Optimal design of electromagnetic metamaterial electronic device sensor with specific performance based on multivariate big data fusion

Abstract As the basic unit structure of electromagnetic metamaterial, the structure size of open resonant ring directly determines the constitutive parameters of SRR (dielectric constant ε and permeability μ). In order to improve the energy exchange efficiency of the electromagnetic acoustic transducer, the coil backplane of the electromagnetic ultrasonic shear wave sensor was optimized. First, the influence of the thickness of the coil backplane on the ultrasonic signal is studied by the experimental method, and then, the magnetic field distribution of the coil backplane is simulated by the finite element simulation software. Finally, the SNR and lift distance of the shear wave sensor before and after the coil backplane optimization are compared by experiments. In this article, a multi-hypothesis data fusion method in distributed detection system is proposed, which extends the multi-sensor data fusion rules to more general cases. The results show that the optimum thickness of the coil back plate in the electromagnetic ultrasonic transverse wave sensor is 1.5–2.0 mm. Using iron powder with the same length and width as the working area of the coil as the coil backplane can significantly increase the magnetic field strength in the working area of the sensor. Compared with the coil backplane made of non-magnetic materials, the optimized backplane can increase the signal-to-noise ratio of the sensor by about one time and the lift-off distance by about 1 mm.


Introduction
Electromagnetic metamaterial is a new kind of artificial synthetic material or composite structure, which makes up for the abnormal physical characteristics that do not exist in nature through the orderly design of the structure on the key physical scale [1].
Electromagnetic metamaterials in a broad sense mainly include left-handed materials, photonic crystals, supermagnetic materials and so on [2].It has broken people's understanding of traditional medium materials and was named as one of the 'Top Ten scientific breakthroughs' in 2003 and 2006 by the American magazine Science [3].
The relative permittivity and permeability of the left-handed material are less than 0 in a certain frequency range, so it has negative refraction characteristics.When the electromagnetic wave is refracted at the interface between metamaterial and conventional material, the refracted wave and the incident wave are on the same side of the normal line [4].When the electromagnetic wave is incident on the left-handed material, the electric field intensity, magnetic field intensity and the direction of the wave vector will form the lefthanded coordinate system, and at this time, it has the characteristics of backward wave (that is, the direction of the phase velocity is opposite to the group velocity), inverse Doppler shift, inverse Cherenkov radiation and a series of abnormal characteristics [5].
An important research direction in the field of metamaterials is to study chiral and related electromagnetic phenomena [6].Chirality refers to the geometric property that a structure cannot coincide with its mirror image after translation and rotation.Chiral metamaterials are one kind of chiral materials, which can exhibit two important electromagnetic properties: circular birefringence and circular dichroism.Circular birefringence refers to the ability of a structure to rotate the polarization plane of electromagnetic waves.Circular dichroism refers to the difference in the propagation of right-handed circularly polarized (RCP) and left-handed circularly polarized (LCP) waves in chiral media.Subsequent studies have shown that planar chiral metamaterials can also produce another novel phenomenon: asymmetric transmission (AT).This special phenomenon was first discovered by Fedotov and others in 2006 [7].Due to these special electromagnetic characteristics of electromagnetic metamaterials, many researchers have designed a variety of miniature microwave components and applied them in the field of wireless communication and defense industry [8].The structural loss of metamaterials has become a major problem in its application field [9].It has certain practical value and is beneficial to broaden the application of electromagnetic metamaterial in the field of antenna and microwave devices [10].
Electromagnetic acoustic transducers (EMATs) can directly stimulate ultrasonic waves on the surface of the tested object, which has the characteristics of no coupling agent and noncontact detection [11].Therefore, EMATs does not have high requirements on the roughness of the surface of the tested object and is suitable for detection under harsh conditions such as surface isolation layer, high temperature and high-speed online [12].In addition, electromagnetic ultrasound generates ultrasonic waves in conductive or magnetically conductive metal materials based on electromagnetic coupling [13].By changing the combination of permanent magnet and coil, it can easily generate shear wave, surface wave, Lamb wave, longitudinal wave and other wave types [14].Therefore, electromagnetic ultrasonic testing technology has been applied in many fields, such as automatic thickness measurement of steel pipe, automatic inspection of rail wheel, high temperature pipeline inspection of nuclear power, high temperature forging thickness measurement and flaw detection [15].
Compared with the traditional piezoelectric ultrasonic detection method, the limitations of electromagnetic ultrasonic technique are to switch to low efficiency, resulting in its low SNR of ultrasonic signal, at the same time as the electromagnetic ultrasonic transducer liftoff distance work increases, the attenuation of SNR exponential rule, lift-off distance is too low will greatly limit the application scope of electromagnetic ultrasonic technology [16].In order to increase the signal to noise ratio and lift distance of the electromagnetic acoustic transducer, many scholars have done a lot of research work, but this work mainly focused on the optimization of the sensor magnet combination form and coil design, such as, while the research on the coil backplane in the sensor is relatively few [17].
The preliminary study shows that the size parameters and material selection of the coil backplane have great influence on the sensor performance [18].In this article, a new fabrication process of the coil backplane is proposed, and the influence of the magnetic conductive material on the magnetic field distribution in the working area of the sensor is analysed [19].First, the influence of coil backplane thickness on ultrasonic signal is studied by experimental method, and then, the magnetic field distribution of coil backplane is simulated by finite element simulation software.Finally, the signal-to-noise ratio and lift-off distance of transverse wave sensor before and after coil backplane optimization are compared through experiments.

Structural optimization theory
Structure optimization can be divided into three levels: size optimization, shape optimization and topology optimization [20].
Size optimization is a method to find the optimal structure by changing the geometric dimensions of the optimized structure (such as the thickness of the plate and shell, the cross-sectional area of the rod, the length and width of the rectangular section of the rod and the radius of the circular section of the rod, etc.) [21].The characteristic of this method is that the geometry and topological form of the optimized structure are not changed.It is the most commonly used optimization method in engineering practice because it has few design variables, simple analysis and easy practice.
Different from size optimization, shape optimization allows the geometry of the optimized structure to change [22].It optimizes some parameters that control the geometry change of the structure to obtain the optimal structure shape.The key point of this method is to correctly define the control parameters describing the shape of the structure boundary.The difficulty lies in deriving the sensitivity of the objective function to the shape parameters and adjusting the finite element mesh in the optimization process.Therefore, the realization process is more difficult than the structure size optimization.However, for some problems, the optimization results may be more satisfactory.
Neither shape optimization nor size optimization can change the topological configuration of the structure.Topology optimization is a method to obtain the optimal topological configuration of the structure by optimizing the material layout in the structure and establishing the optimal topology connection form [23]. Compared with size optimization and shape optimization, topology optimization can not only optimize the geometric size and shape of the structure, but also design the number, position and shape of the holes inside the structure.

Overview of electromagnetic metamaterials
As a new type of synthetic materials, electromagnetic metamaterial has strange electromagnetic properties [24].This chapter will mainly introduce the basic principles of electromagnetic metamaterials and other applications in the field of electromagnetism.The details are as follows.
In the last few years, a theory of optical transformations based on the formal invariance of Maxwell's equations has been developed.Based on this theory, we can make electromagnetic metamaterials with various properties.With the development of modern electromagnetic metamaterial technology, materials are endowed with versatility and complexity, such as independent control of positive or negative permittivity and permeability; the anisotropic parameter values or the design of the gradual refractoriness.However, before the optical transformation was proposed, it was not very clear how to design electromagnetic devices for multipurpose media.Optical transformation techniques provide an intuitive, direct design approach in an expanded material parameter space.We imagine an imaginary space with certain geometric properties in which the desired electromagnetic phenomena can be achieved.The transformation method can be used to design the material properties that produce the phenomenon.For example, to design an invisibility cloak for an object, we imagine that the object is in a space with a hole, and then, we transform the coordinates in the space with the hole, which is the area to be invisible.With this method, a set of material parameters can be calculated to realize the cloaking property of the object in real space.
Electromagnetic metamaterials also have a wide range of applications in the terahertz band (0.1 Thz-10 Thz).Terahertz wave is a fairly wide range of electromagnetic radiation between millimetre wave and infrared wave, terahertz wave is also known as T-ray, also known as sub-millimetre wave, it has great application prospects in physics, material science, medical imaging, radio astronomy, broadband and secure communication, especially in the communication between satellites.For a long time, the lack of effective methods for generating and detecting THZ radiation, as well as few materials in nature that can respond to this band, has led to the 'THZ gap' in the electromagnetic spectrum.At the same time, compared with microwave technology and optoelectronics technology, THZ technology has made slow progress, and functional THZ wave devices, such as filters, switches, modulators, phase shifters and beam control devices, are still unable to be applied [25].

Basic principles of EMATs
Generally, EMATs is composed of magnet, coil and measured object, and the backplane of coil is also an essential part of the sensor.The measured object in this article is the aluminium plate, and the generation of ultrasonic wave is based on Lorentz force principle, as shown in Figure 1.Among them, permanent magnets are used to provide static bias magnetic field, when in Zhongtong into high frequency alternating current coil will induce eddy current on the surface of measured object, the eddy current in the vertical static generation under the action of alternating magnetic field of Lorentz force, the particle on the surface of the object under the action of Lorentz force, produce regular high frequency vibration, thus in the ultrasonic shock excitation in object.
In the system composed of the coil of EMATs and the measured object, there is no free charge.If the influence of displacement current is ignored, the dynamic magnetic field equation of pulsed eddy current is: where l represents the permeability of the material, A is the vector magnetic potential, r represents the conductivity of the material and J is the source current density.Without considering the skin effect and proximity effect of the coil, the average current density distribution of the coil was obtained by current approximation.
where I is the total current and S is the cross-sectional area of the coil conductor.The eddy current density Je and the total current density Jt in the coil and the tested sample are: Then, the total current I and the source current density can be expressed as: The electromagnetic intensity E of each region and the vector magnetic potential A meet the following requirements: According to the Lorentz force definition, the force within the skin depth of the surface of the non-ferromagnetic sample is related to the static magnetic field strength Bq provided by the permanent magnet and the magnitude of the induced eddy current on the conductor surface, namely: The aluminium plate is the isotropic material and satisfies the assumption of linear elasticity and continuity.Elastic deformation occurs under the action of Lorentz force nine, and the equation of motion is: Among them, r is stress tension, w is displacement matrix, q is the bulk density of aluminium.
The receiving of ultrasonic signal is the inverse process of excitation.When the ultrasonic wave propagates to the receiving coil of EMATs, the moving charged particles in the aluminium plate generate dynamic current under the action of the applied bias magnetic field and its current density is: where V represents the vibration speed of charged particles, the dynamic current density in the aluminium plate will generate a dynamic magnetic field around it, and the EMATs receiving coil in this dynamic magnetic field will generate the induced electromotive force, which is the received signal of the coil.
In the process of receiving the signal in the coil, the magnetic field in the solution area is provided by the eddy current density in the aluminium plate and the source current density in the coil.Generally speaking, the receiving coil is open circuit and its total current is 0. Then the governing equation of the receiving coil and each area of the tested sample is The electromotive force of a conductor at a certain point in the coil can be obtained by line integration of the electric field strength, The output voltage of the coil can be obtained by averaging the electromotive force of the point conductor contained in the coil, that is For the EMATs coil in the mode of spontaneous and self-collecting operation, the voltage signal when received can be expressed as: where N represents the number of coil turns, Z represents the acoustic impedance of aluminium material under test, A is the geometric correlation constant of the object under test, / represents the distance from the coil to the surface of the aluminium plate under test, and D is the diameter of the working coil.It can be seen that the size of the ultrasonic signal is proportional to the square of the strength of the static magnetic field.In this article, the selection of material for the backplane of the coil is based on increasing the strength of the static magnetic field in the working area of the coil, so magnetic conductive material is selected.

Optimization design of coil backplane in S-wave EMATs
The optimum design of coil backplane includes size determination and material selection.
When the coil backplane is non-conductive magnetic material, its length and width changes have no effect on the sensor performance, so the plastic plate is used as the coil backplane, and the optimal thickness of the coil backplane is determined through experimental research.When the magnetic conductive material is selected as the backplane of the coil, it will affect the static magnetic field in the working area of the sensor.In this article, the iron powder particles with diameter of 5.5-7 are selected to be pressed into the backplane of the coil by insulation treatment and resin.The length and width of the backplane are optimized by magnetic field simulation.
Using conductive material as the coil backplane will reduce the induced eddy current intensity of the coil in the measured object, thus reducing the energy transfer efficiency of the sensor, so the coil backplane needs to use non-conductive material.Coil backplane is an indispensable part of electromagnetic acoustic transducer, and its thickness has great influence on the performance of sensor.In order to ensure the consistency of the magnetic field, the plastic plate (non-magnetic material) is used as the coil back plate in this experiment.It mainly includes Ritec RAM-5000 test system, 50 Q load, duplexer, EMAT and oscilloscope.In this experiment, the sensor works by self-absorption.Ritec RAM-5000 test system provides high frequency alternating current for EMAT through a 50 Q load and duplex.The ultrasonic transverse wave excited by EMATs in the aluminium plate propagates along its thickness direction and is reflected when it reaches the bottom surface of the aluminium plate, and the reflected wave is sensed After receiving, the sensor enters Ritec RAM-5000 system, and the signal voltage processed by the system is displayed on the oscilloscope.In other words, the sensor performance is evaluated by the thickness signal quality of the aluminium plate.The thickness of the plastic backplane in the sensor is the main optimization object in this section.The plastic plate on the aluminium plate is used to adjust the working lifting distance of the sensor.Plastic plates of different thicknesses are placed as required.
The operating frequency selected in this article is 2 MHz, and the sensor is mainly composed of a permanent magnet, a plastic backplane and a coil.The permanent magnet is a N50 iron boron magnet, the size is 30 mmX30 mmX40 mm, in its lower surface affixed with a layer of copper foil is to reduce the coil in the magnet eddy current induction; The coil is a butterfly shaped coil made of a printed circuit board (PCB), consisting of a printed circuit board (PCB) with a working area of 16 mm X16 mm.The size of the plastic backplane is 30 mmX30 mm.The relationship between the thickness of the coil backplane and the signal amplitude received by the sensor at different lifting distances is shown in Figure 2.
When the coil back plate thickness is less than 1.5 mm, the sensor signal amplitude increases significantly with the increase in the coil back plate thickness.When the thickness of the coil backplane is greater than 2 mm, the signal amplitude gradually decreases with the increase of its thickness, so the optimal thickness of the coil backplane is about 1.5-2mm.By comparing the signal amplitude laws under the three lift-off distances, it can be seen that the optimal thickness of the coil backplane does not change with the change of the working lift-off distance of the sensor.
In order to study the influence of the magnetic material and its size on the magnetic field distribution of the sensor, the following three cases were simulated: the plastic plate was used as the coil back plate; the iron powder plate is used as the coil back plate, and the length of the iron powder plate is equal to the length of the magnet, which is 30 mm; the iron powder plate is used as the coil back plate, and the length of the iron powder is equal to the length of the coil working area, which is 16 mm.The lift-off distance of the simulation model is 2 mm.The simulation results of the three simulation models show that the carbonyl iron powder backplane with the same size as the working area of the coil should be selected when packaging the sensor, which can significantly increase the magnetic flux density of the working area of the coil and thus enhance the signal of the sensor.
The objective of the optimization is to improve the AT performance of metamaterial structures, and the asymmetric transmission coefficient is used to describe the strength of AT performance.The asymmetric transmission coefficient of a linearly polarized wave is defined as Here, Txy and Tyx represent the number of cross-polarized transmission systems of linearly polarized waves, and T-þ and Tþ-represent the cross-polarized transmission coefficients of circularly polarized waves.The closer the asymmetric transmission coefficient is to 1/-1, the stronger the AT performance of the supermaterial is.Taking the absolute value of the number of asymmetric transmission systems of linearly polarized waves as the objective function, the topology optimization design can be expressed as maxA x 1 , x 2 , . . ., The design frequency range is represented by W, and the value is 12 GHz x 30GHz.The genetic algorithm is used for topology optimization, and the optimal combination of grid value 0 or 1 is constantly searched.Each generation of genetic algorithm will generate 60 populations, and the upper limit of the iteration of the whole algorithm is 100 times.The individual hybridization probability and mutation probability in each generation are set as 0.8 and 0.08, respectively.For each combination of grid values generated, the commercial electromagnetic analysis software CSTMicrowaveStudio will generate and simulate a corresponding layout.With the progress of topology optimization, the value combination of the grid is constantly changing, the corresponding layout is also changed, and the corresponding objective function A is also increasing.When the whole optimization process is complete, the interface operation can be used to find the optimal layout.

Verifying the optimization result
In order to verify the optimization results, a simulation model of the structure was established by commercial electromagnetic analysis software CSTMicrowaveStudio.The boundary conditions in X-Y plane were set as UnitCell boundary conditions, and the boundary conditions in Z direction were set as Open (Addspace).The frequency domain solver was used to calculate the transmission coefficient matrix Txy, Tyx, Txx and Tyy, respectively, represent the four elements of the transmission matrix, where Txx and Tyy are the co-polarization transmission coefficients and Txy and Tyx are the cross-polarization transmission coefficients.In order to facilitate comparison, the transmission coefficient matrix of the initial structure and the optimized structure is calculated here, and the results are shown in Figure 3.It can be seen that the cross-polarization transmission coefficient of the initial structure reaches the transmission peak at 15.525 ghz in the Ku band and 23.5 ghz in the K band, which are 0.8264 and 0.7097, respectively.
At the corresponding frequency point, the value of the other cross-polarization transmission coefficient is limited below 0.2, and at the same time, the co-polarization transmission coefficient is equal to and is limited below 0.5 at the resonant frequency point.As a comparison, the cross-polarization transmission coefficient of the optimized structure reaches the transmission peak at 20.075 GHz and 21.65 GHz in the K band and 28.575 GHz in the Ka band, which are 0.9146, 0.9276 and 0.9043, respectively.At the corresponding frequency point, the value of the other cross-polarization transmission coefficient is limited to below 0.1, and at the same time, the co-polarization transmission coefficient is equal to and is limited to below 0.3 at the resonant frequency point.By comparison, the cross-polarization transmission coefficient and difference in the optimized structure are more significant, and the AT phenomenon is stronger.
Figure 4 shows the comparison between experimental results and simulation results.The blue dashed line represents the experimental measurement curve, and the red solid line represents the simulation calculation curve.It can be seen that the experimental results are in good agreement with the simulation results.At the resonant frequency point, the amplitude of the cross-polarization transmission coefficient measured by experiment is slightly different from that calculated by simulation, and the possible causes can be attributed to the following two points: First, the processing accuracy of the sample is not enough.Second, the experimental environment has a certain influence on the measurement.
Based on the optimization results of the first two sections, the sensors with two different coil backplanes are compared.The size of the coil working area is 16 mm Â 16 mm, the coil back plate is made of plastic plate and iron powder plate, both of which are 16 mm Â 16 mmÂ 2 mm in size.The size of the selected magnet is 30 mm Â 30 mmÂ 40 mm.Paste copper foil with a thickness of 0.2 mm on the magnet surface to prevent the coil from inducing eddy currents in the magnet.The above two sensors are used to measure the thickness of the aluminium plate with a thickness of 25 mm, and the performance of the two sensors is compared by the quality of the thickness signal.When the working lift distance is 2 mm, the signals measured by the two sensors are shown in Figure 5.It can be seen from the figure that the time interval between primary echo and secondary return wave is about 15.5.Thus, the calculated wave speed is 3 225 m/s, which is consistent with the wave speed of shear wave.The amplitude of primary echo and secondary echo obtained by the sensor is increased by about 50% and 100%, respectively, while the noise level of the two sensors is similar.Therefore, the optimized backplane can significantly improve the signal-to-noise ratio of the electromagnetic ultrasonic shear wave sensor.
As can be seen from the figure, with the increase in the lifting distance, the signal amplitude drops sharply, which is consistent with the conclusion of the literature.However, when the iron powder is used as the backplane of the coil, the signal attenuation rate of the sensor decreases with the increase in the lifting distance.In this experiment, the working lifting distance of the sensor using the backboard of the dial iron powder can reach 4.8 mm, which is about 1 mm more than that when the plastic plate is used as the backboard of the coil.

Influence of geometric parameters on at characteristics
Firstly, the influence of the change of medium layer thickness D is analysed.Let d be 0.6,0.7,0.8,0.9 and 1.0 mm, respectively, the thickness of the surface and bottom metal structure t ¼ 0.036 mm, the mesh side length b ¼ 1mm, and the width of the medium layer a ¼ 8mm in the optimization process.At this time, the asymmetric transmission coefficient of the structure is shown in Figure 6.With the increase in the medium layer thickness d, the resonant frequency redshifts.AT the same time, the peak value AT the resonant frequency does not change consistently with the increase of the dielectric layer thickness, but increases first and then decreases.When D ¼ 0.9 mm, the asymmetric transmission coefficient reaches the maximum value of 0.91, and the AT effect of the structure is the best.
From the above analysis, it can be seen that the geometric parameters of the optimized structure have a great influence on its resonant frequency and AT characteristics.Therefore, better AT characteristics can be obtained by adjusting structural parameters reasonably through adjustable design.
By adjusting h1 and h2 from 0 to 90 , the performance of metamaterial structure AT was observed.Select representative results: When h1 ¼ 15 , it will be adjusted from 0 to 90 .For the asymmetric transmission coefficient of the linear polarized wave metamaterial structure, as shown in Figure 7, with the increase of the Angle, the asymmetric transmission coefficient first gradually increases, then decreases, and then increases again, and the resonant frequency point also moves.When h2 ¼ 15 , the number of asymmetric transport systems of the metamaterial structure reaches 0.63, and when h2 ¼ 75 , the asymmetric transport coefficient Lin tends to 0, indicating that the chiral metamaterial structure changes from asymmetric transport metamaterial to symmetric transport metamaterial for linearly polarized waves.It also shows that the transmission mode of the chiral metamaterial structure to the linearly polarized wave can be effectively controlled by changing the rotation Angle.
Based on the above analysis, when h 1 ¼ 15 , h 2 ¼45 , the asymmetric transmission coefficient of the chiral metamaterial structure for linearly polarized and circularly polarized waves reaches 0.5 at 21 GHz and 0.66 at 24.5 GHz, indicating that the change of rotation angle can not only regulate the AT performance of the structure, but also enable the structure to realize the AT phenomenon of linearly polarized and circularly polarized waves at the same time in the K-band.This kind of electromagnetic metamaterial structure, which can regulate AT phenomenon and has multiple functions, has extensive application value in practical applications.

Conclusion
In order to improve the signal-to-noise ratio and lift off distance of the electromagnetic ultrasonic shear wave sensor, this article proposes to use iron powder as the coil back plate material and optimize its design.The results show that the optimum thickness of the coil back plate in the electromagnetic ultrasonic transverse wave sensor is 1.5-2.0mm.Using iron powder with the same length and width as the working area of the coil as the coil backplane can significantly increase the magnetic field strength in the working area of the sensor.Compared with the coil backplane made of non-magnetic materials, the optimized iron powder backplane can increase the signal-to-noise ratio of the sensor by about one time and the lift off distance by about 1 mm.The optimized coil backplane can significantly increase the signal-to-noise ratio and lift off distance of the shear wave sensor, which is of great significance for promoting the industrial application of electromagnetic ultrasonic technology.In this article, in the sensor design based on microstrip line type metamaterial, the detection target is defined as the thickness and dielectric constant of plane uniform medium, and it is hopeful to apply it to the detection of non-uniform medium according to the distribution of sensitivity in different regions or the tracking of multiple monitoring variables.At the same time, it also has certain application potential in liquid resolution, non-destructive testing, aircraft skin and other fields, which is worthy of in-depth study.

Figure 1 .
Figure 1.Working principle of electromagnetic ultrasonic shear wave sensor based on Lorentz force principle.

Figure 2 .
Figure 2. Relation curve between signal amplitude and thickness of coil backplane.

Figure 3 .
Figure 3. Initial structure transmission coefficient (amplitude) of electromagnetic wave along the Z direction.

Figure 4 .
Figure 4. Cross-polarization transmission coefficient of the initial structure.

Figure 5 .
Figure 5. Echo signals of sensors before and after optimization, respectively.

Figure 6 .
Figure 6.Influence of the dielectric layer thickness D of the optimized structure on the asymmetric transmission coefficient when the linear X-polarized wave is incident along the z direction.