A method and system for contactless current measurement of single-core cables

Abstract

The application discloses a kind of non-contact single-core cable current measurement method and system, belong to current measurement field, the method is: obtaining the magnetic field component collected by three magnetic sensors that are uniformly distributed in circumference and sensitive axis is arranged along tangential direction and radial direction respectively;Construct magnetic field direction prediction vector and determine the intersection coordinates of adjacent vector, determine the initial position and initial current of single-core cable according to intersection coordinates;Iterative calculation of magnetic field theoretical data based on position and current, until the sum of the residual vector module length of theoretical data and measured component is less than the preset threshold value;Residual and historical theoretical data and measured data are calculated at each iteration Proportion coefficient, if the positive and negative of residual is consistent, then update current based on proportion coefficient, otherwise update position, finally output current as measurement result. By implementing the present application, the problem that the non-contact current measurement in the prior art is prone to local optimum and slow convergence speed under the eccentric working condition of single-core cable can be solved.

Description

Technical Field

[0001] This invention belongs to the field of current measurement and relates to a method and system for measuring the current of a non-contact single-core cable. Background Technology

[0002] With the advancement of smart grid construction, real-time monitoring of the operating status of single-core power cables has become a crucial link in ensuring power supply safety. Non-contact current measurement technology has been widely used in distribution automation and load monitoring scenarios due to its advantages such as no power outage installation and good electrical isolation. Existing non-contact current measurement schemes are mainly divided into two categories: those based on single-sensor perception and those based on multi-sensor arrays combined with general optimization algorithms. The former usually assumes that the cable is located at the center of the sensor and infers the current by combining a single magnetic field observation value with a fixed proportional coefficient. The latter uses multiple sensors to simultaneously collect spatial magnetic field data, constructs an objective function based on the law of electromagnetic fields, and uses general nonlinear optimization strategies such as particle swarm optimization and gradient descent to iteratively search in the entire space range to simultaneously invert the current amplitude and cable coordinates. However, the aforementioned existing technologies have significant drawbacks when dealing with the eccentricity phenomenon commonly found in the actual installation of single-core cables. The single-sensor solution, lacking spatial dimensional constraints, cannot distinguish whether the magnetic field change is caused by current fluctuations or positional shifts, resulting in severe measurement distortion. The array solution based on general optimization algorithms, due to its high dependence on randomly or empirically set initial values, is prone to getting trapped in local optima in nonlinear magnetic field models, leading to inversion failure. Furthermore, the full-space search process involves complex matrix operations and a large number of iterations, resulting in huge computational overhead that is difficult to meet the real-time dynamic monitoring requirements of embedded terminals. Summary of the Invention

[0003] This application provides a non-contact current measurement method and system for single-core cables, which can solve the problem that non-contact current measurement in the prior art is prone to getting trapped in local optima and has a slow convergence speed under the eccentric working condition of single-core cables.

[0004] To achieve the above objectives, in a first aspect, the present invention provides a method for measuring the current of a non-contact single-core cable, comprising: The magnetic field component data collected by three magnetic sensors are obtained; the three magnetic sensors are evenly distributed at 120 degrees intervals around the single-core cable to be tested on a plane circumference perpendicular to the cable axis, and the first sensitive axis of each magnetic sensor is arranged along the tangent direction of the circumference and the second sensitive axis is arranged along the radius direction of the circumference pointing towards the center of the circle. Based on the data of each magnetic field component, a prediction vector of the magnetic field direction is constructed. The set of coordinates of the intersection points of adjacent prediction vectors is determined. Combined with the position of each magnetic sensor, the initial position and initial current of the single-core cable are calculated. Based on the initial position and initial current, the theoretical magnetic field data of each magnetic sensor is iteratively calculated, and the residual between the current theoretical magnetic field data and the corresponding magnetic field component data is calculated, as well as the proportional coefficient between the previous round's historical theoretical magnetic field data and the corresponding magnetic field component data. If the signs of the residuals are consistent, the current initial current is updated based on the proportional coefficients; otherwise, the current initial position is updated based on the proportional coefficients. This process continues until the sum of the vector magnitudes of the component residuals between the theoretical magnetic field data and the corresponding magnetic field component data is less than a preset threshold. Then, the current initial current is output as the current measurement result.

[0005] Compared with existing technologies, the embodiments of this application have the following beneficial effects: Magnetic field component data is acquired, and three magnetic sensors are uniformly distributed at 120-degree intervals on a circle, with their sensitive axes arranged along the tangent and radial directions, respectively. This constructs a minimalist array with geometric symmetry and orthogonal sensing capabilities, reducing hardware costs and calibration difficulty, while providing complete geometric constraint information for subsequent spatial positioning. Furthermore, a magnetic field direction prediction vector is constructed based on the magnetic field component data, and the set of intersection coordinates of adjacent vectors is determined. The magnetic field angle information is directly mapped to position cues using the physical laws of electromagnetic fields, achieving a leap from simple numerical fitting to geometric analysis and avoiding blind searching. Then, the initial position is determined based on the intersection coordinate set, and the initial current is calculated. A high-confidence iterative initial value is obtained through physical model inversion, solving the technical problem that traditional nonlinear optimization algorithms are prone to getting trapped in local optima due to random initial value selection. Then, iterative calculations are performed based on the initial data until the sum of the magnitudes of the component residual vectors is less than a preset threshold. A strict convergence criterion is established to ensure the accuracy and reliability of the output results. In each iteration, the residual and the proportional coefficient are calculated, and the parameter evolution type is intelligently determined based on the consistency of the positive and negative signs of the residuals. If the positive and negative signs are consistent, the current is updated; otherwise, the position is updated. This "step-by-step correction" strategy decouples the coupled nonlinear inversion problem into two independent single-variable optimization processes. The residual sign distribution characteristics are used to adaptively identify whether the source of error is current amplitude deviation or position offset, thereby significantly reducing the number of invalid iterations and improving the convergence speed. The above technical features work together to realize a fast and high-precision current measurement that can avoid local optimum traps and meet the real-time requirements of embedded terminals under the eccentricity of single-core cables. This overcomes the shortcomings of existing technologies, which are difficult to balance weak anti-eccentricity capability and high computational cost.

[0006] In some embodiments of the first aspect of this application, calculating the initial position of the single-core cable includes: Determine whether the coordinates of each intersection point in the set of intersection point coordinates coincide. If they coincide, the coordinates of the coincident point are directly used as the initial position. If they do not coincide, the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of the intersection points are used as the initial position.

[0007] Compared with existing technologies, the above embodiments have the following advantages: By determining whether the coordinates of each intersection point in the set of intersection point coordinates coincide, and directly selecting the coordinates of the coincident point as the initial position when they coincide, the characteristics of rays intersecting at a point under the ideal physical model are utilized, achieving zero-error rapid positioning under ideal working conditions without noise interference. When the intersection points do not coincide, the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of each intersection point are used as the initial position. This is to address the situation in actual measurements where rays cannot intersect accurately due to sensor noise or environmental interference. The geometric center approximation algorithm is used to obtain the most probable position estimate. This segmented processing logic not only ensures the computational efficiency under ideal conditions, but also enhances the robustness of the algorithm under non-ideal working conditions, ensuring that the initial position data is always within the minimum neighborhood of the true value, laying a solid geometric foundation for subsequent iterative convergence.

[0008] In some embodiments of the first aspect of this application, calculating the initial current of a single-core cable includes: Based on the initial position and the coordinate positions of each magnetic sensor, the Euclidean distance from each magnetic sensor to the initial position is calculated using Biot-Savart's law. Substitute the magnitudes of the Euclidean distances and magnetic field components into the inverse function of the Biot-Savart law formula to calculate the independent current estimates for each magnetic sensor. The initial current is obtained by performing an arithmetic mean operation on each of the independent current estimates.

[0009] Compared with existing technologies, the above embodiments have the following advantages: By calculating the Euclidean distance based on the initial position and the coordinate positions of each magnetic sensor, the spatial geometric relationship between the cable and each sensing node is accurately quantified, providing accurate spatial scale parameters for the physical modeling of magnetic field strength; further, by substituting the Euclidean distance and the magnitude of the magnetic field component data into the inverse function of the Biot-Savart law formula, and utilizing the forward reversibility of the fundamental law of electromagnetic fields, the independent current estimates from the perspective of each sensor are directly derived from the observed magnetic field strength, realizing the initial value of parameters driven by physical mechanisms; finally, the arithmetic mean is performed on each independent current estimate, and statistical smoothing is performed using the redundancy characteristics of multi-sensor data, effectively suppressing the random measurement noise or instantaneous abnormal fluctuations that may exist in a single sensor, thereby obtaining a high-confidence and stable initial current, significantly reducing the sensitivity of the subsequent iteration process to the initial current value.

[0010] In some embodiments of the first aspect of this application, the calculation of the theoretical magnetic field data for each magnetic sensor includes: Based on the initial position of the single-core cable in this round and the coordinate positions of each magnetic sensor, calculate the Euclidean distance data from each magnetic sensor to the initial position of the single-core cable. Substituting the Euclidean distance data and the initial current of the single-core cable in this round into the Biot-Savart law formula, the theoretical magnetic field modulus data at each magnetic sensor location is calculated. Based on the definition of the sensitive axis direction of each magnetic sensor, the theoretical magnetic field modulus data corresponding to each magnetic sensor is decomposed into theoretical data of the tangential component along the first sensitive axis direction and theoretical data of the radial component along the second sensitive axis direction, which are used as the theoretical magnetic field data of each magnetic sensor in the current cycle.

[0011] Compared with existing technologies, the above embodiments have the following beneficial effects: By calculating Euclidean distance data based on the current position and sensor coordinates, the spatial geometric topology is dynamically updated during the iteration process, ensuring that the theoretical model can reflect the changes in cable position in real time; furthermore, the distance data and current are substituted into the Biot-Savart law formula to calculate the theoretical magnetic field modulus data, realizing a positive and accurate mapping from decision variables to physical observations, providing a benchmark for error assessment; at the same time, the theoretical modulus data is decomposed into tangential and radial component theoretical data according to the definition of the sensitive axis direction, completing the projection transformation from scalar magnetic field strength to vector component space, providing necessary data dimension support for subsequent refined residual calculation and convergence judgment based on component level differences, ensuring the comparability of theoretical predictions and actual observations in the same coordinate system.

[0012] In some embodiments of the first aspect of this application, the calculation of the scaling factor between the theoretical historical magnetic field data and the corresponding magnetic field component data of the previous round includes: The magnitude of the magnetic field component data of each magnetic sensor is extracted as the observed magnetic field magnitude data, and the magnitude of the theoretical magnetic field data at the location of each magnetic sensor obtained in the previous iteration is extracted as the theoretical magnetic field magnitude data. Calculate the ratio of the observed magnetic field modulus data to the theoretical magnetic field modulus data for each magnetic sensor to obtain the independent proportionality coefficient for each magnetic sensor.

[0013] Compared with existing technologies, the above embodiments have the following beneficial effects: by extracting the magnitude of the magnetic field component data as the observed magnetic field magnitude data and the magnitude of the theoretical data from the previous round as the theoretical magnetic field magnitude data, feature extraction from vector components to scalar magnitude is completed, eliminating the interference of direction factors on amplitude error assessment; further, the ratio of the observed magnetic field magnitude data to the theoretical magnetic field magnitude data is calculated to obtain an independent proportionality coefficient. This ratio directly quantifies the relative deviation multiple between the current model estimate and the actual observation value, transforming the absolute magnetic field strength difference into a dimensionless correction factor. This normalization processing method makes the correction strategy no longer dependent on the absolute magnitude of the current or the specific sensitivity of the sensor, but focuses on the elimination of relative errors, providing a unified and stable mathematical driving quantity for subsequent adaptive adjustment of current or position.

[0014] In some embodiments of the first aspect of this application, updating the current initial current based on various scaling factors includes: The current correction coefficient is obtained by performing an arithmetic average on the proportional coefficients corresponding to all magnetic sensors. The initial current from the previous round is multiplied by the current correction coefficient to obtain the updated initial current.

[0015] Compared with existing technologies, the above embodiments have the following advantages: by performing an arithmetic average operation on the proportional coefficients corresponding to all magnetic sensors to obtain the current correction coefficient, the spatial diversity gain of the multi-sensor array is utilized to fuse the local deviation information of each node into a globally consistent current adjustment trend, effectively suppressing the misleading effect of single-point measurement noise on the overall correction direction; furthermore, the current and the current correction coefficient of the previous round are multiplied, and the current amplitude is directly corrected by using a proportional scaling method. This multiplication update mechanism conforms to the linear proportional relationship between magnetic field and current in Biosavart's law, and can approximate the true current value in one step with the minimum computational cost under the condition that the residual sign is consistent (i.e., the position is accurate and only the current is wrong), avoiding the cumbersome process of adjusting the learning rate step size required in the traditional gradient descent method, and significantly improving the convergence efficiency of the current dimension.

[0016] In some embodiments of the first aspect of this application, updating the current initial position based on each scaling factor includes: For each magnetic sensor, construct a relative position vector from the coordinate position of the magnetic sensor to the initial position of the single-core cable in the previous round; Calculate the reciprocal of the proportional coefficient of each magnetic sensor and subtract one to obtain the displacement coefficient of each magnetic sensor. The relative position vector corresponding to each magnetic sensor is multiplied by the displacement coefficient to obtain the local displacement vector corresponding to each magnetic sensor. Then, the local displacement vectors of all magnetic sensors are summed to obtain the global position correction vector. Perform vector addition between the initial position from the previous round and the global position correction vector to obtain the updated initial position.

[0017] Compared to existing technologies, the above embodiments have the following advantages: By constructing a relative position vector pointing from the sensor coordinates to the previous round position, the geometric guidance direction of spatial correction is clarified, ensuring that the position update always proceeds along the radial path connecting the sensor and the cable, conforming to the physical gradient direction of the magnetic field changing with distance; further, the displacement coefficient is obtained by subtracting one from the reciprocal of the proportional coefficient, transforming the relative deviation of the magnetic field amplitude into a correction weight for spatial distance, and deriving the driving force for position adjustment using the inverse nonlinear relationship between the magnetic field and distance; subsequently, the relative position vector and the displacement coefficient are multiplied by vector and summed to obtain the global position correction vector, realizing the vector synthesis of multi-source position correction information, which can integrate the observation differences of multiple sensors to correct the two-dimensional coordinates of the cable; finally, the position is updated by vector addition while keeping the current constant in the process. This decoupled update strategy ensures that when the residual signs are inconsistent (i.e., there is a position deviation), the algorithm can concentrate computing power to prioritize the correction of spatial geometric relationships, avoiding convergence difficulties caused by the mutual coupling oscillation of current and position parameters, and greatly improving the stability of the nonlinear inversion process.

[0018] In some embodiments of the first aspect of this application, the sum of the magnitudes of the component residual vectors is calculated in the following manner, including: For each magnetic sensor, calculate the first difference between the theoretical data of the tangential component in the magnetic field theoretical data and the observed value of the tangential component in the magnetic field component data, and the second difference between the theoretical data of the radial component in the magnetic field theoretical data and the observed value of the radial component in the magnetic field component data. Then, square the first difference and the second difference respectively and sum them. Finally, take the square root of the summation result to obtain the component residual vector magnitude corresponding to each magnetic sensor. Divide the magnitude of the component residual vector corresponding to each magnetic sensor by the magnitude of the corresponding magnetic field component data to obtain the normalized residual data corresponding to each magnetic sensor. The normalized residual data corresponding to each magnetic sensor are summed to obtain the sum of the magnitudes of the component residual vectors.

[0019] Compared to existing technologies, the above embodiments have the following advantages: By calculating the difference between the theoretical and observed values ​​of the tangential and radial components and performing square root operations on the sum of squares, a component residual vector magnitude based on vector Euclidean distance is constructed. Compared to only comparing the total magnetic field magnitude, this method simultaneously constrains the consistency of components in two orthogonal directions, enabling more sensitive detection of magnetic field direction distortion caused by small positional shifts and improving the sensitivity of error detection. Furthermore, the component residual vector magnitude is divided by the magnitude of the corresponding magnetic field component data to obtain normalized residual data, eliminating the difference in absolute error weights under different current levels. This ensures that the convergence criterion has a unified accuracy standard under different load currents, avoiding the problem of overly strict criteria at small currents or overly lenient criteria at large currents. Finally, the normalized residual data of each sensor are summed and compared with a threshold to establish a global relative error convergence condition. This ensures that the iteration terminates only when the relative errors of all sensors in all axes are reduced to within the allowable range, thereby guaranteeing that the final output current measurement value has extremely high accuracy, consistency, and reliability.

[0020] Secondly, the present invention also provides a current measurement system for a non-contact single-core cable, comprising: a data acquisition module, an initial data calculation module, and an iterative output module; The data acquisition module is used to acquire magnetic field component data collected by three magnetic sensors. The three magnetic sensors are evenly distributed at 120-degree intervals around the single-core cable under test on a plane circumference perpendicular to the cable axis, and the first sensitive axis of each magnetic sensor is arranged along the tangent direction of the circumference and the second sensitive axis is arranged along the radius direction of the circumference pointing towards the center of the circle. The initial data calculation module is used to construct a prediction vector of the magnetic field direction based on the data of each magnetic field component, determine the set of coordinates of the intersection of adjacent prediction vectors, and calculate the initial position and initial current of the single-core cable by combining the position of each magnetic sensor. The iterative output module is used to iteratively calculate the theoretical magnetic field data of each magnetic sensor based on the initial position and initial current, and calculate the residual between the current theoretical magnetic field data and the corresponding magnetic field component data, as well as the proportional coefficient between the previous round's historical theoretical magnetic field data and the corresponding magnetic field component data. If the signs of the residuals are consistent, the current initial current is updated based on the proportional coefficients; otherwise, the current initial position is updated based on the proportional coefficients. The process continues until the sum of the vector magnitudes of the component residuals of each theoretical magnetic field data and the corresponding magnetic field component data is less than a preset threshold, at which point the current initial current is output as the current measurement result.

[0021] Compared with the prior art, the above embodiments of this application have the following beneficial effects: Magnetic field component data is acquired, and three magnetic sensors are uniformly distributed at 120-degree intervals on the circumference, with their sensitive axes arranged along the tangent and radial directions, respectively. This constructs a minimalist array with geometric symmetry and orthogonal sensing capabilities, reducing hardware costs and calibration difficulty, while providing complete geometric constraint information for subsequent spatial positioning. Furthermore, a magnetic field direction prediction vector is constructed based on the magnetic field component data, and the set of intersection coordinates of adjacent vectors is determined. The magnetic field angle information is directly mapped to position cues using the physical laws of electromagnetic fields, achieving a leap from simple numerical fitting to geometric analysis and avoiding blind searching. Then, the initial position is determined based on the set of intersection coordinates, and the initial current is calculated. A high-confidence iterative initial value is obtained through physical model inversion, solving the technical problem that traditional nonlinear optimization algorithms are prone to getting trapped in local optima due to random initial value selection. Subsequently, iterative calculations are performed based on the initial data until the sum of the magnitudes of the component residual vectors is less than a preset threshold. A strict convergence criterion is established to ensure the accuracy and reliability of the output results. In each iteration, the residual and the scaling factor are calculated, and the parameter evolution type is intelligently determined based on the consistency of the positive and negative signs of the residuals. If the signs are consistent, the current is updated; otherwise, the position is updated. This "step-by-step correction" strategy decouples the coupled nonlinear inversion problem into two independent single-variable optimization processes. The residual sign distribution characteristics are used to adaptively identify whether the source of error is current amplitude deviation or position offset, thereby significantly reducing the number of invalid iterations and improving the convergence speed. The above technical features work together to achieve a fast and high-precision current measurement that can avoid local optimum traps and meet the real-time requirements of embedded terminals under the eccentricity condition of single-core cables. This overcomes the shortcomings of existing technologies, which are difficult to balance weak anti-eccentricity capability and high computational cost.

[0022] In some embodiments of the second aspect of this application, the initial data calculation module includes: an initial position calculation unit; The initial position calculation unit is used to determine whether the coordinates of each intersection point in the set of intersection point coordinates coincide. If they coincide, the coordinates of the coincident point are directly used as the initial position. If they do not coincide, the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of each intersection point are used as the initial position.

[0023] Compared with existing technologies, the above embodiments have the following advantages: By determining whether the coordinates of each intersection point in the set of intersection point coordinates coincide, and directly selecting the coordinates of the coincident point as the initial position when they coincide, the characteristics of rays intersecting at a point under the ideal physical model are utilized, achieving zero-error rapid positioning under ideal working conditions without noise interference. When the intersection points do not coincide, the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of each intersection point are used as the initial position. This is to address the situation in actual measurements where rays cannot intersect accurately due to sensor noise or environmental interference. The geometric center approximation algorithm is used to obtain the most probable position estimate. This segmented processing logic not only ensures the computational efficiency under ideal conditions, but also enhances the robustness of the algorithm under non-ideal working conditions, ensuring that the initial position data is always within the minimum neighborhood of the true value, laying a solid geometric foundation for subsequent iterative convergence. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a non-contact single-core cable current measurement method provided in some embodiments of the present invention.

[0025] Figure 2 This is a design diagram of a magnetic sensor array provided in some embodiments of the present invention.

[0026] Figure 3 This is a schematic diagram of the structure of a non-contact single-core cable current measurement system provided in some embodiments of the present invention. Detailed Implementation

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

[0028] Example 1: Please refer to Figure 1 To address the problem that existing non-contact current measurement methods are prone to getting stuck in local optima and have slow convergence speed under eccentric conditions in single-core cables, an embodiment of the present invention provides a non-contact current measurement method for single-core cables, comprising steps S1 to S3: Step S1: Acquire magnetic field component data collected by three magnetic sensors; the three magnetic sensors are evenly distributed at 120-degree intervals around the single-core cable to be tested on a plane circumference perpendicular to the cable axis, and the first sensitive axis of each magnetic sensor is arranged along the tangent direction of the circumference and the second sensitive axis is arranged along the radius direction of the circumference pointing towards the center of the circle. Step S2: Based on the data of each magnetic field component, construct the prediction vector of the magnetic field direction, determine the set of coordinates of the intersection of adjacent prediction vectors, and combine the positions of each magnetic sensor to calculate the initial position and initial current of the single-core cable. Furthermore, the initial position and initial current can be obtained through the following preferred embodiments, including steps S21-S24: S21: Determine whether the coordinates of each intersection point in the set of intersection point coordinates coincide. If they coincide, use the coordinates of the coincident point as the initial position. If they do not coincide, use the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of each intersection point as the initial position.

[0029] In this preferred embodiment, by determining whether the coordinates of each intersection point in the set of intersection point coordinates coincide, and directly selecting the coordinates of the coincident point as the initial position when they coincide, the characteristic that rays must intersect at a point under the ideal physical model is utilized to achieve zero-error rapid positioning under ideal working conditions without noise interference. When the intersection points do not coincide, the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of each intersection point are used as the initial position. This is to address the situation in actual measurement where rays cannot intersect accurately due to sensor noise or environmental interference. The geometric center approximation algorithm is used to obtain the most probable position estimate. This segmented processing logic not only ensures the computational efficiency under ideal conditions, but also enhances the robustness of the algorithm under non-ideal working conditions, ensuring that the initial position data is always within the minimum neighborhood of the true value, laying a solid geometric foundation for subsequent iterative convergence.

[0030] S22: Based on the initial position and the coordinate positions of each magnetic sensor, calculate the Euclidean distance from each magnetic sensor to the initial position using Biot-Savart's law; S23: Substitute the magnitudes of the Euclidean distances and magnetic field components into the inverse function of the Biot-Savart law formula to calculate the independent current estimates for each magnetic sensor. S24: Perform an arithmetic average operation on each of the independent current estimates to obtain the initial current.

[0031] In this preferred embodiment, the spatial geometric relationship between the cable and each sensing node is accurately quantified by calculating the Euclidean distance based on the initial position and the coordinate positions of each magnetic sensor, providing accurate spatial scale parameters for the physical modeling of the magnetic field strength. Furthermore, the Euclidean distance and the magnitude of the magnetic field component data are substituted into the inverse function of the Biot-Savart law formula. Utilizing the forward reversibility of the fundamental law of electromagnetic fields, the independent current estimates from the perspective of each sensor are directly derived from the observed magnetic field strength, realizing the initialization of parameters driven by the physical mechanism. Finally, an arithmetic mean is performed on each independent current estimate, and statistical smoothing is performed using the redundancy characteristics of multi-sensor data. This effectively suppresses random measurement noise or instantaneous abnormal fluctuations that may exist in a single sensor, thereby obtaining a high-confidence and stable initial current, significantly reducing the sensitivity of subsequent iterations to the initial current value.

[0032] Step S3: Based on the initial position and initial current, iteratively calculate the theoretical magnetic field data of each magnetic sensor, and calculate the residual between the current theoretical magnetic field data and the corresponding magnetic field component data, as well as the proportional coefficient between the previous round's historical theoretical magnetic field data and the corresponding magnetic field component data. If the signs of the residuals are consistent, update the current initial current based on the proportional coefficients; otherwise, update the current initial position based on the proportional coefficients. Continue until the sum of the vector magnitudes of the component residuals of each theoretical magnetic field data and the corresponding magnetic field component data is less than a preset threshold, and output the current initial current as the current measurement result.

[0033] Furthermore, the theoretical magnetic field data can be calculated through the following preferred implementation method, including steps S301-S303: S301: Based on the initial position of the single-core cable in this round and the coordinate positions of each magnetic sensor, calculate the Euclidean distance data from each magnetic sensor to the initial position of the single-core cable. S302: Substitute the Euclidean distance data and the initial current of the single-core cable in this round into the Biot-Savart law formula to calculate the theoretical magnetic field modulus data at each magnetic sensor position; S303: Based on the definition of the sensitive axis direction of each magnetic sensor, the theoretical magnetic field modulus data corresponding to each magnetic sensor is decomposed into theoretical data of the tangential component along the first sensitive axis direction and theoretical data of the radial component along the second sensitive axis direction, which are used as the theoretical magnetic field data of each magnetic sensor in the current cycle.

[0034] In this preferred embodiment, the spatial geometric topology is dynamically updated by calculating Euclidean distance data based on the current position and sensor coordinates, ensuring that the theoretical model can reflect changes in cable position in real time. Furthermore, the distance data and current are substituted into the Biot-Savart law formula to calculate the theoretical magnetic field modulus data, achieving a positive and accurate mapping from decision variables to physical observations, providing a benchmark for error assessment. Simultaneously, based on the definition of the sensitive axis direction, the theoretical modulus data is decomposed into tangential and radial component theoretical data, completing the projection transformation from scalar magnetic field strength to vector component space. This provides necessary data dimension support for subsequent refined residual calculation and convergence judgment based on component level differences, ensuring the comparability of theoretical predictions and actual observations in the same coordinate system.

[0035] Furthermore, the proportionality coefficient can be calculated through the following preferred embodiments, including steps S304-S305: S304: Extract the magnitude of the magnetic field component data of each magnetic sensor as the observed magnetic field magnitude data, and extract the magnitude of the theoretical magnetic field data at the location of each magnetic sensor obtained in the previous iteration as the theoretical magnetic field magnitude data. S305: Calculate the ratio of the observed magnetic field modulus data to the theoretical magnetic field modulus data for each magnetic sensor to obtain the independent proportionality coefficient for each magnetic sensor.

[0036] In this preferred embodiment, by extracting the magnitude of the magnetic field component data as the observed magnetic field magnitude data and the magnitude of the theoretical data from the previous round as the theoretical magnetic field magnitude data, feature extraction from vector components to scalar magnitude is completed, eliminating the interference of direction factors on amplitude error assessment. Furthermore, the ratio of the observed magnetic field magnitude data to the theoretical magnetic field magnitude data is calculated to obtain an independent proportionality coefficient. This ratio directly quantifies the relative deviation multiple between the current model estimate and the actual observation value, transforming the absolute difference in magnetic field strength into a dimensionless correction factor. This normalization processing method makes the correction strategy no longer dependent on the absolute magnitude of the current or the specific sensitivity of the sensor, but focuses on eliminating relative errors, providing a unified and stable mathematical driving quantity for subsequent adaptive adjustment of current or position.

[0037] Furthermore, the update current can be implemented through the following preferred embodiments, including steps S306-S307: S306: Perform an arithmetic average of the proportional coefficients corresponding to all magnetic sensors to obtain the current correction coefficient; S307: Perform a multiplication operation between the initial current of the previous round and the current correction coefficient to obtain the updated initial current.

[0038] In this preferred embodiment, the current correction coefficient is obtained by performing an arithmetic average operation on the proportional coefficients corresponding to all magnetic sensors. By utilizing the spatial diversity gain of the multi-sensor array, the local deviation information of each node is fused into a globally consistent current adjustment trend, effectively suppressing the misleading effect of single-point measurement noise on the overall correction direction. Furthermore, the current from the previous round is multiplied by the current correction coefficient, and the current amplitude is directly corrected by scaling. This multiplication update mechanism conforms to the linear proportional relationship between magnetic field and current in Biosavart's law. Under the condition of consistent residual sign (i.e., accurate position but incorrect current), it can approximate the true current value in one step with minimal computational cost, avoiding the cumbersome process of adjusting the learning rate step size required in the traditional gradient descent method, and significantly improving the convergence efficiency of the current dimension.

[0039] Furthermore, the updated position can be implemented through the following preferred embodiments, including steps S308-S311: S308: For each magnetic sensor, construct a relative position vector from the coordinate position of the magnetic sensor to the initial position of the single-core cable in the previous round; S309: Calculate the reciprocal of the proportional coefficient of each magnetic sensor and subtract one to obtain the displacement coefficient of each magnetic sensor. S310: Perform vector multiplication on the relative position vector and displacement coefficient corresponding to each magnetic sensor to obtain the local displacement vector corresponding to each magnetic sensor, and perform vector summation on the local displacement vectors of all magnetic sensors to obtain the global position correction vector. S311: Perform vector addition operation between the initial position of the previous round and the global position correction vector to obtain the updated initial position.

[0040] In this preferred embodiment, by constructing a relative position vector pointing from the sensor coordinates to the previous position, the geometric guidance direction for spatial correction is clarified, ensuring that position updates always proceed along the radial path connecting the sensor and the cable, conforming to the physical gradient direction of the magnetic field changing with distance. Further, the displacement coefficient is obtained by subtracting one from the reciprocal of the proportionality coefficient, transforming the relative deviation of the magnetic field amplitude into a correction weight for spatial distance. The driving force for position adjustment is derived using the inverse nonlinear relationship between the magnetic field and distance. Subsequently, the relative position vector and displacement coefficient are multiplied and summed to obtain the global position correction vector, realizing the vector synthesis of multi-source position correction information. This allows for the comprehensive correction of the cable's two-dimensional coordinates by integrating the observation differences from multiple sensors. Finally, the position is updated by vector addition while maintaining a constant current. This decoupled update strategy ensures that when the residual signs are inconsistent (i.e., position deviation exists), the algorithm can concentrate computing power to prioritize the correction of spatial geometric relationships, avoiding convergence difficulties caused by the coupling oscillation between current and position parameters, and greatly improving the stability of the nonlinear inversion process.

[0041] Further, the sum of the magnitudes of the component residual vectors is calculated in the following manner, including steps S312-S314: S312: For each magnetic sensor, calculate the first difference between the theoretical data of the tangential component in the magnetic field theoretical data and the observed value of the tangential component in the magnetic field component data, and the second difference between the theoretical data of the radial component in the magnetic field theoretical data and the observed value of the radial component in the magnetic field component data. Then, square the first difference and the second difference respectively and sum them up. Then, take the square root of the summation result to obtain the component residual vector magnitude corresponding to each magnetic sensor. S313: Divide the magnitude of the component residual vector corresponding to each magnetic sensor by the magnitude of the corresponding magnetic field component data to obtain the normalized residual data corresponding to each magnetic sensor. S314: Accumulate the normalized residual data corresponding to each magnetic sensor to obtain the sum of the magnitudes of the component residual vectors.

[0042] In this preferred embodiment, by calculating the difference between the theoretical and observed values ​​of the tangential and radial components and performing square root operations on the sum of squares, a component residual vector magnitude based on vector Euclidean distance is constructed. Compared to comparing only the total magnetic field magnitude, this method simultaneously constrains the consistency of components in two orthogonal directions, enabling it to more sensitively capture magnetic field direction distortions caused by minute positional shifts and improve the sensitivity of error detection. Furthermore, the component residual vector magnitude is divided by the magnitude of the corresponding magnetic field component data to obtain normalized residual data, eliminating the difference in absolute error weights under different current levels. This ensures that the convergence criterion has a unified accuracy standard under different load currents, avoiding the problem of overly strict criteria at small currents or overly lenient criteria at large currents. Finally, the normalized residual data of each sensor are summed to obtain a total and compared with a threshold, establishing a global relative error convergence condition. This ensures that the iteration terminates only when the relative errors of all sensors in all axes are reduced to within the allowable range, thereby guaranteeing that the final output current measurement value has extremely high accuracy, consistency, and reliability.

[0043] In specific implementation, refer to Figure 2 The diagram shown illustrates a magnetic sensor array design, using a single-core cable as an example, with a rated current of... Assuming a current of 600A and that the single-core cable is an infinitely long straight cable, establish a Cartesian coordinate system with the center of the circular array as the origin O. The actual coordinates of the cable are: The current flowing through it is the rated current; In this embodiment, a TMR sensor is preferably used as the magnetic sensor. Three TMR sensors are distributed at 120° intervals on the array circumference, with coordinates as follows: , The array radius R = 50 mm. The axis 1 direction of each sensor is set counterclockwise along the tangent direction of the array circumference, and the axis 2 direction is set towards the center of the circle along the radius direction of the circumference. The two axes are perpendicular to each other.

[0044] Next, the initial current and initial position of the single-core cable are determined as follows: Magnetic sensor The magnetic field observation components of axis 1 and axis 2 are as follows , At this point, a ray with the sensor position as its endpoint is selected as the position prediction line, and the angle between the vector parallel to the ray and axis 1 is... satisfy: ; Therefore, for sensor n, the angle between the vector containing its position prediction line and the x-axis is... satisfy: ; At this time, the points on the three rays of the three sensors A straight line that satisfies The equation is: ; United ,So intersection satisfy: ; ; and intersection , coordinate Similarly, we can obtain the following.

[0045] If the intersection point , , If they coincide, then take the coordinates of the coincident point. This serves as the initial value for the position of the cable (single-core cable). If the intersection... , , If the three points do not coincide, then take the incenter of the triangle formed by the three points. As the initial value for the cable position; Magnetic field measurement at the sensor satisfy: ; According to the Biot-Savart law, for an infinitely long straight cable... Magnetic field at a certain point for: ; By inputting the initial coordinates and the coordinates of sensor 1, the estimated current value of sensor 1 can be obtained. for: ; Similarly, the current estimates for sensors 2 and 3 are also available. , for: ; ; At this point, the initial current value can be obtained as follows: .

[0046] During iteration, define the iteration term at the end of the k-th iteration. Modular residual of each sensor (This refers to the residual mentioned in claim 1, which is a difference in scalar quantities (magnetic field modulus) and has a definite positive or negative sign), satisfying: ;in For the first The magnitude of the magnetic field observations (i.e., magnetic field component data) from each sensor. Let be the decision variables after the k-th iteration, and be the function. This is determined by the Biot-Savart law, namely: ; in, Let n be the distance from the cable position to sensor n. The k-th iteration ends. For the _th iteration... One sensor, if If the model estimate is too high, then consider that the estimated value is too large; if If the model estimate is too small, then consider that the data from all sensors should be combined to determine the optimal value. Conduct joint analysis: If the signs are the same, then cable current correction should be considered.

[0047] If the numbers are different, then the cable position should be adjusted accordingly.

[0048] When making corrections, the correction method is as follows: Current correction: In the k-th round, calculate the sensor n observations. Compared with the calculated value in the (k-1)th round (i.e., the theoretical data of the magnetic field). The ratio is used as the coefficient for current correction in the k-th iteration. Thus, the current in the kth round is obtained: .

[0049] Position correction: In the k-th round, calculate the coordinates of the sensor and the cable in the (k-1)-th round. The relative position vector between them is Meanwhile, based on the observations of sensor n The calculated value of the (k-1)th round Calculate displacement coefficient Then, the coordinates of the cable in the kth round are obtained: .

[0050] The convergence condition for the iteration is as follows: If the calculated value of sensor 1 model at the end of the kth round is At this time, the axis 1 and axis 2 components of the magnetic field measurement value of sensor 1 are respectively: ; Similarly, we can conclude that: ; ; The convergence condition is: ; Cable current that satisfies the above formula With cable location That is, the final measured value that meets the required accuracy, where, The preset threshold can be set according to the actual accuracy requirements and the noise level of the sensor itself.

[0051] In summary, compared with the prior art, the above embodiments of this application have the following beneficial effects: By acquiring magnetic field component data and constraining three magnetic sensors to be evenly distributed at 120-degree intervals on a circle with their sensitive axes arranged along the tangent and radial directions respectively, a minimally sized array with geometric symmetry and orthogonal sensing capabilities is constructed, reducing hardware costs and calibration difficulty, while providing complete geometric constraint information for subsequent spatial positioning; furthermore, based on the magnetic field component data, a magnetic field direction prediction vector is constructed and the set of intersection coordinates of adjacent vectors is determined. The magnetic field angle information is directly mapped to position cues using the physical laws of electromagnetic fields, achieving a leap from simple numerical fitting to geometric analysis and avoiding blind searching; then, the initial position is determined based on the set of intersection coordinates, and the initial current is calculated. A high-confidence iterative initial value is obtained through physical model inversion, solving the technical difficulty that traditional nonlinear optimization algorithms are prone to getting trapped in local optima due to random initial value selection. The problem is solved by iteratively calculating the residual vector magnitudes of the components until the sum of the magnitudes is less than a preset threshold. A strict convergence criterion is established to ensure the accuracy and reliability of the output results. In each iteration, the residual and the proportional coefficient are calculated, and the parameter evolution type is intelligently determined based on the consistency of the positive and negative signs of the residuals. If the signs are consistent, the current is updated; otherwise, the position is updated. This "step-by-step correction" strategy decouples the coupled nonlinear inversion problem into two independent single-variable optimization processes. The residual sign distribution characteristics are used to adaptively identify whether the source of error is current amplitude deviation or position offset, thereby significantly reducing the number of invalid iterations and improving the convergence speed. The above technical features work together to achieve a fast and high-precision current measurement that can avoid local optimum traps and meet the real-time requirements of embedded terminals under the eccentricity of single-core cables. This overcomes the shortcomings of existing technologies, which are difficult to balance weak anti-eccentricity capability and high computational cost.

[0052] Example 2: Please refer to Figure 3 Based on the same inventive concept, the present invention discloses a non-contact single-core cable current measurement system, comprising: a data acquisition module M1, an initial data calculation module M2, and an iterative output module M3; The data acquisition module M1 is used to acquire magnetic field component data collected by three magnetic sensors. The three magnetic sensors are evenly distributed at 120-degree intervals around the single-core cable under test on a plane circumference perpendicular to the cable axis, and the first sensitive axis of each magnetic sensor is arranged along the tangent direction of the circumference and the second sensitive axis is arranged along the radius direction of the circumference pointing towards the center of the circle. The initial data calculation module M2 is used to construct a prediction vector of the magnetic field direction based on the data of each magnetic field component, determine the set of coordinates of the intersection of adjacent prediction vectors, and calculate the initial position and initial current of the single-core cable by combining the position of each magnetic sensor. Furthermore, the initial data calculation module M2 includes: an initial position calculation unit; The initial position calculation unit is used to determine whether the coordinates of each intersection point in the set of intersection point coordinates coincide. If they coincide, the coordinates of the coincident point are directly used as the initial position. If they do not coincide, the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of each intersection point are used as the initial position.

[0053] In this preferred embodiment, by determining whether the coordinates of each intersection point in the set of intersection point coordinates coincide, and directly selecting the coordinates of the coincident point as the initial position when they coincide, the characteristic that rays must intersect at a point under the ideal physical model is utilized to achieve zero-error rapid positioning under ideal working conditions without noise interference. When the intersection points do not coincide, the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of each intersection point are used as the initial position. This is to address the situation in actual measurement where rays cannot intersect accurately due to sensor noise or environmental interference. The geometric center approximation algorithm is used to obtain the most probable position estimate. This segmented processing logic not only ensures the computational efficiency under ideal conditions, but also enhances the robustness of the algorithm under non-ideal working conditions, ensuring that the initial position data is always within the minimum neighborhood of the true value, laying a solid geometric foundation for subsequent iterative convergence.

[0054] Furthermore, the initial data calculation module M2 also includes: a first distance calculation unit, an independent current calculation unit, and an initial current calculation unit; The first distance calculation unit is used to calculate the Euclidean distance from each magnetic sensor to the initial position based on the initial position and the coordinate positions of each magnetic sensor, using Biot-Savart's law. The independent current calculation unit is used to substitute the magnitudes of each of the Euclidean distances and each of the magnetic field component data into the inverse function of the Biot-Savart law formula to calculate the independent current estimate for each magnetic sensor. The initial current calculation unit is used to perform an arithmetic average operation on each of the independent current estimates to obtain the initial current.

[0055] In this preferred embodiment, the spatial geometric relationship between the cable and each sensing node is accurately quantified by calculating the Euclidean distance based on the initial position and the coordinate positions of each magnetic sensor, providing accurate spatial scale parameters for the physical modeling of the magnetic field strength. Furthermore, the Euclidean distance and the magnitude of the magnetic field component data are substituted into the inverse function of the Biot-Savart law formula. Utilizing the forward reversibility of the fundamental law of electromagnetic fields, the independent current estimates from the perspective of each sensor are directly derived from the observed magnetic field strength, realizing the initialization of parameters driven by the physical mechanism. Finally, an arithmetic mean is performed on each independent current estimate, and statistical smoothing is performed using the redundancy characteristics of multi-sensor data. This effectively suppresses random measurement noise or instantaneous abnormal fluctuations that may exist in a single sensor, thereby obtaining a high-confidence and stable initial current, significantly reducing the sensitivity of subsequent iterations to the initial current value.

[0056] The iterative output module M3 is used to iteratively calculate the theoretical magnetic field data of each magnetic sensor based on the initial position and initial current, and calculate the residual between the current theoretical magnetic field data and the corresponding magnetic field component data, as well as the proportional coefficient between the previous round's historical theoretical magnetic field data and the corresponding magnetic field component data. If the signs of the residuals are consistent, the current initial current is updated based on the proportional coefficients; otherwise, the current initial position is updated based on the proportional coefficients. The process continues until the sum of the vector magnitudes of the component residuals of each theoretical magnetic field data and the corresponding magnetic field component data is less than a preset threshold, at which point the current initial current is output as the current measurement result.

[0057] Furthermore, the iterative output module M3 includes: a second distance calculation unit, a first modulus calculation unit, and a theoretical data calculation unit; The second distance calculation unit is used to calculate the Euclidean distance data from each magnetic sensor to the initial position of the single-core cable based on the initial position of the single-core cable in this round and the coordinate position of each magnetic sensor. The first modulus calculation unit is used to substitute the Euclidean distance data and the initial current of the single-core cable in this round into the Biot-Savart law formula to calculate the theoretical modulus data of the magnetic field at each magnetic sensor position. The theoretical data calculation unit is used to decompose the theoretical magnetic field modulus data corresponding to each magnetic sensor into tangential component theoretical data along the first sensitive axis direction and radial component theoretical data along the second sensitive axis direction, according to the definition of the sensitive axis direction of each magnetic sensor, as the magnetic field theoretical data of each magnetic sensor in the current cycle.

[0058] In this preferred embodiment, the spatial geometric topology is dynamically updated by calculating Euclidean distance data based on the current position and sensor coordinates, ensuring that the theoretical model can reflect changes in cable position in real time. Furthermore, the distance data and current are substituted into the Biot-Savart law formula to calculate the theoretical magnetic field modulus data, achieving a positive and accurate mapping from decision variables to physical observations, providing a benchmark for error assessment. Simultaneously, based on the definition of the sensitive axis direction, the theoretical modulus data is decomposed into tangential and radial component theoretical data, completing the projection transformation from scalar magnetic field strength to vector component space. This provides necessary data dimension support for subsequent refined residual calculation and convergence judgment based on component level differences, ensuring the comparability of theoretical predictions and actual observations in the same coordinate system.

[0059] Furthermore, the iterative output module M3 also includes: a second modulus calculation unit and a scaling factor calculation unit; The second modulus calculation unit is used to extract the modulus of the magnetic field component data of each magnetic sensor as the observed magnetic field modulus data, and to extract the modulus of the theoretical magnetic field data at the position of each magnetic sensor obtained in the previous iteration as the theoretical magnetic field modulus data. The proportionality coefficient calculation unit is used to calculate the ratio of the observed magnetic field modulus data to the theoretical magnetic field modulus data for each magnetic sensor, so as to obtain the independent proportionality coefficient for each magnetic sensor.

[0060] In this preferred embodiment, by extracting the magnitude of the magnetic field component data as the observed magnetic field magnitude data and the magnitude of the theoretical data from the previous round as the theoretical magnetic field magnitude data, feature extraction from vector components to scalar magnitude is completed, eliminating the interference of direction factors on amplitude error assessment. Furthermore, the ratio of the observed magnetic field magnitude data to the theoretical magnetic field magnitude data is calculated to obtain an independent proportionality coefficient. This ratio directly quantifies the relative deviation multiple between the current model estimate and the actual observation value, transforming the absolute difference in magnetic field strength into a dimensionless correction factor. This normalization processing method makes the correction strategy no longer dependent on the absolute magnitude of the current or the specific sensitivity of the sensor, but focuses on eliminating relative errors, providing a unified and stable mathematical driving quantity for subsequent adaptive adjustment of current or position.

[0061] Furthermore, the iterative output module M3 also includes: a current correction coefficient calculation unit and a current correction unit; The current correction coefficient calculation unit is used to perform an arithmetic average operation on the proportional coefficients corresponding to all magnetic sensors to obtain the current correction coefficient. The current correction unit is used to perform a multiplication operation between the initial current of the previous round and the current correction coefficient to obtain the updated initial current.

[0062] In this preferred embodiment, the current correction coefficient is obtained by performing an arithmetic average operation on the proportional coefficients corresponding to all magnetic sensors. By utilizing the spatial diversity gain of the multi-sensor array, the local deviation information of each node is fused into a globally consistent current adjustment trend, effectively suppressing the misleading effect of single-point measurement noise on the overall correction direction. Furthermore, the current from the previous round is multiplied by the current correction coefficient, and the current amplitude is directly corrected by scaling. This multiplication update mechanism conforms to the linear proportional relationship between magnetic field and current in Biosavart's law. Under the condition of consistent residual sign (i.e., accurate position but incorrect current), it can approximate the true current value in one step with minimal computational cost, avoiding the cumbersome process of adjusting the learning rate step size required in the traditional gradient descent method, and significantly improving the convergence efficiency of the current dimension.

[0063] Furthermore, the iterative output module M3 also includes: a relative position calculation unit, a displacement coefficient calculation unit, a global correction unit, and a position update unit; The relative position calculation unit is used to construct a relative position vector for each magnetic sensor, pointing from the coordinate position of the magnetic sensor to the initial position of the single-core cable in the previous round. The displacement coefficient calculation unit is used to calculate the reciprocal of the proportional coefficient of each magnetic sensor and then subtract one to obtain the displacement coefficient corresponding to each magnetic sensor. The global correction unit is used to perform vector multiplication on the relative position vector and displacement coefficient corresponding to each magnetic sensor to obtain the local displacement vector corresponding to each magnetic sensor, and to perform vector summation on the local displacement vectors of all magnetic sensors to obtain the global position correction vector. The position update unit is used to perform vector addition operation on the initial position of the previous round and the global position correction vector to obtain the updated initial position.

[0064] In this preferred embodiment, by constructing a relative position vector pointing from the sensor coordinates to the previous position, the geometric guidance direction for spatial correction is clarified, ensuring that position updates always proceed along the radial path connecting the sensor and the cable, conforming to the physical gradient direction of the magnetic field changing with distance. Further, the displacement coefficient is obtained by subtracting one from the reciprocal of the proportionality coefficient, transforming the relative deviation of the magnetic field amplitude into a correction weight for spatial distance. The driving force for position adjustment is derived using the inverse nonlinear relationship between the magnetic field and distance. Subsequently, the relative position vector and displacement coefficient are multiplied and summed to obtain the global position correction vector, realizing the vector synthesis of multi-source position correction information. This allows for the comprehensive correction of the cable's two-dimensional coordinates by integrating the observation differences from multiple sensors. Finally, the position is updated by vector addition while maintaining a constant current. This decoupled update strategy ensures that when the residual signs are inconsistent (i.e., position deviation exists), the algorithm can concentrate computing power to prioritize the correction of spatial geometric relationships, avoiding convergence difficulties caused by the coupling oscillation between current and position parameters, and greatly improving the stability of the nonlinear inversion process.

[0065] Furthermore, the iterative output module M3 also includes: a third module length calculation unit, a normalized residual calculation unit, and an accumulation unit; The third module length calculation unit is used to calculate, for each magnetic sensor, the first difference between the theoretical data of the tangential component in the magnetic field theoretical data and the observed value of the tangential component in the magnetic field component data, and the second difference between the theoretical data of the radial component in the magnetic field theoretical data and the observed value of the radial component in the magnetic field component data. The first difference and the second difference are squared and summed, and then the square root of the summation result is performed to obtain the module length of the component residual vector corresponding to each magnetic sensor. The normalized residual calculation unit is used to divide the magnitude of the component residual vector corresponding to each magnetic sensor by the magnitude of the corresponding magnetic field component data to obtain the normalized residual data corresponding to each magnetic sensor. The accumulation unit is used to accumulate the normalized residual data corresponding to each magnetic sensor to obtain the sum of the magnitudes of the component residual vectors.

[0066] In this preferred embodiment, by calculating the difference between the theoretical and observed values ​​of the tangential and radial components and performing square root operations on the sum of squares, a component residual vector magnitude based on vector Euclidean distance is constructed. Compared to comparing only the total magnetic field magnitude, this method simultaneously constrains the consistency of components in two orthogonal directions, enabling it to more sensitively capture magnetic field direction distortions caused by minute positional shifts and improve the sensitivity of error detection. Furthermore, the component residual vector magnitude is divided by the magnitude of the corresponding magnetic field component data to obtain normalized residual data, eliminating the difference in absolute error weights under different current levels. This ensures that the convergence criterion has a unified accuracy standard under different load currents, avoiding the problem of overly strict criteria at small currents or overly lenient criteria at large currents. Finally, the normalized residual data of each sensor are summed to obtain a total and compared with a threshold, establishing a global relative error convergence condition. This ensures that the iteration terminates only when the relative errors of all sensors in all axes are reduced to within the allowable range, thereby guaranteeing that the final output current measurement value has extremely high accuracy, consistency, and reliability.

[0067] In summary, compared with the prior art, the embodiments of this application have the following beneficial effects: By acquiring magnetic field component data and constraining three magnetic sensors to be uniformly distributed at 120-degree intervals on a circle with their sensitive axes arranged along the tangent and radial directions respectively, a minimally sized array with geometric symmetry and orthogonal sensing capabilities is constructed, reducing hardware costs and calibration difficulty, while providing complete geometric constraint information for subsequent spatial positioning; furthermore, based on the magnetic field component data, a magnetic field direction prediction vector is constructed and the set of intersection coordinates of adjacent vectors is determined. The magnetic field angle information is directly mapped to position cues using the physical laws of electromagnetic fields, achieving a leap from simple numerical fitting to geometric analysis and avoiding blind searching; then, the initial position is determined based on the set of intersection coordinates, and the initial current is calculated. A high-confidence iterative initial value is obtained through physical model inversion, solving the technical problem that traditional nonlinear optimization algorithms are prone to getting trapped in local optima due to random initial value selection. Subsequently, iterative calculations are performed based on the initial data until the sum of the magnitudes of the component residual vectors is less than a preset threshold. A strict convergence criterion is established to ensure the accuracy and reliability of the output results. In each iteration, the residual and the proportional coefficient are calculated, and the parameter evolution type is intelligently determined based on the consistency of the positive and negative signs of the residuals. If the positive and negative signs are consistent, the current is updated; otherwise, the position is updated. This "step-by-step correction" strategy decouples the coupled nonlinear inversion problem into two independent single-variable optimization processes. The residual sign distribution characteristics are used to adaptively identify whether the source of error is current amplitude deviation or position offset, thereby significantly reducing the number of invalid iterations and improving the convergence speed. The above technical features work together to realize a fast and high-precision current measurement that can avoid local optimum traps and meet the real-time requirements of embedded terminals under the eccentricity condition of single-core cables. This overcomes the shortcomings of existing technologies, which are difficult to balance weak anti-eccentricity capability and large computational overhead.

[0068] The specific working processes of each module described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. The division of modules is only a logical functional division, and there may be other division methods in actual implementation. For example, multiple modules may be combined or integrated into another system.

[0069] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A method for measuring the current of a non-contact single-core cable, characterized in that, include: The magnetic field component data collected by three magnetic sensors are obtained; the three magnetic sensors are evenly distributed at 120 degrees intervals around the single-core cable to be tested on a plane circumference perpendicular to the cable axis, and the first sensitive axis of each magnetic sensor is arranged along the tangent direction of the circumference and the second sensitive axis is arranged along the radius direction of the circumference pointing towards the center of the circle. Based on the data of each magnetic field component, a prediction vector of the magnetic field direction is constructed. The set of coordinates of the intersection points of adjacent prediction vectors is determined. Combined with the position of each magnetic sensor, the initial position and initial current of the single-core cable are calculated. Based on the initial position and initial current, the theoretical magnetic field data of each magnetic sensor is iteratively calculated, and the residual between the current theoretical magnetic field data and the corresponding magnetic field component data is calculated, as well as the proportional coefficient between the previous round's historical theoretical magnetic field data and the corresponding magnetic field component data. If the signs of the residuals are consistent, the current initial current is updated based on the proportional coefficients; otherwise, the current initial position is updated based on the proportional coefficients. This process continues until the sum of the vector magnitudes of the component residuals between the theoretical magnetic field data and the corresponding magnetic field component data is less than a preset threshold. Then, the current initial current is output as the current measurement result.

2. The current measurement method for a non-contact single-core cable as described in claim 1, characterized in that, The calculation of the initial position of the single-core cable includes: Determine whether the coordinates of each intersection point in the set of intersection point coordinates coincide. If they coincide, the coordinates of the coincident point are directly used as the initial position. If they do not coincide, the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of the intersection points are used as the initial position.

3. The current measurement method for a non-contact single-core cable as described in claim 1, characterized in that, The calculation of the initial current of a single-core cable includes: Based on the initial position and the coordinate positions of each magnetic sensor, the Euclidean distance from each magnetic sensor to the initial position is calculated using Biot-Savart's law. Substitute the magnitudes of the Euclidean distances and magnetic field components into the inverse function of the Biot-Savart law formula to calculate the independent current estimates for each magnetic sensor. The initial current is obtained by performing an arithmetic mean operation on each of the independent current estimates.

4. The current measurement method for a non-contact single-core cable as described in claim 1, characterized in that, The calculation of the theoretical magnetic field data for each magnetic sensor includes: Based on the initial position of the single-core cable in this round and the coordinate positions of each magnetic sensor, calculate the Euclidean distance data from each magnetic sensor to the initial position of the single-core cable. Substituting the Euclidean distance data and the initial current of the single-core cable in this round into the Biot-Savart law formula, the theoretical magnetic field modulus data at each magnetic sensor location is calculated. Based on the definition of the sensitive axis direction of each magnetic sensor, the theoretical magnetic field modulus data corresponding to each magnetic sensor is decomposed into theoretical data of the tangential component along the first sensitive axis direction and theoretical data of the radial component along the second sensitive axis direction, which are used as the theoretical magnetic field data of each magnetic sensor in the current cycle.

5. The current measurement method for a non-contact single-core cable as described in claim 1, characterized in that, The calculation of the ratio coefficients between the theoretical historical magnetic field data and the corresponding magnetic field component data of the previous round includes: The magnitude of the magnetic field component data of each magnetic sensor is extracted as the observed magnetic field magnitude data, and the magnitude of the theoretical magnetic field data at the location of each magnetic sensor obtained in the previous iteration is extracted as the theoretical magnetic field magnitude data. Calculate the ratio of the observed magnetic field modulus data to the theoretical magnetic field modulus data for each magnetic sensor to obtain the independent proportionality coefficient for each magnetic sensor.

6. The current measurement method for a non-contact single-core cable as described in claim 5, characterized in that, The process of updating the current initial current based on each scaling factor includes: The current correction coefficient is obtained by performing an arithmetic average on the proportional coefficients corresponding to all magnetic sensors. The initial current from the previous round is multiplied by the current correction coefficient to obtain the updated initial current.

7. The current measurement method for a non-contact single-core cable as described in claim 5, characterized in that, The process of updating the current initial position based on each scaling factor includes: For each magnetic sensor, construct a relative position vector from the coordinate position of the magnetic sensor to the initial position of the single-core cable in the previous round; Calculate the reciprocal of the proportional coefficient of each magnetic sensor and subtract one to obtain the displacement coefficient of each magnetic sensor. The relative position vector corresponding to each magnetic sensor is multiplied by the displacement coefficient to obtain the local displacement vector corresponding to each magnetic sensor. Then, the local displacement vectors of all magnetic sensors are summed to obtain the global position correction vector. Perform vector addition between the initial position from the previous round and the global position correction vector to obtain the updated initial position.

8. The current measurement method for a non-contact single-core cable as described in claim 1, characterized in that, The sum of the magnitudes of the component residual vectors is calculated in the following ways: For each magnetic sensor, calculate the first difference between the theoretical data of the tangential component in the magnetic field theoretical data and the observed value of the tangential component in the magnetic field component data, and the second difference between the theoretical data of the radial component in the magnetic field theoretical data and the observed value of the radial component in the magnetic field component data. Then, square the first difference and the second difference respectively and sum them. Finally, take the square root of the summation result to obtain the component residual vector magnitude corresponding to each magnetic sensor. Divide the magnitude of the component residual vector corresponding to each magnetic sensor by the magnitude of the corresponding magnetic field component data to obtain the normalized residual data corresponding to each magnetic sensor. The normalized residual data corresponding to each magnetic sensor are summed to obtain the sum of the magnitudes of the component residual vectors.

9. A non-contact single-core cable current measurement system, characterized in that, include: Data acquisition module, initial data calculation module, and iterative output module; The data acquisition module is used to acquire magnetic field component data collected by three magnetic sensors. The three magnetic sensors are evenly distributed at 120-degree intervals around the single-core cable under test on a plane circumference perpendicular to the cable axis, and the first sensitive axis of each magnetic sensor is arranged along the tangent direction of the circumference and the second sensitive axis is arranged along the radius direction of the circumference pointing towards the center of the circle. The initial data calculation module is used to construct a prediction vector of the magnetic field direction based on the data of each magnetic field component, determine the set of coordinates of the intersection of adjacent prediction vectors, and calculate the initial position and initial current of the single-core cable by combining the position of each magnetic sensor. The iterative output module is used to iteratively calculate the theoretical magnetic field data of each magnetic sensor based on the initial position and initial current, and calculate the residual between the current theoretical magnetic field data and the corresponding magnetic field component data, as well as the proportional coefficient between the previous round's historical theoretical magnetic field data and the corresponding magnetic field component data. If the signs of the residuals are consistent, the current initial current is updated based on the proportional coefficients; otherwise, the current initial position is updated based on the proportional coefficients. The process continues until the sum of the vector magnitudes of the component residuals of each theoretical magnetic field data and the corresponding magnetic field component data is less than a preset threshold, at which point the current initial current is output as the current measurement result.

10. The current measurement system for a non-contact single-core cable as described in claim 9, characterized in that, The initial data calculation module includes: an initial position calculation unit; The initial position calculation unit is used to determine whether the coordinates of each intersection point in the set of intersection point coordinates coincide. If they coincide, the coordinates of the coincident point are directly used as the initial position. If they do not coincide, the coordinates of the center of the inscribed circle of the triangle formed by the coordinates of each intersection point are used as the initial position.

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