Magnetic Sensor Array Research Articles

Magnetic Moment Measurement Method Based on Magnetic Sensor Array

The magnetic moment measurement method based on magnetic sensor array is proposed to solve the problems of cumbersome calculation process and low inversion accuracy in the current magnetic moment calculation methods. Based on the concepts of magnetic field intensity, magnetic gradient tensor and Frobenius norm, this method can use the magnetic field information collected by magnetic sensor array to calculate the magnetic moment vector. The factors that may affect the measurement effect, such as sensor array structure, sensor precision and baseline size, are analyzed by simulation, and the advantages and disadvantages of three magnetic moment measurement methods based on magnetic sensor array are compared. Simulation results show that the proposed method is flexible in use, convenient in measurement, accurate in results, and has strong feasibility and reliability in geological survey and other applications.

A Practicable Method for Calibrating a Magnetic Sensor Array

Magnetic sensor array has become increasingly widespread in use. Because of the manufacturing process, magnetic sensors in an array inevitably experience calibration factor errors. Therefore, the calibration of a magnetic sensor array is very important before use. However, it lacks explicit and quantitative measures on how to calibrate a magnetic sensor array. By using magnetic fields produced by a standard magnetic source at different locations, a practicable method was proposed based on the least-squares method to calibrate a magnetic sensor array. The dimensions of sensor array are about $50\times 50\times50$ cm3 and the level of magnetic field aiming to be measured is ~nT. Both the simulation and experimental results demonstrate that the proposed method is effective in identifying the calibration factor of a magnetic sensor array.

A Wideband Current Transducer Based on an Array of Magnetic Field Sensors for Rectangular Busbar Current Measurement

Recently, the current transducer based on an array of magnetic field sensors has attracted a lot of attention. For busbars of circular cross section, many studies have been conducted and many results have been obtained. However, for the rectangular cross section busbar, the skin effect causes the frequency response curve of the magnetic flux density $B$ generated by the current-carrying conductor to appear nonlinear, which brings challenges to the wideband current measurement of the rectangular busbar. This article presents a wideband current transducer based on the array of magnetic field sensors for the current measurement of the rectangular busbar. First, according to the rectangular busbar, select reasonable magnetic field detection points to arrange the sensor array. Then, the frequency response curve of the magnetic flux density $B$ at each detection point around the rectangular busbar is obtained by simulation. After that, all frequency response curves are averaged, and the proper digital filter is designed according to the averaged frequency response curve to perform frequency compensation. The compensated frequency response curve is basically flat, so the wideband current measurement of the rectangular busbar can be realized. The bandwidth and overall performance of the designed wideband current transducer are verified through experiments, and experimental results show that the designed transducer can meet the requirements of relevant standards for the class 0.5 current transducer.

Nonintrusive Current Sensing for Multicore Cables Considering Inclination With Magnetic Field Measurement

Magnetic sensor arrays have been employed to measure currents for multicore cables due to their advantages of compact size, lightweight, low power consumption, and large dynamic range. However, the existing methods are applicable only to cases where the cable must be perpendicular to the sensor array plane due to the lack of capability of the 2-D magnetic field model to consider conductor inclination. To solve this problem, this article presents a method using a circular array of single-axis magnetic sensors to measure magnetic fields along and perpendicular to the sensor array plane. A 3-D magnetic field model that involves conductor incline angles is first derived. On the basis of the derived model, two main steps are performed to realize current sensing. First, an off-site calibration method is used to calibrate magnetic sensor parameters, including sensor position, orientation, gain factor, and phase shift. Second, not only the conductor currents and positions but also the incline angles are simultaneously calculated based on the detected magnetic fields and calibrated sensor parameters. Both steps are formulated as nonlinear least-square problems and solved efficiently. Both simulation and experiment are performed to demonstrate the superiority of the proposed method compared to the existing ones based on the 2-D magnetic field model when inclinations are introduced. The proposed method may have the potential for designing a clamp-on current sensor dedicated to multicore cables similar to hand-held current probes with a relatively large inner diameter for single-conductor systems.

Busbar Current Measurement With Elliptical Sensor Arrays Without Conductor Specific Calibration

In highly efficient power electronic systems, circular arrays of magnetic field sensors offer numerous advantages compared to older magnetic core-based sensors. They feature low power consumption, low weight, and high immunity to external magnetic fields. In power converters, conductors with a rectangular cross section, a small height, and a large width are widely used. Thus, an elliptical sensor array could reduce the space needed for the current sensor, e.g., in a power converter by a factor of four or more compared to a circular sensor array. In this work, we theoretically and experimentally study the sensitivity error caused by the change of the conductor geometry. Therefore, we calibrated different elliptical sensor arrays on a circular conductor and determined the sensitivity error for the use of flat conductors with different widths. This calibration on a circular conductor avoids a costly conductor-specific calibration of the sensor array in the application. Two different distribution methods for elliptical sensor arrays and different ratios of the semiaxes are considered. In addition, the influence of the number of sensors and the starting position for the sensors are examined. The presented elliptical sensor arrays can be used to measure the current carried by a flat conductor largely independent of its width. For some aspect ratios, they even offer a lower sensitivity error than circular sensor arrays. In this article, design considerations for those elliptic sensor arrays are given.

Stator End-Winding Thermal and Magnetic Sensor Arrays for Online Stator Inter-Turn Fault Detection

In this paper, two novel stator inter-turn fault sensing schemes, based on infrared (IR) thermopile sensor array (IRSA) and Hall-effect sensor array (HESA) are proposed. These circular sensing arrays are mounted along the inner wall of the stator's casing facing the end-winding region. This enables a direct measurement of temperature and magnetic flux distribution along the end-winding region in a non-contact way. Thus, the deviation in thermal and magnetic symmetry introduced by an inter-turn short circuit fault can be readily assessed. The proposed sensing schemes provides an intuitive and straight forward approach to inter-turn fault monitoring compared to the conventional methods, which depend on detecting fault induced secondary effects on external signals (motor currents, casing vibration, and temperature). The practicality and the diagnostic ability of the end-winding sensor array approaches in detecting the stator inter-turn faults is demonstrated using a 1.5 kW induction motor test rig. Compared to IRSA, HESA is found to be more versatile and with better early fault detection capability. Hence, an embedded online monitoring algorithm based on HESA is developed and demonstrated using the test rig.

Imaging of Defect Signal of Reinforcing Steel Bar at High Lift-Off Using a Magnetic Sensor Array by Unsaturated AC Magnetic Flux Leakage Testing

Reinforcing steel bars (rebars) in the concrete need to be inspected to prevent the structure from collapsing. Magnetic nondestructive testing methods can inspect the rebar without the influence of concrete. However, since the inspection is performed at a high lift-off on concrete, a strong applied magnetic field is required in order to measure a sufficient magnetic signal generated from the rebar. In addition, if a single sensor is used to measure the rebar, this requires the scanning of extensive area along the invisible rebar covered with the concrete. To overcome these problems, we have developed a method to detect and image the defect signal using unsaturated ac magnetic flux leakage (USAC-MFL) testing combining a magnetic sensor array probe. The USAC-MFL is a method that uses an alternating magnetic field in the initial magnetization characteristics of steel, which does not require a strong applied magnetic field compared to the conventional MFL method. By measuring the magnetic flux from the rebar in a wide area using the magnetic sensor array probe, the defect signal was able to be detected and imaged. The defect signal was able to be confirmed up to the lift-off of 100 mm even when the defect was half length of the rebar or located on the back side.

Misalignment Error Suppression Between Host Frame and Magnetic Sensor Array

Magnetic sensor array is usually designed for object detection and localization, where sensor coordinate is required to be consistent. Misalignment angles between coordinates should be calculated and calibrated. A new calibration method is proposed in order to calibrate the misalignment error between host frame and sensors. Host platform frame and perpendicular platform are used to obtain misalignment angles of sensor array. Experiment results show that it can estimate all angles of magnetic sensors and suppress misalignment error. Misalignment rms error is a reduction from 1109.7 to 27.6 nT, which means 2.48% indeed, thus improving the remote sensing accuracy of array which is unified to host frame coordinate.

Parametric Reconstruction of Multiple Line Currents Based on Magnetic Sensor Array

Current measurement is of great importance for the state monitoring and parameter identification in a power grid. This article proposed a contactless magnetic-based sensor array method for the acquisition of line current parameters, aiming at the measurement for arbitrary line currents. The inverse problem between the line current with arbitrary parameters and the magnetic field was introduced. Due to the nonlinearity of the inverse problem, a comprehensive algorithm consisting of metaheuristic algorithms and interior point method was employed. The influences of structural parameters on the calculation accuracy have been explicitly studied, indicating the optimal sensor array design parameters concerning the number of sensors, the distance between adjacent sensors, and the shape of sensor array. The sensor array was implemented by utilizing the dual-axial tunneling magnetoresistive (TMR) magnetic-field measurement device. In terms of the 2-D magnetic-field measurement results for two currents with all parameters unknown, the current magnitude error was 0.6%, proving the effectiveness of the comprehensive algorithm together with the annular sensor array. The proposed method for current measurement gives a promising solution for various line current measurement requirements in the power grid.

An Innovative Magnetic Anomaly Detection Algorithm Based on Signal Modulation

Magnetic anomaly detection (MAD) is a passive method used to detect the ferromagnetic objects by revealing the anomalies in the ambient Earth magnetic field. This article proposed a novel MAD algorithm based on signal modulation for magnetic sensor array. The new method transforms the original magnetic anomaly into a modulated signal and then detects the target magnetic anomaly signal by using a time–frequency analysis method. Compared with traditional algorithms, the MAD algorithm proposed in this article has three advantages: first, the influence of geomagnetic background is suppressed by calculating the magnetic field difference of the array sensor, and the trend of magnetic field difference is removed by empirical mode decomposition. Second, it properly fuses the magnetic anomaly signal of the sensor array and uses the time–frequency analysis method, which can improve the detection ability of weak magnetic anomaly signals. Third, the new method does not depend on the motion state and characteristics of the target, and it has a good adaptability to the background magnetic field. The simulation results show that this novel detection method has a good ability in the low signal-to-noise ratio (SNR) anomalies detection. For weak magnetic anomaly with an SNR of −6.9 dB, the detection probabilities and false alarm rate are about 0.9648 and 0.001, respectively. The real-world detection experiment proved that this algorithm can detect the weak magnetic anomaly in the geomagnetic background.

264-channel high-performance magnetic field detection system for transcranial magnetic stimulation (TMS)

Abstract To calibrate transcranial magnetic stimulation (TMS) devices before clinical trials, a 264-channel high-performance magnetic field detection system for TMS is proposed in this paper. The magnetic field detection system consists of three parts: 3D magnetic field measurement sensor (MFMS) array, 264-channel data acquisition (DAQ) card and monitor software. The 3D MFMS array is made of induction coils according to the structure of human brain. The DAQ card has 264 channels, with 4 MSps/ch maximum sampling rate and 14-bit resolution, and a good signal noise and distortion (SINAD) and crosstalk of 65.1 dB and −83.4 dB respectively. FPGA is used to control and process high-speed signals in the DAQ card. The monitor software is developed in QtCreator5.12 to process, display and backup data. The system, which is suitable for various TMS devices, can detect TMS magnetic field in real time with a relative error (RE) of 2.19%. Finally, the proposed system is used to calibrate our TMS device. The results show a good match between measurements and simulations of the TMS device with an average RE of 3.72%, which proves the system has outstanding advantages in multi-channel, synchronization, dynamic performance, data throughput, data visualization and so on.

A Machine Learning Enabled Wireless Intracranial Brain Deformation Sensing System.

A leading cause of traumatic brain injury (TBI) is intracranial brain deformation due to mechanical impact. This deformation is viscoelastic and differs from a traditional rigid transformation. In this paper, we describe a machine learning enabled wireless sensing system that predicts the trajectory of intracranial brain deformation. The sensing system consists of an implantable soft magnet and an external magnetic sensor array with a sensing volume of 12 × 12 × 4 mm3. Machine learning algorithm predicts the brain deformation by interpreting the magnetic sensor outputs created by the change in position of the implanted soft magnet. Three different machine learning models were trained on calibration data: (1) random forests, (2)k-nearest neighbors, and (3) a multi-layer perceptron-based neural network. These models were validated using both in vitro (a needle inserted into PVC gel) and in vivo (blast exposure to live and dead rat brains) experiments. The in vitro gel deformation predicted by these machine learning models showed excellent agreement with the camera measurements and had absolute error = 138 μm, Fréchet distance = 372 μm with normalized Procrustes disparity = 0.034. The in vivo brain deformation predicted by these models had absolute error = 50 μm, Fréchet distance = 95 μm with normalized Procrustes disparity = 0.055 for dead animal and absolute error = 125 μm, Fréchet distance = 289 μm with normalized Procrustes disparity = 0.2 for live animal respectively. These results suggest that the proposed machine learning enabled sensor system can be an effective tool for measuring in situ brain deformation.

Inspection of Mine Wire Rope Using Magnetic Aggregation Bridge Based on Magnetic Resistance Sensor Array

Early detection of damage to wire ropes used in coal mine winching and traction systems is important for avoiding production delays and for the safety of personnel entering the mine. This article proposes a new magnetic aggregation bridge detection method utilizing a magnetic resistance (MR) sensor array, which addresses the shortcomings of the present methods for testing the integrity of wire ropes used in coal mining operations. First, the structure and types of damage incurred by such ropes are analyzed. The detection principle of the proposed method and the optimization of magnetic induction strength regions are then described. The selection of three types of magnetic sensitivity detection elements is compared and analyzed. On this basis, the magnetic aggregation method for inspecting wire rope, based on MR sensor array, is studied in detail, including the detection effect of including or omitting a magnetic aggregation device. Different structures and sizes of magnetic aggregation devices are examined for their performance effect, showing measures to improve the effect of magnetization detection and selection methods for the MR sensor. A detection method using an MR sensor array combination matched with the magnetic field focusing model was discussed in detail. Finally, the proposed method is experimentally verified. The results show that the prototype sensor based on the proposed method can clearly detect multiple types of damage to wire rope, achieving a maximum signal-to-noise ratio of 60 dB and a considerable detection effect, compared with the conventional magnetic flux leakage defect detection sensor.

MARG Attitude Estimation Using Gradient-Descent Linear Kalman Filter

The magnetic, angular rate, and gravity (MARG) sensor array has been widely used for attitude estimation tasks. In this article, we report our new advances on related fusion algorithm based on the gradient-descent algorithm (GDA). Combining with complementary filters, GDA has been very popular for attitude estimation in industrial applications. The integration of the Kalman filter introduces covariance information and significantly improves in-run quality control. Some useful results are derived to build up the framework of a novel linear Kalman filter called GDA-LKF. A new simplified linear measurement quaternion model is proposed. This article also deals with the analytical adaptive problem of determining gradient-descent step length. We, for the first time, give the solution in the sense of least square based on aided vector measurements. Simulations are carried out to validate the noise sensitivity and covariance characteristics. The proposed schemes are also evaluated by real-world experiments that provide the audience with comparisons on accuracy, convergence, and execution time consumption performances between the proposed GDA-LKFs and recent representative methods. The results show that the proposed GDA-LKF can accurately estimate attitude with fast convergence and high accuracy. Note to Practitioners —Attitude estimation using magnetic, angular rate, and gravity (MARG) sensors is very common for ground, air, and underwater vehicles. The novel findings in this article aim to give the engineers a brand new perspective on the related filter design according to the widely employed gradient-descent algorithm (GDA) method. Some specific techniques, e.g., optimal adaptive law of the designed scheme, will also bring flexibility to the implementation with multiple considerations of object motions.

A Novel Fuzzy-Adaptive Extended Kalman Filter for Real-Time Attitude Estimation of Mobile Robots.

This paper proposes a novel fuzzy-adaptive extended Kalman filter (FAEKF) for the real-time attitude estimation of agile mobile platforms equipped with magnetic, angular rate, and gravity (MARG) sensor arrays. The filter structure employs both a quaternion-based EKF and an adaptive extension, in which novel measurement methods are used to calculate the magnitudes of system vibrations, external accelerations, and magnetic distortions. These magnitudes, as external disturbances, are incorporated into a sophisticated fuzzy inference machine, which executes fuzzy IF-THEN rules-based adaption laws to consistently modify the noise covariance matrices of the filter, thereby providing accurate and robust attitude results. A six-degrees of freedom (6 DOF) test bench is designed for filter performance evaluation, which executes various dynamic behaviors and enables measurement of the true attitude angles (ground truth) along with the raw MARG sensor data. The tuning of filter parameters is performed with numerical optimization based on the collected measurements from the test environment. A comprehensive analysis highlights that the proposed adaptive strategy significantly improves the attitude estimation quality. Moreover, the filter structure successfully rejects the effects of both slow and fast external perturbations. The FAEKF can be applied to any mobile system in which attitude estimation is necessary for localization and external disturbances greatly influence the filter accuracy.

Design and optimization of sensor array for magnetic gradient tensor system

PurposeThe differential magnetic gradient tensor system is usually constructed from the three-axis magnetic sensor array. While the effects of measurement error, sensor performance and baseline distance on localization performance of such systems have been widely reported, the research about the effect of spatial design of sensor array is less presented. This paper aims to provide a spatial design method of sensor array and corresponding optimization strategy to localization based on magnetic tensor gradient to get the optimum design of the sensor array. Based on the results of simulation, magnetic localization systems constructed from the proposed array and the traditional array have been built to carry out a localization experiment. The results of experiment have verified the effectiveness of magnetic localization based on the proposed array.Design/methodology/approachThe authors focus on the localization of the magnetic target based on magnetic gradient by using three-axis magnetic sensor array and combine a design method with corresponding optimization strategy to get the optimum design of the sensor array.FindingsThis paper provides an array design and optimization method for magnetic target localization based on magnetic gradient to improve the localization performance.Originality/valueIn this paper, the authors focus on the magnetic localization based on magnetic gradient by using three-axis magnetic sensors and study the effect of the spatial design of sensor array on localization performance.

Mechanically Flexible Sensor Array for Current Measurement

Contactless galvanically isolated magnetic field-based current sensors utilizing hard ferromagnetic cores are widely used in many applications, for example, power converters for drives or wind turbines. New measurement methods, e.g., circular arrays of magnetic field sensors, offer some advantages, such as low weight, mechanical flexibility, and independence of the nonlinear and hysteretic behavior of the core. Those sensor arrays can be operated in an open-loop manner or in a closed-loop manner with an additional compensation coil. The advantages of the open-loop design, which we use in this article, are lower cost, lower weight, and the opportunity to realize a mechanically flexible sensor array. In this article, we show the theoretical and experimental influence of the mechanical bending on the accuracy of circular arrays of magnetic field sensors used for current measurement. Furthermore, the inner displacement of the conductor in combination with different bendings is considered. The experimental results were taken with 12, 6, 4, and 3 Hall effect sensors that were uniformly placed on the circular array.

Crosstalk analysis and Current Measurement Correction in Circular 3D Magnetic Sensors Arrays

The circular array of magnetic sensors is a research hotspot in the field of power electronics, especially for the measurement of direct current(DC). The high linearity, large dynamic range, small size and low power consumption of circular magnetic sensors arrays for current measurement are an improvement over the current sensors utilizing a ferromagnetic core. However, due to the absence of core magnetization, the external magnetic field can easily enter the magnetic sensors, which will affect the measurement accuracy. Therefore, this paper focuses on the influence of the interference field from the conductor positioned outside the circular array and proposes a model of the target conductor penetrating the circular array with the interference conductor outside the circular array. This model is used to analyze the influence of relevant parameters of the interference conductor and the target conductor on the crosstalk error. An interference-rejecting method of circular 3D magnetic sensor arrays is proposed, which establishes the model of magnetic flux density measurement to calculate the target conductor current. The simulation results show theoretically that the method can greatly reduce the crosstalk error and correct current measurement. 3-D tunnel magnetoresistance (TMR) chip is selected as the magnetic sensors of the circular array in the laboratory experiment, and the experiment errors can be reduced to around 1%. The simulation and experiment results verify that the interference-rejecting method can correct measurement results and improve the accuracy of the target current.

Reconstruction of Dexterous 3D Motion Data from a Flexible Magnetic Sensor with Deep Learning and Structure-Aware Filtering

We propose IM3D+, a novel approach to reconstructing 3D motion data from a flexible magnetic flux sensor array using deep learning and a structure-aware temporal bilateral filter. Computing the 3D configuration of markers (inductor-capacitor (LC) coils) from flux sensor data is difficult because the existing numerical approaches suffer from system noise, dead angles, the need for initialization, and limitations in the sensor array's layout. We solve these issues with deep neural networks to learn the regression from the simulation flux values to the LC coils' 3D configuration, which can be applied to the actual LC coils at any location and orientation within the capture volume. To cope with the influence of system noise and the dead-angle limitation caused by the characteristics of the hardware and sensing principle, we propose a structure-aware temporal bilateral filter for reconstructing motion sequences. Our method can track various movements, including fingers that manipulate objects, beetles that move inside a vivarium with leaves and soil, and the flow of opaque fluid. Since no power supply is needed for the lightweight wireless markers, our method can robustly track movements for a very long time, making it suitable for various types of observations whose tracking is difficult with existing motion-tracking systems. Furthermore, the flexibility of the flux sensor layout allows users to reconfigure it based on their own applications, thus making our approach suitable for a variety of virtual reality applications.

Real-time sensor fault detection in Tokamak using different machine learning algorithms

The “Tokamak” is a device that facilitates nuclear fusion between Deuterium and Tritium. Multiple arrays of magnetic sensors are used to detect the plasma position inside a Tokamak. This paper presents the application of different machine learning (ML) based fault detection techniques for the identification and classification of faults that happen in typical magnetic position sensors. The performances of these machine learning based fault detection algorithms are evaluated for two scenarios as follows. Firstly, during the “Self-Test” mode, i.e., before the start-up of the plasma discharge, with known current waveforms in the external coils. Secondly, by using the simulated plasma discharge waveforms. Their performances are compared in terms of computational complexities and latency in view of deciding the best fault detection algorithm. The machine learning techniques are implemented in real-time on the Xilinx Kintex-7 and Xilinx Zync-7 series FPGA. From the obtained comparison results, it is observed that out of the six machine learning approaches, namely Multi-Layer Perceptron (MLP) neural network, K-Nearest Neighbor (KNN), Support Vector Classifier (SVC), Gaussian Naive Bayes (GNB), Decision Tree (DT) and Random Forest classifier (RF) employed for Tokamak sensor fault detection, the Random Forest Classifier based approach was found to be the best in terms of speed and accuracy.