France



Introduction:&lt;br/&gt;Analyzing and processing the non-linear and non-stationary vibration signals is a critical issue in the motor bearing fault diagnosis. In order to solve this problem, Empirical Mode Decomposition (EMD) was proposed, which decomposes the signal in Intrinsic Mode Functions (IMFs) [1]. However, the EMD has the drawback of the so called “mode mixing” phenomenon, which means that the signal components with different amplitudes in one IMF, or the signal components with a similar amplitude in different IMFs. To address this issue, an effective solution was proposed, which suppresses the mode mixing by adding the Gaussian white noise in the original signal, named as “Ensemble Empirical Mode Decomposition (EEMD)” [2-3]. But it brings in some new harmonics in IMFs. To overcome these problems, the Complete Ensemble Empirical Mode Decomposition (CEEMD) was put forward, which adds the opposite Gaussian white noise in the original signal for the EMD respectively [4]. However, the amplitude of the Gaussian white noise is usually estimated by the practical experience rather than calculating by equations. Besides, the inappropriate Gaussian white noise could not mitigate the mode mixing effectively. The essence of mode mixing is the coupling between IMFs, and IMFs are not orthogonal to each other. This paper focuses on the mode mixing, and optimizes the amplitude of the white noise by the genetic algorithm (GA) to minimize the orthogonality among IMFs.&lt;br/&gt;&lt;br/&gt;Optimization Method:&lt;br/&gt;Mutual information is an indictor which symbolizes the correlation between the data. The mutual information between IMFs obtained by the CEEMD will be affected and changed, when the amplitude of the white noise varies. Therefore, the white noise amplitude (All of these values are multiples of the standard deviation of the signal) is used as the input function, and the minimum mean of the mutual information between IMFs is used as the objective function in the GA. As a consequence, it can suppress the mode mixing phenomenon theoretically, when the amplitude of white noise is the minimum mean of the mutual information.&lt;br/&gt;&lt;br/&gt;Results:&lt;br/&gt;The bearing vibration fault signal used in this paper comes from the Case Western Reserve University [5]. In Fig.1, the values in the bar denote the mean of mutual information of IMFs corresponding to different white noise amplitudes, where 0.1103 is the white noise amplitude selected by GA and 0.1 to 0.4 are the values selected by the experience. The mean of mutual information is 0.5728 when the amplitude of the white noise is 0.1103, which is smaller than the amplitudes of 0.1, 0.2, 0.3 and 0.4 that the mean of mutual information is 0.705, 0.6230, 0.6998 and 0.7093, respectively. Fig.2 shows the amplitude of IMFs in figure Fig.2 (a) and the spectrum diagram of IMFs in figure Fig.2 (b) decomposed by the CEEMD with the optimized white noise. It can be seen from the figure Fig.2 (b) that the main components of each IMF are distributed at different frequencies. Meanwhile, it shows in the spectrum of IMF3 that the five times frequency (539.1 Hz) component of the bearing outer race fault. It proves the effectiveness of the proposed method in motor bearing fault diagnosis. Detailed results and discussion will be given in the full paper.

**References:**

[1] N. E. Huang, Z. Shen, S. R. Long, et al.,&lt;i&gt; Proc. R. Soc. Lond. A Math. Phys. Sci.&lt;/i&gt;, vol. 454, p. 903-995, (1998).&lt;br/&gt;[2] Z. WU and N. E. Huang,&lt;i&gt; Adv. Adapt. Data Anal.&lt;/i&gt;, vol. 01, p. 1-41, (2008).&lt;br/&gt;[3] P. Flandrin, G. Rilling and P. Gonçalvès, &lt;i&gt;IEEE Signal Process. Lett.&lt;/i&gt;, vol. 11, p. 112-114, Feb. (2004).&lt;br/&gt;[4] F. Liu, J. Gao and H. Liu, &lt;i&gt;IEEE Access&lt;/i&gt;, vol. 8, p. 19810-19819, (2020).&lt;br/&gt;[5] C. W. R. University,&#39;&#39;https://csegroups.case.edu/bearingdatacenter/pages/12k-drive-end-bearing-fault-data,&quot; (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c71a8b8dc1e20c7f4b86ef846db3f898.jpg)
Fig. 1 The mean mutual information of different amplitude of the white noise.

![](https://assets.underline.io/uploads/markdown_image/1/image/348217bb9979a412c80e3a633833c3b6.jpg)
Fig. 2 IMFs decomposed by the CEEMD with the optimized white noise. (a) Amplitude of IMFs. (b) Spectrum diagram of IMFs.

INTERMAG 2021

 Adaptive Suppression of Mode Mixing in CEEMD Based on Genetic Algorithm for Motor Bearing Fault Diagnosis

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Introduction: Analyzing and processing the non-linear and non-stationary vibration signals is a critical issue in the motor bearing fault diagnosis. In order to solve this problem, Empirical Mode Decomposition (EMD) was proposed, which decomposes the signal in Intrinsic Mode Functions (IMFs) [1]. However, the EMD has the drawback of the so called “mode mixing” phenomenon, which means that the signal components with different amplitudes in one IMF, or the signal components with a similar amplitude in different IMFs. To address this issue, an effective solution was proposed, which suppresses the mode mixing by adding the Gaussian white noise in the original signal, named as “Ensemble Empirical Mode Decomposition (EEMD)” [2-3]. But it brings in some new harmonics in IMFs. To overcome these problems, the Complete Ensemble Empirical Mode Decomposition (CEEMD) was put forward, which adds the opposite Gaussian white noise in the original signal for the EMD respectively [4]. However, the amplitude of the Gaussian white noise is usually estimated by the practical experience rather than calculating by equations. Besides, the inappropriate Gaussian white noise could not mitigate the mode mixing effectively. The essence of mode mixing is the coupling between IMFs, and IMFs are not orthogonal to each other. This paper focuses on the mode mixing, and optimizes the amplitude of the white noise by the genetic algorithm (GA) to minimize the orthogonality among IMFs. Optimization Method: Mutual information is an indictor which symbolizes the correlation between the data. The mutual information between IMFs obtained by the CEEMD will be affected and changed, when the amplitude of the white noise varies. Therefore, the white noise amplitude (All of these values are multiples of the standard deviation of the signal) is used as the input function, and the minimum mean of the mutual information between IMFs is used as the objective function in the GA. As a consequence, it can suppress the mode mixing phenomenon theoretically, when the amplitude of white noise is the minimum mean of the mutual information. Results: The bearing vibration fault signal used in this paper comes from the Case Western Reserve University [5]. In Fig.1, the values in the bar denote the mean of mutual information of IMFs corresponding to different white noise amplitudes, where 0.1103 is the white noise amplitude selected by GA and 0.1 to 0.4 are the values selected by the experience. The mean of mutual information is 0.5728 when the amplitude of the white noise is 0.1103, which is smaller than the amplitudes of 0.1, 0.2, 0.3 and 0.4 that the mean of mutual information is 0.705, 0.6230, 0.6998 and 0.7093, respectively. Fig.2 shows the amplitude of IMFs in figure Fig.2 (a) and the spectrum diagram of IMFs in figure Fig.2 (b) decomposed by the CEEMD with the optimized white noise. It can be seen from the figure Fig.2 (b) that the main components of each IMF are distributed at different frequencies. Meanwhile, it shows in the spectrum of IMF3 that the five times frequency (539.1 Hz) component of the bearing outer race fault. It proves the effectiveness of the proposed method in motor bearing fault diagnosis. Detailed results and discussion will be given in the full paper.

**References:**

[1] N. E. Huang, Z. Shen, S. R. Long, et al., Proc. R. Soc. Lond. A Math. Phys. Sci., vol. 454, p. 903-995, (1998). [2] Z. WU and N. E. Huang, Adv. Adapt. Data Anal., vol. 01, p. 1-41, (2008). [3] P. Flandrin, G. Rilling and P. Gonçalvès, IEEE Signal Process. Lett., vol. 11, p. 112-114, Feb. (2004). [4] F. Liu, J. Gao and H. Liu, IEEE Access, vol. 8, p. 19810-19819, (2020). [5] C. W. R. University,''https://csegroups.case.edu/bearingdatacenter/pages/12k-drive-end-bearing-fault-data," (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c71a8b8dc1e20c7f4b86ef846db3f898.jpg)
Fig. 1 The mean mutual information of different amplitude of the white noise.

![](https://assets.underline.io/uploads/markdown_image/1/image/348217bb9979a412c80e3a633833c3b6.jpg)
Fig. 2 IMFs decomposed by the CEEMD with the optimized white noise. (a) Amplitude of IMFs. (b) Spectrum diagram of IMFs.

poster

INTRODUCTION In recent years, imaging of magnetic nanoparticles (MNPs) has attracted attention as a new diagnostic imaging technique for the imaging of certain targets, such as cancer cells [1]. We previously proposed an MNP imaging method, “magnetic nanoparticle tomography” (MNT), that uses multiple magnetic sensors [2], [3]. In the previous study, an inverse problem analysis was performed to estimate the position of MNPs using the non-negative least squares method (NNLS), which is often used for magnetic particle imaging (MPI). The NNLS method achieves high sensitivity and spatial resolution. However, due to the existence of measurement noise and high sensitivity of NNLS, some MNPs are incorrectly estimated, that is, some artefacts appear. In this study, we apply the minimum variance spatial filter (MV-SF), which is often used in magnetoencephalography (MEG) inverse problem analysis [4], to reduce the artefacts. METHODS The experimental setup is presented in Fig. 1. The Resovist MNP sample was arranged in a sinusoidal magnetic field, which was generated using an excitation coil. The third harmonic magnetic field from MNPs was detected using 16 detection coils. To improve the sensitivity, a cancelation circuit for the fundamental magnetic field was employed. The two-dimensional concentration map of the MNP sample was subsequently obtained by the application of the MV-SF. The distance between the MNP sample and the imaging system (excitation coil and detection coils) was set from 25 mm to 40 mm at intervals of 5 mm. We used two samples with different concentrations of 100 µg-Fe and 500 µg-Fe and estimated the positions for each of them. RESULTS The result of the reconstructed map when the MNP sample was set at are shown in Fig. 2. The white circle in the figure represents the actual sample position. Fig. 2 (a) depicts the result for a sample containing 500 µg-Fe. This result reveals that a sharp signal peak position is observed in the vicinity of the sample position. Fig. 2 (b) exhibits the result for a sample containing 100 µg-Fe. This result indicates that the error between a sharp signal peak position and the actual sample position is within 10 mm. No artefacts appear in both results, contrary to the results using NNLS [3]. From these results, we can conclude that MV-SF is useful for reducing the artefact and estimating the positions of MNPs in magnetic nanoparticle tomography. ACKNOWLEDGMENTS This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Young Scientists [grant number JP19K14996], and by a research grant from the Mazda Foundation.

**References:**

[1] T. Knopp and T. M. Buzug, “Magnetic Particle Imaging—An Introduction to Imaging Principles and Scanner Instrumentation,” Springer, 2012. [2] T. Sasayama, T. Yoshida, K. Enpuku, “Two-Dimensional Magnetic Nanoparticle Imaging Using Multiple Magnetic Sensors Based on Amplitude Modulation,” Journal of Magnetism and Magnetic Materials, Vol. 505, 2020, Art. no. 166765. [3]T. Sasayama, N. Okamura, and T. Yoshida, “Sensitivity Improvement of Magnetic Nanoparticle Imaging by Compensation with Digital-to-Analog Converter,” IEEE Trans. Magn. In press. DOI: 10.1109/TMAG.2020.3014375. [4] K. Sekihara and S. S. Nagarajan, “Adaptive Spatial Filters for Electromagnetic Brain Imaging,” New York, USA: Springer-Verlag, 2008.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d77d396ce684c3b306bcd9bb12e3471f.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/c12c936808039c93bb5834187a35adca.jpg)

 Inverse Problem Analysis in Magnetic Nanoparticle Tomography with Minimum Variance Spatial Filter

Introduction Magnetocardiography (MCG) is a noninvasive technique that detects the magnetic field generated by the electrical activity of the heart [1]. The estimation of MCG current sources is useful technics for clinical application [2]. Exact low resolution brain electromagnetic tomography (eLORETA) [3] spatial filter is used for visualizing brain activity, as it is a genuine inverse solution with exact, zero error localization in the presence of measurement and structured biological noise. However, it tends to reconstruct a large spatial extension for deep sources due to the decreasing sensitivity of the sensors. In this study, we aim to reduce the influence of the source depth in the reconstructed current sources using multiple spatial filters. Method In order to solve the problem of the large spatial extension for deep sources, in addition to the conventional measurement at the front (chest) of the body, the back is also measured. It is possible to improve the estimation accuracy for a deep signal source. Estimation of MCG current sources was used eLORETA spatial filter. We examined two types of spatial filters for two-side measurement. The first method (128ch method), a spatial filter (128ch) was produced by a read-field matrix using two 64ch sensors as one 128ch sensor. In this method, the regularization parameter λ which determines noise immunity has the same value on the front side and the back side. The second method (2 × 64ch method), two spatial filters (64ch) were separately calculated then one spatial filter (2 × 64ch) was produced from the two spatial filters (64ch). In this method, different λ can be determined on the front side and the back side, and the optimum noise immunity can be given to each. In this study, a spatial filter was created by setting λ as 1% of the maximum eigenvalue in 128ch method, 1% of the maximum eigenvalue on the front side and 5% on the back side in 2 × 64ch method. We estimate MCG current sources within a 175 mm × 175 mm × 995 mm volume. Three thousand two hundred and forty voxels were divided with the size of each voxel being 10 mm × 10 mm × 10 mm. For the forward problem, we calculate the lead-field matrix K using the Biot-Savart Law. For each current source location, K includes two columns that represent X component and Y component, respectively. Results and Discussions We estimated MCG sources at R peak, which indicates the activities of ventricle. Fig.1 (a), (b), and (c) show the estimation results by the conventional 64ch spatial filter, the proposed 128ch spatial filter, and the 2 × 64ch spatial filter, respectively. The upper side is a front view of the heart, and the lower side is a below view of the heart. Each frame represents an analytic space. The estimation result shows voxels with a threshold of 90% or more of the strongest point of the estimated source. Compared to Fig. (a), the estimated sources of Fig. (b) and Fig. (c) are able to suppress the spatial extension of the estimated sources due to the effect of providing the measurement surface on the back side. Moreover, the estimated source of Fig. (b) is not estimated correctly because it appears not only in the ventricle but also in the vicinity of the atrium. It is considered that the estimation is incorrect due to the influence of noise because λ is constant. On the other hand, in Fig. (c), the estimated source appears at the ventricular position, and it is thought that the active position of the heart can be estimated more accurately. Conclusion We proposed two types of spatial filter produced method of eLORETA by two-side measuments of the front and back of the body. By using the back side in addition to the front side, the spatial extension of the estimated source could be suppressed. Among them, the signal source could be estimated at the correct position by produced using a 2 × 64ch spatial filter that can determine the regularization parameter λ on the front side and the back side respectively.

**References:**

 [1] D. Cohen, E.A. Edelsack, J.E. Zimmerman,” Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer”, Applied Physics Letter, Vol. 16, pp. 278-280, 1970. [2] J. S. W. Kwong, B. Leithäuser, J.-W. Park, C.-M. Yu, “Diagnostic value of magnetocardiography in coronary artery disease and cardiac arrhythmias: A review of clinical data,” Int. J. Cardiol., vol. 167, pp. 1835-1842, Sep. 2013. [3] R.D. Pascual-Marqui, “Discrete, 3D distributed, linear imaging methods of electric neuronal activity. Part 1: exact, zero error localization”, Mathmatical Physics, arXiv: 0710. 3341, 2007.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1c828343ab32aef6e8439143ad174be6.jpg)
Fig. 1. The estimation results by (a) the conventional 64ch spatial filter, (b) the proposed 128ch spatial filter, (c) the 2 × 64ch spatial filter. The upper side is a front view of the heart, the lower side is a below view of the heart. Each frame represents an analytic space. The voxel is the estimated source with a threshold of 90% or more of the strongest source.

 Estimation of Magnetocardiography Current Sources using Multiple Spatial Filters

In rotational ac machines, interlocking is a commonly used manufacturing method to fix the silicon steel laminations. To analyze the range of degradated magnetic properties caused by the interlocking process more accurately, the distribution of magnetic properties around the interlock was investigated and the areas damaged to varying degrees was quantified. This work is meaningful for the accurate modeling and simulation of machines. I. Introduction Electrical steel sheets are usually assembled into core laminations through interlocking, welding or gluing. In comparison, interlocking is suitable for batch production and become the main method of fixing among electrical steel sheets currently. However, the deterioration of the magnetic properties caused by interlocking cannot be ignored. The formation of interlocks is always accompanied by plastic deformation and generation of residual stress, which will change the movement of magnetic domain under magnetization, and the hysteresis characteristics will be significantly influenced. Furthermore, the interlocking process destroys the insulation, resulting in inter-lamination short circuits. At high frequencies, the interlaminar eddy current loss even contributes more to the deterioration of magnetic properties. There have been several magnetic measurements of interlocks on lamination ring cores with primary winding and secondary winding before, and they have investigate the effect of the interlocks number, sizes, and shapes on the overall magnetic properties of lamination ring cores[1-3]. However, the overall magnetic properties of ring cores cannot be served for accurate simulation of the interlocking process. Some preliminary attempts for interlocking localized magnetic measurements are also in progress, but they mainly focus on interlocks with a single size and a single magnetization direction[4]. Therefore, a more comprehensive localized magnetic properties measurement is necessary. II. Experimental and Results A localized magnetic measurement sensor with two B-needle probes and a H-coil have been manufactured. The distance between the B-needle probes is 3.5 mm and the size of the H-coil is 3 mm×3 mm. As is shown in Fig. 1(a), the sensor was connected to a three-axis precision positioning table, and the displacement accuracy of the sensor is 0.1 mm. Then four hollow square shaped samples with interlocks were wound by the exciting coils. The detailed information of samples and interlocks was shown in Fig 1(b). More than three hundred measurement points are taken on the concave and convex surfaces around each interlock to achieve higher resolution measurements of the local vector magnetic properties. Due to the length limitation of the abstract, Fig. 2 shows part of measured results at 50 Hz with 0.5 T sinusoidal excitation. The white rectangle represents the the upper part of the interlocking position. For the single sheet, it can be seen that the loss increases and the magnetic permeability decreases near the interlock. This is attributed to the generation of residual stress during the formation of the interlocks. For the ten-layer laminate, in addition to the residual stress, the insulation between laminations is destroyed near the interlocks and interlaminar short circuits is formed, which will produce extra eddy current loss. The ratio of loss increment and the ratio of permeability decrement of the three interlocks at 50Hz and 0.5T magnetic density will be provided in the whole paper. The damaged areas of varying degrees was quantified. Besides, the size of the interlocks can also cause different influence on the magnetic properties near the interlocks. The measurement were performed with Sample 2 and Sample 4, and the results show that the magnetic properties deterioration area around larger interlocks is bigger. The deterioration area hardly change with different magnetic flux. III. Conclusions In this paper, we concluded the influence of interlocks on the magnetic properties as follows: 1) The size of the interlock and the degree of localized magnetic degradation are positively but not linearly correlated. The requirements for fastened strength should be taken into consideration when selecting a appropriate size. 2) The local magnetic degradation caused by interlocking in the rolling direction is much lower than that in the transverse direction. 3) On the basis of planar distribution of magnetic degradation, different levels of magnetic degradation caused by interlocking can be quatified. Applying these results to the electrical machines can contribute to the improvement in simulations of them.

**References:**

[1] J. Shen, G. Zhou, S. Jin and H. Hao, 2015 International Conference on Sustainable Mobility Applications, Renewables and Technology (SMART) IEEE., p.1-4(2015). [2] K. Senda, H. Toda, and M. Kawano, Ieej Journal of Industry Applications., Vol. 4, p.496-502(2015). [3] S. Imamori, S. Steentjes and K. Hameyer. IEEE Transactions on Magnetics., Vol. 53,(2017). [4] S. Imamori, S. Aihara and H. Shimoji, et al. Journal of Magnetism and Magnetic Materials., Vol. 500, (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8931710e06488033fcd3d967d8528c76.jpg)
Fig 1. (a)The measuring device.(b) The detailed information of samples and interlocks.

![](https://assets.underline.io/uploads/markdown_image/1/image/18b10ed4fde7b21f1354a164e8b2d0a2.jpg)
Fig2. Part of the experimentally measured planar distribution of magnetic properties at 50Hz and 0.5T magnetic density. (a) Upper part of the permeability around the interlock on the convex surfaces of Sample 1. (b) Upper part of the loss around the interlock on the concave suface on the Sample 2.

 Localized Magnetic Properties Measurement of Interlocking Core Laminations

In plane magnetization stripes of soft magnetic alloys have been proposed as magnetic information storage devices. In these kind of systems, regions of uniform magnetization with opposite senses are separated by domain walls (DW), known as head-to-head or tail-to-tail walls, that may have different structures depending on the width and thickness of the stripes. Usually, two types of DW are expected, known as transverse or vortex, depending on stripe width and thickness. The work by Nguyen et al [1] has shown that in stripes thicker than 60 nm, a third type of head-to-head DW may exist, the so called Landau wall, with a significant out-of-plane magnetization core that is not homogenous across the film thickness. These walls have three internal degrees of freedom: chirality, determined by the sense of rotation of the in-plane circulation of the magnetization; polarity, defined by the upwards or downwards normal magnetization; and the sense of the Neel caps.This can result in richer topological configurations than the standard vortex and transverse walls. In particular, the Neel caps modify the shape and position of top and bottom vortices, leading to non-trivial magnetic textures and singularities with possible interest in magnetic transport applications. In this work, we have grown 80 nm -150 nm thick permalloy racetracks by sputtering on Si substrates and on 50 nm thick Si-N membranes in order to study their 3D internal structure by a combination of Magnetic Force Microscopy (MFM), X ray magnetic transmission microscopy (MTXM) and magnetic X-ray tomography [2] at the Mistral Beamline of Alba Synchrotron. Briefly, curved permalloy stripes have been defined by e-beam lithography and lift-off with width in the 200 nm - 5000 nm range and several microns length with different degrees of curvature. These structures have been characterized at remanence after saturating them with an in-plane magnetic field transverse to the average stripe orientation in order to nucleate domain walls and inhomogeneous domain structures. Figure 1(a) shows the MFM image of a 140 nm thick permalloy stripe showing a central domain wall bounded by two half vortex structures, together with a rhomboid transverse domain (diamond state) close to the stripe end. Magnetic transmission X-ray microscopy images (Fig. 1(b)) reveal polarity reversals within the core of the central domain wall and the development of a transverse structure near the right end of the permalloy stripe. Micromagnetic simulations, as shown in Fig. 2 confirm that these walls have indeed a complex 3D magnetic structure across the thickness and can display polarity reversals along their length related with the presence of magnetic singularities such as Bloch points and magnetic antivortices. These 3D magnetic configurations will be resolved in more detail with the aid of angular tilt series of MTXM images around different rotation axes which are the basis for a recently developed magnetic X-ray tomography method. Work supported by Spanish MINECO under grant PID2019-104604RB/AEI/10.13039/501100011033.

**References:**

[1] V. D. Nguyen et al. ,“Third type of domain Wall in soft magnetic nanostrips”; Scientific Reports 5 (2015) 12417 [2] A. Hierro-Rodriguez et al. "Revealing 3D magnetization of thin films with soft X-ray tomography: magnetic singularities and topological charges" Nature Communications 11, 6382 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6fe230b1acfa0d166b7eb628e5631a34.jpg)
Fig. 1.(a) MFM image of 140 nm thick permalloy stripe at transverse remanence. (b) MTXM image at normal incidence of permalloy stripe. Note the polarity reversals at domain wall core. Black dots in this image correspond to 100 nm Au nanoparticles used for alignment.

![](https://assets.underline.io/uploads/markdown_image/1/image/25f7f12d5d4c6cd0ce5f1b860b40bea6.jpg)
Fig. 2. Micromagnetic simulations of the magnetic configuraion of thick permalloy stripes at different sample depths (top/central/bottom slices). Note the subtle changes in magnetization orientation at domain wall cores related with the 3D domain wall configuration.

 3D magnetic structure of domain walls in soft magnetic racetracks by MFM and X-ray microscopy

I. Introduction Wireless power transfer (WPT) system can effectively make up for the shortcomings of traditional electric energy transmission and has a wide range of application prospects in the fields of electric vehicles, biomedicine, and portable equipment [1-3]. There are several ways to realize WPT, among which the WPT based on magnetic coupling resonance has many advantages, such as long transmission distance, high efficiency, simple implementation, and so on, which can meet the requirements of most scenarios. The WPT system needs a stable and efficient high-frequency power supply. The Class E Amplifier, with only one switch component, can realize soft-switching by matching the appropriate bypass capacitor and then get a high efficiency (close to 100%) in MHz [4]. Hence, the Class E Amplifier is extremely suitable for a high-frequency WPT system. At present, the scholars’ research generally focuses on the short-range and high-efficiency WPT systems within 20cm, whose transmission distance is insufficient [5-6]. Silicon MOSFET can not meet the needs of the high-frequency power supplies, GaN components can work at a higher frequency and higher efficiency [7]. Herein, a mid-range high-efficiency wireless power transfer system based on class E power amplifier and Gan components is proposed. This paper optimizes the coupling coil and load in theory and simulation and gives the system parameter design method of ZVS (Zero Voltage Switching) operation of the class E power amplifier. Finally, the Wide Band-gap Semiconductor GaN component is used to build the physical model to verify the accuracy of the design. More detailed results and discussion will be presented in the extended paper. II. Double coil wireless power transmission system based on the class E power amplifier The wireless power transmission system mainly includes three subsystems, class E power amplifier, coupling coil, and load. And the topology is shown in Figure 1. According to the circuit model, the factors that affect the transmission efficiency and power of the system are analyzed, and it is concluded that the mutual inductance of the coils, the load, and the AC resistance of the coils have a great influence on the transmission characteristics. III. Design and optimization of the flat spiral coils for the WPT system The parameters of the coupling coils are closely related to the performance of the WPT system. The design and optimization are carried out through theory and simulation, and the comparison is carried out through experimental measurement. a. Calculation of coil self-inductance and mutual-inductance According to Neumann’s formula [8], the mutual inductance calculation method of the flat spiral coil is derived. The self-inductance and mutual-inductance of the coil are calculated by theory and COMSOL electromagnetic field simulation tool. b. Calculation of the coil AC resistance and determination on the spacing between coil turns To reduce the coil AC resistance as much as possible, the relationship between coil AC resistance and turn spacing is analyzed by COMSOL Multiphysics. And then determines the spacing between coil turns is 2mm. The theoretical calculation, finite element simulation, and experimental measurement results are compared and analyzed, and the results are quite consistent. IV. System circuit simulation calculation and experimental verification Powered by a 24V DC power supply, the optimal load resistance is 10Ω and set the transmission distance to 40cm, then we determine the parameters of the system components. a. Circuit simulation using PSIM Build the system simulation model in PSIM, the circuit realizes soft switching, and the simulation results are shown in Figure 2. The output power of the load is 26.85W and the transmission efficiency is 87.89%. b. System experiment verification In particular, in view of the low on-resistance and small parasitic capacitance of GAN devices, which enable them to maintain high efficiency during high-frequency operation, GaN devices are introduced as switching devices in the experiment. According to the design parameters, we build the experimental model and carry out the relevant measurement. The experimental results are in good agreement with the simulation results. When the distance between coils is 40cm, the output power of the load is 25.99W and the transmission efficiency is 87.34%. V. Conclusions Aiming at the problem of low efficiency of medium and long-distance wireless power transmission, this paper conducts comprehensive efficiency optimization from coil parameter optimization, load, and class E power amplifier. Using new GaN devices, a wireless power transmission system that takes into account the characteristics of mid-range and high efficiency has been developed.

**References:**

[1] Y. Bu, S. Endo, T. Mizuno, IEEE Transactions on Magnetics, vol. 54, pp. 1(2018) [2] F. Benassi, D. Masotti, A. Costanzo, 2019 IEEE International Conference on RFID Technology and Applications (RFID-TA), pp. 306(2019) [3] N. Hasegawa, S. Yoshida, S. Furuta, et al., 2014 IEEE Wireless Power Transfer Conference, pp. 21(2014) [4] F. Tamjid, A. Ghahremani, M. Richardson, et al., 2017 IEEE Topical Conference on RF/Microwave Power Amplifiers for Radio and Wireless Applications (PAWR), pp. 25(2017) [5] L. Kou, J. Lu, P. Di Maso, 2019 IEEE 7th Workshop on Wide Bandgap Power Devices and Applications (WiPDA), pp. 205(2019) [6] H. Li, J. Li, K. Wang, W. Chen, et al., IEEE Transactions on Power Electronics, vol. 30, pp. 3998(2014) [7] J. Song, M. Liu, C. Ma, IEEE Transactions on Industrial Electronics, vol. 67, pp. 8281(2019) [8] H. A. Wheeler, Proceedings of the Institute of Radio Engineers, vol. 16, pp. 1398(1928) [9] H. L. Chan, K. W. E. Cheng, D. Sutanto, 2000 Eighth International Conference on Power Electronics and Variable Speed Drives, pp. 69(2000)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e87a9716c1b30438f50eeea535a90b25.jpg)
Fig. 1 Topology of the WPT system

![](https://assets.underline.io/uploads/markdown_image/1/image/ad2c8f9ba024d557ada47c36613f662c.jpg)
Fig. 2 System circuit simulation results using PSIM

 Research on Mid-distance High-efficiency Wireless Power Transmission System using Class E Amplifier

As one of the emerging neurostimulation techniques, the Transcranial Magnetic Stimulation (TMS) regulates the synaptic activity of neurons to treat several psychiatric conditions and neurological disorders. During TMS, E-fields are induced within the brain through the application of time-varying magnetic fields, using coils located outside the head [1-4]. Different definitions are proposed in the literature to measure the focality of the E-field in the brain and estimate the stimulated area during TMS. However, most of them differ in measurement methodologies, showing lack of homogeneity and diverse criteria toward a unique conception, without evaluating possible scenarios of under or overstimulation of the biological tissue. Another common fact in the field is the use of definitions of “focality” without reference to a target area and/or focal distance, parameters intrinsically related and required for comparison between coils. Furthermore, to evaluate the degree of stimulation, a criterion indicating how well the stimulated area overlaps the targeted area is required. This work proposes a generalized function and methodology for the focality quantification in TMS coils, considering target area, focal distance, maximum magnitude and stimulation threshold. New definitions such as “specific focality (sf)” and “focality form factor (dn)” are introduced, seeking to describe the suitability of coils for specific stimulation applications. The proposed definitions also offer a general framework to compare coils using homogeneous methodology, parameters and nomenclature, with potential impact in the industry on the standardization of TMS measurement methods. We have performed finite element simulations over an anatomically accurate human head model, including three of the common TMS coils in the literature (single circular coil, figure of eight coil and quadruple butterfly coil [5]). The head model was built based on MRI of an adult healthy subject and defined by layer including the scalp, skull, cerebrospinal fluid, gray matter and white matter. All the layers were assigned typical electromagnetic properties reported in the literature. Magnetic flux densities and electric fields were obtained in the surface of the primary motor cortex (M1) using the head model, over the subregion that controls the first dorsal interosseous (FDI) muscle. Then, the introduced "specific focality" measure was used. This is defined as the normalized dimensionless focality based on new proposed mathematical functions. The functions designed are called Adjusted Even Symmetry Error Function Complement (AES-erfc) and Corrected-Adjusted Even Symmetry Error Function Complement (CAES-erfc). They define the focality as a quantity between zero and one (interchangeable to a percentage notation), as a function of the defined "focality form factor" (dn), a normalized ratio between the stimulated area and the targeted area. The result is a measurement system that identifies different scenarios of focal stimulation (dn=0), overstimulation (dn≥0), understimulation (dn ≤ 0) or no stimulation (dn=-1 in CAES-erf) [see Fig.1]. The calculated results of the specific focality over target areas and volumes were compared with other pre-existing measures in the literature, such as the area of the half-value (AE½) [6] and area of the half-energy (AEE) [67], for the surface specific focality [Fig.2, table 1], and area of the half-value (A½) and tangential fields spread (S½) [6-7], for the volumetric specific focality [Fig.2, table 2]. Our study shows -consistently with other currently used measures- that the QBC is the coil with highest focality for the defined target, followed by the F8C. The proposed specific focality measure assigns a dimensionless value to each coil compared to results in surface units of existing definitions. With this new parameter definition, it becomes easier to evaluate the focality of a TMS coils in the context of a specific target area -or volume- and focal distance, as well as to identify scenarios of stimulation that is focal and with either understimulation or overstimulation with respect to the target size.

**References:**

[1] M. T. Wilson, A. D. Tang, K. Iyer, H. McKee, J. Waas, and J. Rodger, “The challenges of producing effective small coils for transcranial magnetic stimulation of mice,” Biomed. Phys. Eng. Express, vol. 4, no. 3, Apr. 2018, doi: 10.1088/2057-1976/aab525. [2] P. Rastogi, E. G. Lee, R. L. Hadimani, and D. C. Jiles, “Transcranial Magnetic Stimulation-coil design with improved focality,” AIP Adv., vol. 7, no. 5, May 2017, doi: 10.1063/1.4973604. [3] Z.-D. Deng, S. H. Lisanby, and A. V Peterchev, “Electric field depth-focality tradeoff in transcranial magnetic stimulation: simulation comparison of 50 coil designs.,” Brain Stimul., [4] I. P. de Sousa, C. R. H. Barbosa, and E. C. Monteiro, “Safe exposure distances for transcranial magnetic stimulation based on computer simulations,” PeerJ, vol. 2018, no. 6, 2018. [5] P. Rastogi, Y. Tang, B. Zhang, E. G. Lee, R. L. Hadimani, and D. C. Jiles, “Quadruple Butterfly Coil with Passive Magnetic Shielding for Focused Transcranial Magnetic Stimulation,” IEEE Trans. Magn., vol. 53, no. 11, Nov. 2017, doi: 10.1109/TMAG.2017.2711962. [6] Z. De Deng, S. H. Lisanby, and A. V. Peterchev, “Electric field depth-focality tradeoff in transcranial magnetic stimulation: Simulation comparison of 50 coil designs,” Brain Stimul., vol. 6, no. 1, pp. 1–13, Jan. 2013, doi: 10.1016/j.brs.2012.02.005. [7] L. M. Koponen, J. O. Nieminen, and R. J. Ilmoniemi, “Minimum-energy coils for transcranial magnetic stimulation: Application to focal stimulation,” Brain Stimul., vol. 8, no. 1, pp. 124–134, Jan. 2015, doi: 10.1016/j.brs.2014.10.002.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/348e03c65e29cc891fd71995cd8244f3.jpg)
Fig.1. Proposed AES-erfc and CAES-erfc functions for the focality assesment.

![](https://assets.underline.io/uploads/markdown_image/1/image/80626ad77508d360116122aabb3f6dff.jpg)
Fig.2. Tables 1 and 2.

 Estimation of the Focality of Coils and Quality of Stimulation of Biological Tissues During Transcranial Magnetic Stimulation

There were many machine failures caused by the damage of the rolling bearing, for which the main reason was the quality of the steel ball [1]. Many works have been reported on assessing the geometric quality of steel balls, such as shape, size, and surface defects. In contrast, testing the material properties of steel balls is rarely mentioned [2]. As the quality and working life of the bearing depend primarily on the material properties of the steel ball, it is necessary to unambiguously classify the properties of steel balls in making bearings and other applications to ensure the reliability of the mechanical machine system. In this digest, we report on the eddy-current technique for the classification of steel balls based on the amplitude and phase of the eddy-current signal. Three types of 4-mm steel balls, including carbon, chrome, and stainless 304 steel balls, were tested to determine if it had undergone the surface hardening process. Fig. 1 shows the components of the RLC-resonance eddy-current system, which was designed to convert the electromagnetic induction of the steel ball into the phase-sensitive voltage output signals. The pickup coil is mounted statically to detect the eddy-current signal when the steel ball moves back and forth through the pickup coil by the stepping motor translation stage. A microcontroller (Arduino Uno) is used as the main unit to gather and process the data of the stage, such as the position and velocity. The micro-step determined on the driver is set to be 1/32. Fig. 1. The experimental eddy-current system for steel ball sorting. To detect the signal, the reference waveform for the lock-amplifier is synchronized to the excitation signal of the eddy current sensor. The lock-in amplifier receives the output signal from the sensor and generates the analog output voltages in proportion to the in-phase (real) and quadrature-phase (imaginary) components of the signal. The voltages are digitized by the data acquisition (DAQ) device NI USB 6008 from the National Instruments. The translation stage and the DAQ device are both controlled by the computer with the graphic user interface software designed using the Visual Studio C# programming language. The real and imaginary voltage components of the recorded eddy-current signals are subsequently converted into the probability map to show whether the steel balls can be classified by eddy-current sensors. The change in the detected signal should be due to the difference in the electromagnetic properties of the steel balls since the ball diameters are all 4 mm with an error less than 10 μm. Fig. 2. Eddy-current classification of steel balls: (a) determining the resonant frequency, (b) finding out the optimal resistance, and (c) voltage probability map of the steel balls before and after the surface hardening process. The impendence of the pickup coil can be calculated according to Dodd and Deeds method [3]: Zc=[(2πωµn2rm)/(l2-l1)2(r2-r1)2]∫I2[(r2,r1)/α5]{(l2-l1)(1+e-α/α)-1/α}dα (1) where Zc is the impedance of the coil (Ohm), µ is the permeability (Henry/meter), I is the applied current (ampere), α is the separation constant (meter-1), r2 is the outer radius of the coil (meter), r1 is the inner radius of the coil (meter), rm is the average radius of the coil, ω is the angular frequency (rad/second), l2 is the distance from metal testing to top of the coil (meter), l1 is the distance from metal testing to bottom of the coil (meter), n is the number of turns (turns), respectively. Fig. 2(a) shows the voltage amplitude measured at the output terminal when the driving frequency varies from 50 kHz to 200 kHz. The output response is maximized at the resonant frequency of 116 kHz for the RLC circuit. To achieve the higher response, the voltage outputs with various resistors are measured, as shown in Fig.2(b), where the optimal resistance is found to be 20 kΩ. The demodulated eddy-current signals were collected and repeated 100 times for each type of ball, and the result is converted into the voltage probability map in Fig. 2(c). It is found that the steel balls before and after the surface hardening treatment can be classified based on the difference in the eddy-current signal caused by the variation in electrical conductivity and permeability. The result indicates that the proposed method is feasible for application in sorting the material quality of steel balls, which plays a crucial role in mechanical systems. The authors would like to thank Tan Kong Precision Tech Co. Ltd. for providing the steel ball samples. This work is supported by the Ministry of Science and Technology of Taiwan under Grant No. MOST108-2221-E992-083MY2.

**References:**

[1]. H. K. D. H. Bhadeshia, "Steels for bearings", Progress in materials Science, 57(2) 268-435 (2012). [2]. D. Rifai, A. N. Abdalla and K. Ali, "Giant magnetoresistance sensors: A review on structures and non-destructive eddy current testing applications", Sensors, 16(3) 298 (2016). [3]. C. V. Dodd, and W. E. Deeds, "Analytical solutions to eddy-current probe-coil problems", Journal of applied physics, 39(6) 2829-2838 (1968).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/94dabd982116d237599a76ed67b91482.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/26fdf226ab9d948c74b150d794f1b90c.jpg)

 Steel ball sorting based on electromagnetic induction using eddy current technique

Background Magnetocardiograms (MCGs) have become increasingly relevant for clinical research, due to its potential to detect early stages of heart disease. Especially, establishment of technology that can detail specify lesion parts of heart disease is expected. The estimation result by the current spatial filter method contains errors (eLORETA[1], and so on …). It cannot be said to be sufficient estimation accuracy for clinical application. If the current spatial filter method is used for magnetocardiography, the estimated solution of the signal source at the deep position tends to be wider than the estimated solution of the signal source at the shallow position. Factors include the fact that the number of sensors in the signal source estimation is very small compared to the unknown number, and that the magnetic field provided by the signal source is greatly attenuated according to the distance from the sensor. To solve these problems, improvement of the measurement system such as increasing the number of sensors is being considered[2], but the increase in equipment and cost becomes an obstacle. Therefore, in this study, we proposed a method focusing on the relationship between the analysis area of signal source estimation and the sensor plane. Methods Conventionally, the sensor plane is bigger than the analysis area at size in the xy plane, because the analysis area is designed the same size of the heart, on the other hand, the sensor plane is designed the sufficiently larger than the heart size. However, in that case, the information of the sensors located at the ends could not be utilized, and the amount of information that affects the estimation result was different for each sensor, which was a cause of deriving a biased estimated solution. Therefore, in this research, we consider that the amount of information of each sensor can be used equally by setting an analysis area larger than the sensor area, and propose a new environment setting method for signal source estimation. Simulation We carried out a simulation to consider which size of the analysis area is the best. We preformed the source signal estimation by eLORETA using the R-wave peak averaging data that the actual MCGs that the xiphoid process of the subject was adjusted to the 51ch sensor. We compared the following three sizes of the analysis area. Analysis area (a) is (x=120 mm, y=120 mm, z=80 mm), (b) is (x=176 mm, y=176 mm, z=80 mm), (c) is (x=224 mm, y=224 mm, z=80 mm). Other simulation conditions are shown in Fig. 1. Simulation Results Fig. 2 shows the signal source estimation result of each analysis area at R-wave peak. Red frame indicate sensor plane, blue frame indicate each analysis area, green frame indicate analysis area (a). Since the signals of the heart are originally considered to be single block, it is desirable that the estimated solution is a single block. Shown in Fig. 2, It was estimated as a single block except for the analysis area (a), which is the conventional method. In addition, the position and size of the estimated solution shown in Fig. 2 are very similar to the area of the heart obtained from CT images. Furthermore, we evaluated three analysis area using GOF (Goodness of fit) that is evaluation method that indicate the degree of agreement between the magnetocardiogram created by the estimated signal source and the measured magnetocardiogram. As a result, the GOF of each analysis area was about 0.996, which was not a big difference. Summary We examined the relationship of the sensor plane and analysis area using the actual MCG data in order to apply the spatial filter method MCG proposed a new analysis setting. By changing the size of the analysis area, the division of the estimated solution was suppressed and the shape of the heart could be roughly estimated. It found that the estimated result by using analysis area (b) and (c) are very similar to the area of the heart obtained from CT images. From these results, it was shown that it is possible to visualize the movement of the myocardium by estimating the time-series waveform of the magnetocardiogram.

**References:**

References: [1] R.D. Pascual-Marqui. Discrete, “3D distributed, linear imaging methods of electric neuronal activity. Part 1: exact, zero error localization.”, arXiv :0710.3341 [math-ph], 2007. [2] W. Sun and K. Kobayashi. “Simulation of Extended Source Localization using sLORETA Method for Magnetocardiography”. Journal of the Magnetics Society of Japan, vol. 41, pp. 75-80, 2017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/eda772818e2a071aa00c1e92b6437aa7.jpg)
Fig. 1 Simulation conditions.

![](https://assets.underline.io/uploads/markdown_image/1/image/d4dd3d9c735a0795d9376c361864fc26.jpg)
Fig. 2 the result of each analysis area's signal source estimation at R-wave peak.

 Study on Sensor and Analysis area in The Signal Source Estimation by Spatial Filter for Magnetocardiogram

Steel wire ropes used in roped transport devices like lifts, hoists, cableways, winches, are subjected to bending fatigue. Many parameters affect bending fatigue lifetime, such as tensile load, sheave diameter, and rope composition. According to the application area, steel wire ropes are often exposed to atmospheric influences, and the impact of corrosion is inevitable [1]. Non-destructive damage detection is a critical way to assess damage states to guarantee wire ropes reliability and safety. With intelligent sensors, signal processing, and pattern recognition technology developing rapidly, this field has made significant progress. Microelectromechanical systems (MEMS) have allowed magnetic field sensors with potential applications such as automotive industry, navigation systems telecommunications, and non-destructive testing [2]. Optically-pumped magnetometers (OPMs) have been developed since the 1960s. OPMs have generated renewed interest over the last 15 years, in part due to their increased sensitivity, when operated in the spin-exchange relaxation free (SERF) regime. Micro-Fabricated Atomic Magnetometer (MFAM) is a magnetometer system which can be used for land, airborne or even marine survey applications [3]. The Geometrics’ MFAM is a laser pumped cesium magnetometer module that measures the total magnetic field strength. It uses cesium atoms contained in a small, evacuated glass vapour cell as the sensing element. The cesium is solid at room temperature. Hence, the cell is heated to increase the vapour pressure and the number density, of the cesium atoms in the cell. The cell is also filled with nitrogen buffer gas. The photon's angular momentum in the pump beam is transferred to the atom in the excitation process. As the atom decays non-radiatively through a quenching pathway provided by the nitrogen buffer gas, it loses random amount of angular momentum. As the spin polarization precesses, the intensity of the probe light transmitted through the cell is modulated at the Larmor frequency. The probe light is detected with a photodiode and the photocurrent amplified to generate the oscillating probe signal. The resultant Larmor spin precession can be detected with near-resonant light and serves as a measure of the ambient magnetic field. A schematic of the sensor is shown in Fig. 1 [4], [5]. The paper presents one of the first applications of MFAM sensors for diagnostics steel wire ropes. The module features two sensors that can be used independently or as an intrinsic gradiometer. The miniature scalar Optical Atomic Magnetometer [OAM] sensor used here, measures only 2.5cm x 2.5 cm x 3 cm. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through non-resonant absorption of a probe beam. The examined cable is the 7x7+7x19W+IWRC steel wire rope type of 6,5 mm diameter, coated, with a metallic central core strand and crossed to the right. Cable construction is robust and widely used in the industrial field, mainly, in lifting applications. The examination aims to check the influence of the Earth's magnetic field on the diagnosis of steel rope using MFAM Technology. The rope permanently attached to the device shown in Fig 2. Under the rope, at a distance of 80mm, an MFAM Magnetometer (2 sensors: M1 and M2) was attached, which with the use of appropriate software could move at a constant speed of 3 mm/s. I recorded the measurement of the magnetic field around the rope over a measuring length of 380 mm. Then I increased the distance between the rope and the sensors to 120mm and 160mm. Each measurement was carried out three times by moving back and forth. I concluded MFAM technology's future on the non-destructive damage detection methods for steel wire ropes based on the research. The MFAM method is future-proof but requires further investigation. It is crucial to choose the appropriate distance from the tested object (the Earth's magnetic field's influence is a significant factor). In practical applications, the biggest challenge in using MFAM sensors is the stability of the vapour cell's operating temperature and need to separate the Earth's magnetic field. A promising avenue for research is to combine various methods to characterize and detect damages from multiple dimensions. For example, the combination of the electromagnetic and optical methods can grasp the size of the effective cross-sectional area of wire ropes. The types of damages are real-time and intuitively master its surface morphology characteristics to provide more valuable steel wire rope health evaluation parameters. Although there are many issues and challenges, as new technologies and algorithms are introduced, it is believed that MFAM technology will realize evident and accurate non-destructive diagnostics of steel wire ropes.

**References:**

[1] M. Al-Shaibah et al., ‘Characterization of a Resonant Lorentz Force MEMS Magnetometer’, in 2020 Symposium on Design, Test, Integration Packaging of MEMS and MOEMS (DTIP), Jun. 2020, pp. 1–2 [2] Z. Guo, X. Xu, and T. Zhang, ‘Research on the calibrated method for MEMS magnetometer arrays’, Feb. 2020 [3] G. Oelsner et al., ‘Integrated optically pumped magnetometer for measurements within Earth’s magnetic field’, arXiv:2008.01570 [physics], Aug. 2020, Accessed: Dec. 09, 2020. [Online] [4] R. Zhang et al., ‘Active Magnetic-Field Stabilization with Atomic Magnetometer’, Sensors, vol. 20, no. 15, Art. no. 15, Jan. 2020 [5] R. Zhang, K. Smith, and R. Mhaskar, ‘Highly sensitive miniature scalar optical gradiometer’, 2016 IEEE SENSORS, 2016

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/28bc2739048ffacbbceee619a6af7ab6.jpg)
Fig.1. Schematics showing the internal structure of the sensor

![](https://assets.underline.io/uploads/markdown_image/1/image/9edfb799edfe8a44a5dac68fd2babc82.jpg)
Fig.2. Measuring device

 Influence of the Earth’s magnetic field on the diagnosis of steel rope with the use of MFAM Technology

In a standard measurement of diamagnetic susceptibility χDIA (per unit mass), it is necessary to prepare a bulk sample that weigh more than ~0.5 mg. In the present report, we show that χDIA of a small particle is determined from its parabolic movement that is induced by a field gradient generated by a Niobium magnetic circuit, without the necessity of knowing mass m of particle. This principle of measuring χDIA is based on a recent finding that acceleration of a translating particle induced in an area of magnetic field gradient is independent to m; it is uniquely determined by intrinsic χDIA value of material [1][2]. This characteristic derives from a well-known fact that a magnetic body force induced in a particle is proportional to m. The observed results overturn a common recognition that ordinary diamagnetic particles are magnetically inert unless a strong field in applied in the experiment [3]; the result indicate that most solid particles composed of diamagnetic or weak paramagnetic materials may potentially show translation at a low field produced by a permanent magnet, which is usable in practical applications. It was proposed that material identification of a particle is possible[4], by collating the obtained χDIA value with a compiled list of published data [5]; unlike many conventional methods of chemical analysis, the identification is conducted without consuming the small sample. In the present experiment, field-induced parabolic translations were observed in three diamagnetic materials, namely graphite, bismuth and diamond. The particles were released at an initial position as shown in Fig.1 with negligibly small initial velocity, and the particles translated in an area with magnetic field gradient in normal gravity. Fig 2 shows the example of the trajectory observed for a graphite particle and a bismuth particle which proceeded in the xz-plane of Fig.1; they were observed by a high-speed camera (CASIO EX-F1, Japan). The χDIA value of each particles were determined from a relationship between velocity of particle v (x,z) and field intensity B (x, z); the theoretical equation used in the calculation was deduced from an assumption that the variance of potential energy (i.e., magnetic & gravitational) of a particle between two arbitrary positions in the trajectory was completely converted to kinetic energy. The χDIA values obtained in this manner was consistent with the published values [5]. The accuracy of the χDIA values obtained by the present apparatus was significantly improved compared to that obtained in the previous research [3]; the improvement was achieved by optimizing the field distribution of the magnetic circuit, thus decreasing the fluctuation of v(x) values. The accuracy was also increased by precisely identifying the initial position of sample improving the observation using the hi-vision camera. Accordingly, accuracy of χDIA obtained for a submillimetre-particle was improved to a level of ~ 4×10-7emu/g, and variance of χDIA between different materials can be distinguished by the proposed method; in previous studies, the accuracy remained at a level of ~10×10-6emu/g [1][2][4]. The experimental techniques achieved in this study will be a milestone in reducing the measurable size of the sample to micrometre scale. According to recent measurements, the velocities of ferro- (ferri-)magnetic particles [6] and paramagnetic particles [2] during their field-induced translation were also independent to m. Hence, similar motions as reported in the present study is generally expected to occur in all categories of magnetic material by a relatively low magnitude of field-gradient. It is expected from the results shown in Fig.2 that an ensemble of heterogeneous particles can be separated into fractions of different materials [2][4] by releasing the ensemble from the initial position in Fig.1. By improving the compact system, a non-destructive chemical analysis can be conducted shortly after collecting the heterogeneous particles at the site of material explorations in various research fields; such method of pre-treatment will improve the efficiency of reaching a target sample in the research. &lt;div id="UMS_TOOLTIP" style="position: absolute; cursor: pointer; z-index: 2147483647; background-color: transparent; top: -100000px; left: -100000px; background-position: initial initial; background-repeat: initial initial;"&gt; &lt;/div&gt;

**References:**

[1] C. Uyeda, K. Hisayoshi and S. Kano, J. Phys. Soc. Jpn. Vol.79, p.064709 (2010). [2] K. Hisayoshi, C. Uyeda and K. Terada, Sci. Rep. vol.6, p.38431 (2016) [3] G. Maret and K. Dransfield, Adv. Appl. Phys. Vol.46, p.143 (1985) [4] C. Uyeda, K. Hisayoshi and K. Terada, Sci. Rep. Vol.9, p.3971 (2019). [5] R. Gupta, Landolt Bornstein. New Series II, Vol.46 “Diamagnetism”, p.445 (19830 [6] C. Uyeda, K. Kuwada and K. Hisayoshi, J. Jpn. Soc. Powder Metall. Vol.61, p.S78 (2014) &lt;div id="UMS_TOOLTIP" style="position: absolute; cursor: pointer; z-index: 2147483647; background-color: transparent; top: -100000px; left: -100000px; background-position: initial initial; background-repeat: initial initial;"&gt; &lt;/div&gt;

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e2339049a76984bb17bb885247799039.jpg)
Fig.1 A top view (above) and a side view (below) of a NdFeB magnetic circuit developed in the present study to observe parabolic translation of a diamagnetic particle in terrestrial gravity.

![](https://assets.underline.io/uploads/markdown_image/1/image/22d65a0cb18c05ff3ed752e42a3fb932.jpg)
Fig.2 Trajectories of a graphite particle and a bismuth particle that translated from the initial position described inFig.1. The particles translated in the xz plane in the figure. The χ values obtained from the trajectories was 49×10-7emu/g for graphite and was 11×10-7emu/g for bismuth; the values were both consistent with the published values [4].

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