Magnetic Dipole Model Research Articles

A Novel Defect Quantification Method Utilizing Multi-Sensor Magnetic Flux Leakage Signal Fusion

In the assessment of pipeline integrity using magnetic flux leakage (MFL) detection, it is crucial to quantify defects accurately and efficiently using MFL signals. However, in complex detection environments, traditional defect inversion methods exhibit low quantification accuracy and efficiency due to the complexity of their algorithms or excessive reliance on a priori knowledge and expert experience. To address these issues, this study presents a novel defect quantification method based on multi-sensor signal fusion (MSSF). The method employs a multi-sensor probe to fuse the MFL signals under multiple lift-off values, enhancing the diversity of defect information. This enables defect-opening profile recognition using the characteristic approximation approach (CAA). Subsequently, the MSSF method is based on a 3D magnetic dipole model and integrates the structural features of multi-sensor probes to develop an algorithm. This algorithm iteratively determines the defect depth at multiple data acquisition points within the defect region to obtain the maximum defect depth. The feasibility of the MSSF quantification method is validated through finite element simulation and physical experiments. The results demonstrate that the proposed method achieves accurate defect quantification while enhancing efficiency, with the number of iterations for each defect depth calculation point consistently requiring fewer than 15 iterations. For rectangular metal loss, perforation, and conical defects, quantification errors are less than 10%, meeting practical inspection requirements.

Study of Noise Reduction and Identification of Internal Damage Signals in Wire Ropes

Mining wire rope, a frequently used load-bearing element, suffers various forms of damage over extended periods of operation. Damage occurring within the wire rope, which is not visible to the naked eye and is difficult to detect accurately with current technology, is of particular concern. Consequently, the identification of internal damage assumes paramount importance in ensuring mine safety. This study proposes a wire rope internal damage noise reduction and identification method, first of all, through a three-dimensional magnetic dipole model to achieve the detection and analysis of the internal damage of the wire rope. Simultaneously, a sensor system capable of accurately detecting the internal damage of wire rope is developed and validated through experimentation. A novel approach is proposed to address the noise reduction issue in the design process. This approach utilizes a particle swarm optimization variational modal decomposition method to enhance the signal-to-noise ratio. Additionally, a dual-attention mode, which combines channel attention and spatial attention, is integrated into the CNN-GRU network model. This network model is specifically designed for the detection of internal damage in steel wire ropes. The proposed method successfully achieves quantitative identification of internal damage in steel wire ropes. The experimental findings demonstrate that this approach is capable of efficiently detecting internal damage in wire rope and possesses the capacity to quantitatively identify such damage, enabling adaptive identification of wire rope.

Development of Precision Controllable Magnetic Field-Assisted Platform for Micro Electrical Machining.

In order to introduce the magnetic field into micro electrical machining technology to explore the influence of magnetic field on micro electrical machining, the development of a precision controllable magnetic field-assisted platform is particularly important. This platform needs to precisely control the spatial magnetic field. This study first completes the hardware design and construction of the magnetic field generation device, using electromagnetic coils with soft iron cores as the sources of the magnetic field. Mathematical models of the magnetic field are established and calibrated. Since the magnetic dipole model cannot effectively describe the magnetic field generated by the electromagnetic coil, this study adopts a more precise description method: the spherical harmonic function expansion model and the magnetic multipole superposition model. The calibration of the magnetic field model is based on actual excitation magnetic field data, so a magnetic field sampling device is designed to obtain the excitation magnetic field of the workspace. The model is calibrated based on a combination of the theoretical model and magnetic field data, and the performance of the constructed setup is analyzed. Finally, a magnetic field-assisted platform has been developed which can generate magnetic fields in any direction within the workspace with intensities ranging from 0 to 0.2 T. Its magnetic field model arrives at an error percentage of 2.986%, a variance of 0.9977, and a root mean square error (RMSE) of 0.71 mT, achieving precise control of the magnetic field in the workspace.

Structural Design and Parameter Optimization of Magnetic Gradient Tensor Measurement System.

Magnetic anomaly detection (MAD) technology based on the magnetic gradient tensor (MGT) has broad application prospects in fields such as unexploded ordnance detection and mineral exploration. The difference approximation method currently employed in the MGT measurement system introduces measurement errors. Designing reasonable geometric structures and configuring optimal structural parameters can effectively reduce measurement errors. Based on research into differential MGT measurement, this paper proposes three simplified planar MGT measurement structures and provides the differential measurement matrix. The factors that affect the design of the baseline distance of the MGT measurement system are also theoretically analyzed. Then, using the magnetic dipole model, the error analysis of the MGT measurement structures is carried out. The results demonstrate that the planar cross-shaped structure is optimal, with the smallest measurement error, only 3.15 × 10-10 T/m. Furthermore, employing the control variable method, the impact of sensor resolution constraints, noise level, target magnetic moment, and detection distance on the design of the optimal baseline distance of the MGT measurement system is simulated and verified. The results indicate that the smaller the target magnetic moment, the farther the detection distance, the lower the magnetometer resolution, the greater the noise, and the greater the baseline distance required. These conclusions provide reference and guidance for the construction of the MGT measurement system based on triaxial magnetometers.

Improving the performance of magnetorheological elastomer-based adaptive isolator through integrated compression-torsion structure

In this paper, a novel magnetorheological elastomer (MRE) isolator with a compression-torsion structure was developed to address existing challenges related to stiffness variation, damping force, and magnetic control range. Through performance testing of the vibration isolator prototype and theoretical analysis based on traditional magnetic dipole model of the MRE, the effects of applied magnetic field and compression displacement on the performance of the designed MRE isolator were systematically evaluated. The results showed that integrating the compression-torsion structure not only enhances the magneto-induced mechanical performance of the MRE but also improves the overall performance of the entire MRE isolator. The output force of the MRE isolator with a compression-torsion structure generally surpasses than that of the MRE isolator lacking this feature. The isolator’s stiffness can vary by up to 119% compared to its initial stiffness when a 2 A current is applied at a compression displacement of 0.5 mm. The proposed design, combining the compression-torsion structure and the MRE isolator, offers new insights for future research and applications in the realm of MRE isolators.

A Compensation Method for the Geomagnetic Measurement Error of an Underwater Ship-Borne Magnetometer Based on Constrained Total Least Squares.

When magnetic matching aided navigation is applied to an underwater vehicle, the magnetometer must be installed inside the vehicle, considering the navigation safety and concealment of the underwater vehicle. Then, the interference magnetic field will seriously affect the accuracy of geomagnetic field measurement, which directly affects the accuracy of geomagnetic matching aided navigation. Therefore, improving the accuracy of geomagnetic measurements inside the vehicle through error compensation has become one of the most difficult problems that requires an urgent solution in geomagnetic matching aided navigation. In order to solve this problem, this paper establishes the calculation model of the internal magnetic field of the underwater vehicle and the geomagnetic measurement error model of the ship-borne magnetometer. Then, a compensation method for the geomagnetic measurement error of the ship-borne magnetometer, based on the constrained total least square method, is proposed. To verify the effectiveness of the method proposed in this paper, a simulation experiment of geomagnetic measurement and compensation of a ship-borne three-axis magnetometer was constructed. Among them, to be closer to the real situation, a combination of the geomagnetism model, the elliptic shell model and the magnetic dipole model was used to simulate the internal magnetic field of the underwater vehicle. The experimental results indicated that the root mean square error of geomagnetic measurement in an underwater vehicle was less than 5 nT after compensation, and the accuracy of geomagnetic measurement met the requirements of geomagnetic matching aided navigation.

Research on the defect depth detection for pipeline steel with double defects using metal magnetic memory method

Metal magnetic memory testing is an effective method to detect the stress state of ferromagnetic materials, and shows great application potential in the field of defect detection of oil and gas pipelines recently. In this paper, the correlation between the normal component of residual magnetic field (RMF) and the defect depth, as well as the applied loading were investigated by tensile tests. The X70 pipeline steels were processed into specimens with double defects of six types of depths and three types of spacings. Some magnetic parameters are defined to characterize the distortion of the RMF in the defect area. The effect of defect depth and applied loading on the magnetic parameters is discussed. The RMF signals measured on the smooth side of the specimens were compared with those on the defective side. Results show that the normal parameters, obtained from the front and back of the specimens, are capable of detecting the defect depth. The slope of the linear relationship between the two increases with the increase of defect spacing. The expressions of normal magnetic parameters were derived based on the Jiles model and magnetic dipole model. The simulation results of defective side and smooth side were compared, as well as the simulation results of different defect spacing. The experimental and numerical simulation results show that the defect depth of pipeline steel can be evaluated by the characteristic parameters of the normal RMF signal under a certain stress level.

Detection and classification of invisible weld defects by magneto-optical imaging under alternating magnetic field excitation

Aiming at the difficult to detect invisible weld defects, a magneto-optical (MO) imaging non-destructive testing (NDT) system excited by an alternating magnetic field is proposed for feature extraction and detection classification of invisible weld defects. The relationship between the MO image features and the magnetic field intensity is analyzed based on the Faraday MO effect. A magnetic dipole model is proposed to study the magnetic field distribution on weld defect. A three-dimensional finite element model of invisible weld defects (with a width of 0.01 mm) is established, and the distribution of leakage magnetic field for different types of invisible defects is analyzed. In order to detect different invisible weld defects under the excitation of alternating magnetic field, MO imaging NDT experiments are carried out. The effectiveness of the finite element model is verified by the experiment. The gray value of the MO image can match the corresponding leakage magnetic field intensity. The Tamura method and gray-level co-occurrence matrix (GLCM) method are used to extract the texture features of natural invisible weld defect’s MO image, and these texture features of MO images are used as input data for the defect classification model established using back propagation (BP) neural network. Experimental results show that the classification accuracy of the GLCM + Tamura-BP model is higher than that of the GLCM-BP model, and its overall classification accuracy reaches 91.1%, indicating that this model can effectively and accurately classify natural invisible weld defects.

Evaluation of residual load-bearing capacity for corroded steel strands via MMM technique

The quantitative evaluation of the residual load-carrying capacity of corroded cables is critical to the safe service of bridge structures. In this study, the locally corroded steel strands with different corrosion degrees were obtained through electrochemical experiments and the metal magnetic memory (MMM) signals were collected by the TSC-9 M-12 tester. The tensile failure tests of corroded steel strands were conducted by the WAW-1000 tensile testing machine. The distribution laws of the normal component Hz signals for steel strands in different corrosion cases were detailed and a three-dimensional (3D) magnetic dipole model of corroded steel strands was developed considering the end effects. The linear relationships between the magnetic characteristic quantity Hn and the corrosion cross-section loss rate As were revealed and verified by the theoretical and finite element simulation results. Based on the above relationships, a quantitative linear relationship between the residual load-carrying capacity F and the corrosion cross-section loss rate As of the corroded steel strand was proposed. The relative errors of the residual load-carrying capacity F calculated by the proposed quantitative method were overall within 20%. This study provides a basis for evaluating the residual load-carrying capacity of corroded cables using the MMM technique.

Magnetic leakage behavior assessment in pipeline stress-concentrated areas using improved force-magnetic coupling model.

Magnetic flux leakage (MFL) technology is remarkable for its capability to detect pipeline geometric deformation and general corrosion defects. However, it cannot characterize the MFL behavior in stress-concentrated areas, thereby greatly challenging the subsequent pipeline maintenance. This study suggests that the MFL characteristics of pipeline in stress-concentrated areas are caused by the combined effect of the face magnetic charge on the deformed end-face and the body magnetic charge of the dislocation stack. In addition, an improved force-magnetic coupling model of the pipeline in stress-concentrated areas is established based on the magnetic dipole model and Jiles-Atherton (J-A) theory. In the verification experiment, the Q235 steel plate is magnetized along the extension direction (axis of the pipeline) through the solenoid coil to obtain the distribution law of the MFL signal in the stress-concentrated area under different excitation intensities. The results show that with the increase in excitation intensity, the deformation of the MFL field signal caused by the end-face of the stress-concentrated area gradually increases to a stable state. Moreover, the internal stress of the MFL field signal generated by the pipe dislocation rapidly increases to a peak value and then decays exponentially to a certain base value. The overall change trend is in good agreement with the calculation results of the established force-magnetic coupling model. Meanwhile, the differentiation research between deformation and internal stress MFL field signals under different magnetic field intensities can provide a reliable theoretical basis for the subsequent accurate identification and quantification of pipeline stress-concentrated areas.

Study on the static normal force of MRF in non-uniform magnetic field

Nowadays, many scholars have been studied the normal force of MRF in the uniform magnetic field. However, the research on the normal force of MRF in the non-uniform magnetic field is relatively limited. The non-uniform magnetic field can cause the MRF to generate normal force of different sizes and directions to cope with different working conditions, thus the normal force generated in the non-uniform magnetic field require more attention. In this paper, a theoretical model of the normal force of MRF in the non-uniform magnetic field was developed based on the enhanced magnetic dipole model. The normal force of MRF within a unit area can be calculated based on this theoretical model. However, the magnetic induction intensity is different at different locations of the non-uniform magnetic field, which leads to the normal force generated by the MRF are not accurately calculated. Therefore, it is necessary to use COMSOL to establish the material model of the MCR-302 plate rheometer and MRF to verify the accuracy of the proposed model. Then a flat-plate rheometer was used to test the static normal force of the MRF in the non-uniform magnetic field. Finally, the simulation and experimental data were compared. The results show that the simulation result with the experimental data is a good agreement, which verifies the reliability of the theoretical model. The static normal force of the MRF increases with the increase of volume fraction and magnetic field intensity.

Magnetic-controlled friction behavior of a water-lubricated magnetorheological rubber bearing under boundary lubrication

To solve the issue of the non-adjustable friction coefficient of water-lubricated bearings in operation, a water-lubricated rubber bearing is designed based on magnetorheological (MR) rubbers in this study. The experimental platform measured the friction coefficients with different magnetic fields and low speed. The friction coefficient of the MR rubber bearing peaks in boundary lubrication. The friction coefficient of the bearings is controlled by the magnetic field, resulting in a reduction of the friction coefficient up to 36%. The theoretical analysis combines the magnetic-dipole model and the theory of friction trinomials. It revealed that the magnetic-controlled modulus of elasticity and loss factor of MR rubber bearings affect the friction coefficient, with the modulus of elasticity factor dominating.

Research on magnetic localization and tracking algorithm based on total magnetic field

There are few studies on the total magnetic field localization and tracking algorithm based on the domestic magnetic dipole model, and the scalar magnetometer’s measurement of magnetic targets is not affected by its own posture. Therefore, a magnetic localization and tracking algorithm based on the total magnetic field is proposed., this method is based on the magnetic dipole model and uses the particle swarm algorithm and the extended Kalman auxiliary algorithm to achieve magnetic localization and tracking. The effectiveness of this method has been verified through simulation experiments. The relative localization error is small and maintained in the range of about 10%.

Research on magnetoelastic coupling model based on magnetic dipole theory

In this paper, a theoretical model of a magnetoelastic coupling magnetic dipole is established to analyse the influence of stress on the magnetic signal in magnetic memory testing. Based on the theory of ferromagnetism, the equivalent field strength under the combined action of stress and the magnetic field is determined and a numerical solution for the stress magnetisation of isotropic ferromagnetic materials under a weak environmental magnetic field is obtained. Based on the assumption of a double rectangular crack in a three-dimensional problem for the magnetic signal, a theoretical analysis model of a magnetoelastic coupling-type magnetic dipole is established. Based on the theory of the magnetoelastic coupling magnetic dipole, the influence factors and rules of the magnetic signal are analysed in detail. The theoretical research shows that the solution based on the theoretical model in this paper can explain some basic experimental phenomena and laws in magnetic memory inspection. The magnetic signal of a defect-free plate shows a 'horseshoe shape'. The length, width and height of the plate will affect Hx but have no effect on Hy . In addition, the lift-off value has a great influence on the magnetic signal of the plate. When the two cracks are a small distance apart, the magnetic signal of the plate is the superposition of the magnetic signals of the two cracks. For plates with cracks, the crack size, spacing, external magnetic field strength and stress will affect the magnetic signal of the plate.

Magnetic Dipole Model and Experimental Analysis of Magnetic Signal Detection Based on Magnetic Memory

By assuming that the magnetic charge is evenly distributed in the defect groove, the linear magnetic dipole is integrated in the depth direction of the defect, and the numerical calculation is carried out by using MATLAB to establish a two-dimensional magnetic dipole theoretical analysis model of double-correlated defects, which is suitable for analyzing the influence of stress on magnetic signal in the magnetic memory detection of rectangular and V-shaped combined macroscopic crack defects. To explore the influence factors and change rules of magnetic memory signal. In order to verify the correctness of the model analysis results, tensile tests were carried out on Q235 steel plate with double associated defects with different morphological characteristics, and the Hp(y) value of the normal component of the leakage magnetic field on the surface of the member was measured. The results show that the model based on magnetic dipole theory can explain some experimental phenomena and rules in magnetic memory detection.

Дослідження моделей та алгоритмів систем локалізацій джерел магнітних аномалій

Introduction. The application of modern geophysical methods are caused by the challenges of nowadays Ukraine standing with. The high efficiency of geophysical research is shown by the methods of magnetic exploration. Method of analyzing the array of data from the magnetometer is used to localize the magnetic anomaly’s sources. Such localization is implemented by using various mathematical models and algorithms of software systems. Purpose. The aim of the article is to show an overview of mathematical models and algorithms for the localization of magnetic anomalies’ sources (disturbances). They allow to speed up the processing of magnetometric research’s data and visualize the obtained results. Methods. The article examines the mathematical models of the magnetic anomaly< such as magnetic dipole model, the Gaussian model, the Schwartz model. The multilayer model, and also provides the overview of the main methods for the localization of the described anomaly – the filtering method, the least square method, the gradient analysis method. A list of software and online resources is given, this software is used to analyze magnetometer data and locate magnetic anomalies’ sources. Results. Four mathematical models of magnetic anomalies that allow describing objects of various configurations are considered in the article, and the main methods of determining these objects in the magnetometer data array are given. The article presents the most popular software used for magnetometric data processing. Most of the software is used in geophysics for deep research and requires significant computing resources. A software application was proposed and developed. It allows importing data from the moving platform and magnetometer, analyzing data and visualizing the results. Conclusion. The results of the review emphasize the importance of improving existing mathematical models and developing specialized software for magnetic anomalies’ source localization.

An improved magnetic dipole model for MFL testing based on non-uniform magnetic charge distribution

ABSTRACT Magnetic flux leakage (MFL) signal prediction is important in ferromagnetic defect evaluation and reconstruction. At present, the magnetic dipole model (MDM) is the most widely applied method because of its high efficiency. However, it has low accuracy when applied to analysing complex defects (complex in profile and magnetic permeability) due to the original setting of uniform magnetic charge distribution. To solve the issue, this paper proposes an improved MDM method for MFL inspection of ferromagnetic materials by calculating the non-uniform magnetic charge distribution. It partly applies the finite volume method (FVM) to derive the magnetic charge distribution on the defect surface, which makes it able to take into account the defect’s profile and magnetic permeability distribution. The new magnetic charge distribution can increase the MDM’s accuracy for complex defect MFL field prediction with little extra cost. Experimental results show that, when compared with traditional MDM, the proposed one can achieve a maximum 69% decrease in root mean squared error when analysing complex defects. Compared with the numerical method, the computation time could reach a great reduction.

Magnetic flux leakage defect size estimation method based on physics-informed neural network.

Magnetic flux leakage (MFL) is a magnetic method of non-destructive testing for in-pipe defect detection and sizing. Despite the fact that recent developments in machine learning have revolutionized disciplines like MFL defect size estimation, the most current methods for quantifying pipeline defects are primarily data-driven, which may violate the underlying physical knowledge. This paper proposes a physics-informed neural network-based method for MFL defect size estimation. The training process of neural network is guided by the MFL data and the physical constraints that is mathematically represented by the magnetic dipole model. We use synthetic MFL data produced by a virtual MFL testing of pipeline defects to validate the proposed method through a comparison to purely data-driven neural networks and support vector machines. The findings imply that the physics-informed strategy can both improve predictive accuracy and mitigate physical violations in MFL testing, providing us with a better knowledge of how neural networks perform in defect size estimation. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 2)'.

Influence of tensile stress on the magnetic flux leakage signal of the coated steel belt

ABSTRACT The safety of coated steel belts (CSBs) is crucial for reliable elevator operation, as they are critical components in elevator systems. Magnetic flux leakage (MFL) testing is the preferred non-destructive method for evaluating CSBs due to its high sensitivity. Previous studies overlooked tensile stress's impact on in-service MFL testing of CSBs, potentially resulting in inaccurate defect assessments. This research aims to investigate the impact of tensile stress on the MFL signal of CSBs by developing a theoretical model, conducting finite element simulations, and performing experimental verification. In this paper, the rectangular edge defects are considered as the primary defect type in CSBs, and the applied stress on the CSBs varies from 30 MPa to 160 MPa. Under the above conditions, a linear relationship between MFL signal of CSBs and stress is established based on the simplified Jiles-Atherton model and magnetic dipole model suitable for CSBs. The finite element simulation and experiments further indicate that the MFL signal of CSBs increases linearly with the increasing tensile stress. The primary contributions of this study are establishing an MFL model suitable for CSBs and uncovering the linear relationship between the MFL signal of CSBs and tensile stress.

2D CNN‐based multi‐feature fusion detection method for the magnetic anomaly generated by submarine wake

A Two-Dimensional Convolutional Neural Network (2D-CNN)-based multi-feature fusion detection method is proposed to improve the detection performance of the submarine wake magnetic anomaly in view of its characteristics of low frequency and low signal-to-noise ratio (SNR). The method involves pre-processing the original signal by using the Savitzky-Golay (S–G) filter, followed by Residual Structure processing to extract the time-domain information, FFT to extract the frequency domain information and Minimum-Entropy Filter (MEF) for noise analysis. The 2D-CNN model with three processing branches is utilised for further feature extraction and signal judgement. To train the method, Simulated target signal dataset is obtained through the submarine wake magnetic anomaly simulation model, and the simulated original signal is acquired by stacking measured noise. The proposed method exhibits great detection performance for signals with different Signal-to-Noise Ratios (SNRs) and various types of noise, achieving a recognition accuracy of 90% for signals with SNRs above -10dB. The theoretical detection range of the submarine has been increased to over 1 km, outperforming similar neural networks based on magnetic dipole models.