential function, which converts the linear temperature difference into a nonlinear weight. λ is the coefficient of thermal expansion of the material, and ΔT is the actual temperature rise, representing the temperature difference between the joint surface and the ambient temperature. max The maximum allowable temperature rise is the limit temperature rise of the cable design; the weight coefficients are optimized using a hybrid genetic algorithm, and the fitness function is F=α·R. j,pred +β·ΔT pred The weight matrix is ​​used to measure the overall performance of the weights; smaller values ​​are better. α and β are dynamic coefficients generated by the genetic algorithm, used to balance the importance of the predicted contact resistance and temperature difference, respectively. R j,pred To predict contact resistance, the contact resistance value ΔT output by the support vector machine model is used. pred To predict the temperature difference, the simulation model outputs the steady-state temperature difference.

[0022] The crossover probability of the hybrid genetic algorithm is set to 0.8, the mutation probability is set to 0.01, and the number of iterations is ≥100 generations.

[0023] Step Six: Quantitative Evaluation and Output. Input the real-time data into the trained model and output the quantitative value of contact resistance R. j The error analysis report is generated by comparing the value with the actual value measured by the micro-ohmmeter. An error of ≤1.5% is considered qualified; otherwise, an early warning is triggered. Specifically, error compensation involves introducing an ambient temperature compensation term ΔR. env =K·(T env -T ref ), where K is a temperature coefficient taken as 0.02 / ℃, representing the rate of change of contact resistance with temperature, and T env The ambient temperature (T) represents the real-time temperature of the cable's operating environment. ref The reference temperature is set to 25℃, representing the calibration reference temperature; the electromagnetic interference correction factor F is calculated. em =1 / (1+ε·B 2 ), where ε is the permeability and B is the effective value of the magnetic flux density; the final output R j,comp =R j,raw ·ΔR env ·F em Rj,comp To calculate the quantitative value of the contact resistance after compensation, the final output evaluation result is R. j,raw The original predicted contact resistance is the uncompensated output value of the support vector machine model.

[0024] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for quantitatively evaluating the contact resistance of a submersible electric pump power cable joint, characterized in that, Includes the following steps: Step 1: Multi-source data acquisition. Temperature distribution data of the cable joint surface and body are collected using distributed fiber optic temperature measurement technology. At the same time, the magnetic induction intensity at the joint is measured using a Rogowski coil, and the cable operating current, voltage and environmental parameters are recorded to form a multi-dimensional time series dataset. Step 2: Electromagnetic-thermal coupling simulation modeling. An electromagnetic-thermal coupling simulation model is built in COMSOL Multiphysics. Cable structural parameters and material properties are input, and steady-state temperature difference ΔT and contact resistance R under different operating conditions are calculated using finite element analysis. j The mapping relationship; Step 3: Feature extraction and data fusion. The collected magnetic induction intensity signal is subjected to discrete wavelet transform noise reduction processing to extract the steady-state component after high-frequency noise suppression. Combined with the ΔT data output by the simulation model, a multi-dimensional feature vector containing magnetic induction intensity gradient, temperature gradient and current density distribution is constructed. Step 4: Machine learning model training. A contact resistance inversion model is constructed using the support vector machine algorithm. The hyperparameters of the support vector machine are optimized using the bat algorithm, and the bat positions are iteratively updated until convergence. Step 5: Dynamic weight allocation and error compensation. A dynamic weight matrix for contact resistance, temperature, and current is established based on historical data. The weight matrix is ​​adaptively adjusted using a hybrid genetic algorithm to compensate for measurement deviations caused by environmental temperature drift and electromagnetic interference. Step Six: Quantitative Evaluation and Output. Input the real-time data into the trained model and output the quantitative value of contact resistance R. j The error analysis report is generated by comparing the value with the actual value measured by the micro-ohmmeter. An error of ≤1.5% is considered qualified; otherwise, an early warning is triggered.

2. The method for quantitatively evaluating the contact resistance of a submersible electric pump power cable joint according to claim 1, characterized in that: In step two, the contact surface between the first cable core and the second cable core on the inner surface of the crimped copper tube is set as the key calculation area in the simulation model.

3. The method for quantitatively evaluating the contact resistance of a submersible electric pump power cable joint according to claim 1, characterized in that: The establishment of the electromagnetic-thermal coupling simulation model in step two specifically involves setting up a two-dimensional axisymmetric model in COMSOL, dividing it into hexahedral meshes, and setting boundary conditions including current density J=I / (πr²). 2 ) and thermal convection coefficient h = 10 W / (m 2 ·K), where I is the total current and r is the conductor radius; the current loading process is simulated using a transient solver to solve the Poisson equation ∇·(σ∇V)=0 and the heat conduction equation ∇·(k∇T)=Q, where σ is the electrical conductivity, V is the electric potential, k is the thermal conductivity, T is the temperature distribution of the cable joint and the cable body, and Q is the Joule heat; the output results include the contact resistance R of the contact surface. j1 R j2 R j3 Distribution cloud map and corresponding heat loss power density.

4. The method for quantitatively evaluating the contact resistance of a submersible electric pump power cable joint according to claim 1, characterized in that: The feature extraction in step three includes performing discrete wavelet transform decomposition on the magnetic induction intensity signal, selecting the db4 wavelet basis function, decomposing it into 5 layers, and retaining the low-frequency component a5 as the effective signal; calculating the temperature gradient ∇T=∂T / ∂x, where T is the temperature value collected by the distributed optical fiber temperature measurement technology, x is the coordinate along the cable axis, and combining the current density J=σE from the finite element simulation results for feature fusion, where σ is the conductivity and E is the electric field strength.

5. The method for quantitatively evaluating the contact resistance of a submersible electric pump power cable joint according to claim 1, characterized in that: In step four, the fitness function of the bat algorithm is defined as the mean squared error of the support vector machine model on the validation set.

6. The method for quantitatively evaluating the contact resistance of a submersible electric pump power cable joint according to claim 1, characterized in that: The process of optimizing the support vector machine hyperparameters using the bat algorithm in step four includes: S1. Initialize the bat population N=30, frequency range f min =0-2, pulse emission rate r0=0.5; S2. Calculate the fitness function f = 1 / MSE, where the mean square error MSE = 1 / N∑(y i - i ) 2 N is the sample size, y i For actual measured temperature, i To predict temperature; S3, Update Bat Speed ,Location pulse frequency ,in Let be the speed of the i-th bat in the (t+1)th iteration. Let i be the position of the i-th bat in the (t+1)th iteration. Let be the pulse frequency of the i-th bat in the (t+1)th iteration. Let be the speed of the i-th bat in the t-th iteration. Let i be the position of the i-th bat in the t-th iteration. f is the current globally optimal position. i Let f be the pulse frequency of the i-th bat. min f is the minimum pulse frequency. max This represents the maximum pulse frequency. S4. If the fitness does not improve for 5 consecutive generations, perform a mutation operation to generate a new bat individual.

7. The method for quantitatively evaluating the contact resistance of a submersible electric pump power cable joint according to claim 1, characterized in that: The construction of the dynamic weight matrix in step five specifically involves establishing a historical database to store data on different ambient temperatures T. env Contact resistance R under operating current I j Correlation data with temperature T; define the weighting function w=exp(-λ·ΔT / ΔT) max ), where λ is the coefficient of thermal expansion of the material, ΔT is the actual temperature rise, and ΔT max To determine the maximum allowable temperature rise, a hybrid genetic algorithm is used to optimize the weight coefficients, with the fitness function being F = α·R. j,pred +β·ΔT pred, Where α and β are the dynamic coefficients generated by the genetic algorithm, and R0 j,pred To predict contact resistance, ΔT pred To predict temperature differences.

8. The method for quantitatively evaluating the contact resistance of a submersible electric pump power cable joint according to claim 1, characterized in that: In step six, the error compensation specifically involves introducing an ambient temperature compensation term ΔR. env =K·(T env -T ref ), where K is a temperature coefficient taken as 0.02 / ℃, T env For ambient temperature, T ref The reference temperature is taken as 25℃; calculate the electromagnetic interference correction factor F. em =1 / (1+ε·B 2 ), where ε is the permeability and B is the effective value of the magnetic flux density; the final output R j,comp =R j,raw ·ΔR env ·F em R j,comp To determine the quantitative value of the contact resistance after compensation, R j,raw This is the original predicted contact resistance.