Research Article  Open Access
Shuanfeng Zhao, Yao Miao, Rongxia Chai, Jiaojiao Zhao, Yunrui Bai, Zheng Wei, Simin Ren, "HighPrecision Electrical Impedance Tomography for Electrical Conductivity of Metallic Materials", Advances in Materials Science and Engineering, vol. 2022, Article ID 3611691, 16 pages, 2022. https://doi.org/10.1155/2022/3611691
HighPrecision Electrical Impedance Tomography for Electrical Conductivity of Metallic Materials
Abstract
Metal materials are subject to deformation, internal stress distribution, and cracking during processing, all of which affect the distribution of electrical conductivity of the metal. Suppose we can detect the conductivity distribution of metal materials in real time. In that case, we can complete the inverse imaging of metal material properties, structures, cracks, etc. and realize nondestructive flaw detection. However, metal materials' small resistance, high electrical conductivity, and susceptibility of voltage signals to noise signal interference make an accurate measurement of metal conductivity challenging. Therefore, this paper addresses the problem of detecting the conductivity distribution of metals by investigating a highprecision fourelectrode AC measurement method. This technical approach combines laminar imaging techniques with highprecision weak signal extraction methods. On this basis, a method and equipment for highprecision electrical impedance tomography of metallic materials’ electrical conductivity were established. The way specifies a new number of electrodes and adopts a model of spaced excitation reference measurements. Singlefrequency sinusoidal AC signal is used for excitation, and Shannon wavelet analysis is used for signal extraction and noise reduction. Superresolution reconstruction algorithms are used for resistivity distribution image reconstruction to improve image quality. Based on the results of various comparative experiments, it is clear that this new functional technique method has good imaging stability and operability and can perform tasks such as analyzing the internal conductivity distribution of metals. This research provides an effective way of new ideas for the safe detection of metal structures, the changes in crystal tissue structure, and the study of metal properties. In particular, it expands the scope of research in the development and application of resistance tomography, which has tremendous commercial potential research significance.
1. Introduction
Changes in external factors such as deformation and heat to the metal will cause changes in the lattice composition or metallographic organization, which will result in changes in the electrical conductivity of the metal. Based on the above metal properties, it is known that the resistivity of the strange metal region will have a significant variation. However, unlike conventional nonconductors, metallic materials are good conductors with very low resistivity [1]. This makes the inductive electromotive force generated at energization higher than the measurement signal, making measurement very difficult. Therefore, it is very challenging to extract tiny signals under high noise conditions. Conventional resistive tomography techniques are typically used in subjects with high resistivities, such as lung imaging [2]. For metallic materials with small resistivity, this paper assigns frequency characteristics to the excitation current signal by singlefrequency AC excitation. Then, the Shannon wavelet extracts the feature signal to complete the work of removing the tiny measurement signal in the case of solid noise. Finally, the electrical impedance tomography of the metal conductivity is completed.
For example, Mandal et al. studied radiation detectors and measured object voltage signals [3]. At present, domestic and foreign measuring instruments of this type are expensive and have low accuracy. Its function is limited to the measurement of resistance, and this paper goes deeper to study the resistivity distribution. Milne and Carter proposed detecting metals by thermal waves, which can detect the thickness of metal media and the distribution of internal defects. Infrared thermography requires a high level of the external environment and detection equipment, and the detection results are easily affected by the external environment [4]. Zhao et al. completed the overdetection of coal mine inclined shafts by measuring the soil conductivity [5, 6]. However, the objects studied in these studies were nonmetallic objects or susceptible to environmental influences. Traditional crack detection techniques such as ultrasonic and radiographic detection apply to the overall detection of macroscopic aspects. With the trend towards high precision in industrial technology, metallic materials have become more demanding in detecting defects in microscopic crystal organization and presenting the results in the form of images. This facilitates timely understanding of the location of faults and rapid remedial action.
Electrical resistance tomography (ERT) as an imaging method for structural health inspection has been widely used in various research fields [7]. Many scholars have investigated ERT technology from several aspects. For example, in the area of geological assessment, it can detect and analyze subsurface rock structures [8], primarily historical and cultural monuments [9], and observe the migration of subsurface water in the soil [10, 11]. In biomedical applications, ERT technology is often used to detect the lung region. In industrial engineering, ERT is used to evaluate different pipes and various tanks to observe liquidsolid and gasliquidsolid processes [12], as well as composite structure imaging [13] and bone cement imaging [14], among many other applications. China University of Mining and Technology completed a study on detecting soil resistivity using ERT technology [15]. Karhunen et al. performed electrical resistance tomography imaging tests on cement mortar specimens containing cracks, reinforcement, and holes. They succeeded in accurately locating damage such as reinforcement, cracks, and gaps within the models, verifying the feasibility of the ERT technique in terms of damage detection [16]. The ERT method also allows quantitative evaluation in nonionic solutions [17] and monitoring of crystallization processes [18]. For example, Boulanger studied the crystallization process of low conductivity solutions by the ERT technique [19]. These applications demonstrate that ERT imaging can be accomplished in low conductivity environments with different spatial dimensions and different conductivity distributions in the target region. Meanwhile, resistance tomography imaging systems have been widely used. To ensure the safety of metal structures and reduce the occurrence of engineering accidents, this paper explores and investigates the application of ERT technology to the nondestructive testing of high conductivity metal materials.
Therefore, we propose an ERT metal detection method and device. The new plan aims to improve the traditional ERT method by combining the properties of metallic materials: First, the new way is not to study and analyze a specific influencing factor, but to optimize the hardware and reconstruction algorithm of traditional ERT around the research object, to achieve the purpose of detecting the internal structure of the metal. In signal acquisition and processing, Hornik et al. studied voltage signal acquisition considering only the problem of sensitive field voltage variation [20], ignoring the effect of other factors such as voltage signal distortion on raw data variation during the acquisition process. In this paper, the input impedance is increased by differential acquisition when acquiring voltage signals—measurement acquisition of small voltage signal data based on the subtraction of two calls to reduce commonmode interference. Based on the relationship between current and voltage, the RMS value of the voltage signal is calculated, and all RMS values are formed into a measurement array to provide data support for the inversion work. Regarding noise reduction of measurement data, when a metallic material of a good conductor is in a complex electromagnetic environment, the surface generates an induced electric potential higher than the excitation signal as an interference signal. The noise signal can reach the volt unit level when the RMS value of the measured signal is the nanovolt unit level. Therefore, how to extract the metal object measurement signal under high noise conditions is the first problem to be solved. Kolehmainen et al. studied the discomfort and inverse problems of the reconstruction algorithm. They did a sensitivity analysis of the noise and numerical errors in the experimental voltage signal data [21]. This paper addresses this problem by proposing a specific frequency AC signal as the excitation signal, which effectively solves the problem that the DC excitation signal is difficult to extract directly and prone to polarization effect. At the same time, this paper removes the singlefrequency components of the measured signal using signal analysis to achieve noise separation. The singlefrequency components are extracted using the Shannon wavelet method to complete the single frequency feature analysis. In terms of image reconstruction, conductivity σ was elaborated in an inverse problem study by Ciulli et al. [22]. Martins et al. investigated the inverse problem in the reconstruction algorithm. They analyzed the inverse problem by solving the positive problem and the potential measurements on the surface of the object under study [23]. In this paper, the inverse problem of ERT is modelled and analyzed for research and image reconstruction. Meanwhile, to reduce the influence of measurement resistance, this paper invokes the superresolution resistance tomography method to improve the quality of reconstructed images. Superresolution reconstruction is a process of extracting feature information of the study object from many lowresolution images of traditional reconstruction algorithms and generating highresolution images after several iterations. In summary, the contributions of this paper are fourfold:(1)A novel highprecision chromatographic imaging technique is proposed, and a highprecision electrical impedance tomography device for electrical conductivity of metallic materials is developed.(2)A Shannon wavelet extraction measurement signal technique is proposed; while selecting a single frequency sinusoidal AC signal as the excitation, the noise reduction problem of the measurement signal is solved.(3)The laminar imaging technique is combined with a highprecision weak signal extraction method, and a new mode of electrode number and interval excitation reference measurement is specified. Meanwhile, the electric field distribution model for each excitation mode is established.(4)In the image reconstruction technique, superresolution reconstruction algorithms are used to improve the accuracy of the reconstructed images.
The rest of this paper is organized as follows. Section 2 describes the principle of the ERT system to provide a theoretical basis for the highprecision laminar imaging technique for the resistivity of metallic materials. Based on the comparative analysis of experimental results, Section 3 discusses the relationship between data noise reduction, number of electrodes, excitation measurement mode, superresolution reconstruction method, and measurement data. The analysis of the experimental temperature results is discussed in Section 3.3. Finally, Sections 4 and 5 discuss and give concluding remarks and suggestions for future work.
2. Materials and Methods
2.1. Basic Principles of Metal Conductivity Chromatography Imaging
Conductivity tomography is one of the electrical detection techniques, which has the advantages of visualization, noninvasiveness, low cost, and high accuracy. Conductivity is one of the critical physical parameters of metals. When the sensitive field medium distribution of the study object changes, the conductivity distribution within the field will change simultaneously.
Figure 1 shows the block diagram of the metal conductivity electrical resistance tomography system. As shown in the figure, the ERT system in this paper mainly includes [24] sensitive field electrode array, single frequency AC excitation unit, weak signal amplification unit, data acquisition and processing unit, and image reconstruction unit. Among them, the image reconstruction unit contains Shannon wavelet analysis and superresolution image reconstruction. First, the singlefrequency AC excitation unit generates a singlefrequency excitation current with a characteristic signal, which is fed into the metalsensitive field through the electrode array. The weak signal amplification unit improves weak feature signals, which are passed to the data processing postacquisition and processing unit after the initial filtering and amplification process. Then, the noise reduction of the data and the extraction of feature signals are made by Shannon wavelet analysis to reach the information of the internal conductivity distribution of the metal. Finally, the image reconstruction unit reconstructs the media distribution image based on this to visualize the internal structure of the metal [25].
Figure 2 shows the block diagram of excitation and measurement electrode switching selection. The signal source generates a sine wave signal as the control signal of the voltagecontrolled constantcurrent source module, which will output the sinusoidal AC power required after conversion by the voltagecontrolled constantcurrent source module [26]. The signal source program controls the frequency of the sinusoidal voltage signal. The voltagecontrolled current source circuit converts the output sinusoidal voltage signal into the sinusoidal current signal required by the system [27]. The ADG1406 highspeed analogue toggle switch is a chip for switching electrodes with a fast switching speed of about 10 ns. The switching circuit consists of a total of 4 pieces of ADG1406 [28]. The data acquisition and processing unit is the central part of the ERT system. The weak signal amplification unit adjusts the gain to enable better data processing by the conditioning circuit in the later stage [29]. This unit is responsible for acquiring the weak output voltage signal in the measurement electrode array, completing the processing, and then sending the received data signal to the host computer to complete the image reconstruction [30, 31].
For metals, the resistivity comes mainly from the scattering effect of lattice vibrations on electrons. Suppose that the phonon system consists of socalled average phonons. The momentum of each photon is equal to the average rate of the phonons in the original electronic system. Although there are many electrons in the metal, it is only the electrons near the Fermi surface that are involved in conducting electricity.where Z is a constant representing the sum of the electronic states other than the K state on the Fermi surface, is the scattering angle resulting from electron scattering action, and is the collision probability of electrons with phonons.where is the average relative velocity of electrons and phonons near the Fermi surface. The number of collisions between a certain A molecule and B molecule per unit time is directly proportional to the relative velocities of A and B and the concentration of B molecules.
The presence of impurities and defects in the actual material affects the periodic potential field and causes the scattering of electrons. Small impurity concentrations, the lattice vibrations, and the distribution of impurities and defects are independent. The sum of the total scattering probabilities can be expressed in terms of the chirality time as
denotes the contribution of lattice vibration scattering. denotes the contribution of impurity and defect scattering.where represents the resistivity of the pure metal and indicates the effect of scattering of impurities and defects and is temperaturedependent. When T is stable, is 0 and is the residual resistivity of the metal. Therefore, the presence of impurities and defects can change the value of metal resistivity. When the atomic spacing is changed, the energy band structure is changed, and the internal weaknesses and electronic form are changed, thus affecting the electrical conductivity of the metal.
2.2. Mathematical Model for Metal Conductivity Tomography
2.2.1. Positive Problem
The reconstruction method for reconstructing the conductivity distribution inside a metal is essentially an illposed problem: the positive and the inverse problem. The inverse problem of ERT is solved, which requires a positive problem model [32, 33]. In the forward problem, the electric field, boundary conditions, and assumed conductivity distribution in the geometric region of the object of study are obtained.
Figure 3 shows a twodimensional illustration of the heterogeneous body problem in electrical impedance tomography. Observing the twodimensional region and the boundary region , it is assumed that the positive problem of quasistatic charge distribution allows obtaining a partial differential equation to model the twodimensional region , which can be expressed aswhere u is the electric potential and is the internal conductivity of the twodimensional region . Based on the seemingly stable field theory and combined with Maxwell’s equation, a mathematical model of the electrical orthogonality of the metal structure is established as follows:where H represents the magnetic field strength; J represents the current density; E represents the electric field strength; Y represents the potential shift vector; represents the charge density; and B represents the magnetic induction strength. Maxwell’s system of differential equations is used to model the positive electrical problem of metallic materials. The positive problem model is built and solved using the finite element method to provide a computational model for the subsequent inverse problem algorithm.
2.2.2. Inverse Problem
There is no unique solution to the inverse problem, and small changes in the data can lead to significant changes in the reconstructed image [34]. Figure 4 illustrates the process of solving the ERT inverse problem.
The observational model for the process of solving the positive metal conductivity problem is expressed aswhere denotes the measured voltage vector at the electrode and indicates the conductivity of the metal in the detection zone. The relationship between the change in conductivity and the change in voltage can be expressed as
It is known during the forward simulation that the value of is generally small, so the higherorder terms obtained from the expansion can be neglected, where is called the sensitivity matrix and can be represented by . (8) can be expressed as
Dividing the sensitive field region into m cells, if k independent measured voltage data are obtained, the discretized and normalized (9) can be expressed as
The equation of the inversion process can be expressed aswhere is the conductivity distribution with dimension , is the measured voltage vector with dimension , and is the dimensional sensitivity matrix.
The reconstruction algorithm for the superresolution inverse problem is used to solve the static measurement problem in ERT [35]. The equation of the objective function can be expressed aswhere , is the calculated voltage, is the measured voltage, ρ is the matrix, and α is the regularization parameter.
Figure 5 shows the schematic diagram of the superresolution reconstructed image. Superresolution image reconstruction obtains feature information from lowresolution images of traditional reconstruction algorithms and generates highresolution images after several iterations. The image acquisition process at a discrete moment t is expressed aswhere and denote the vectorized representations of the degraded image and the original image, respectively; D denotes the quadratic sampling modeling matrix; H denotes the fuzzy modeling matrix during acquisition; and denotes the noise model.
The total change in conductivity is defined as [36]where is the conductivity vector and is the area to be imaged. In static image reconstruction, the goal is to obtain the electrical conductivity of the analyzed area.
2.3. Modeling Study of Metal Conductivity Chromatography Imaging
ERT techniques have been used for qualitative imaging, especially for simulation studies of quantitative information [37]. In this paper, a disc model with a diameter of 30 mm is evaluated and studied and segmented in different iterations using an adaptive threshold segmentation method [38]. Figure 6 shows the modeling diagram of the forward and reverse problems.
Figure 7 shows the different finite element meshes generated [39–42]. The finite element model is obtained after the grid dissection of the ERT sensitive field. The limited element model grid image affects data analysis progress, and numerous triangular domain cells and boundary cells form the complete grid [43]. With the gradual denseness of the mesh profile and the gradual increase in the number of meshes, the data obtained from the simulation will be closer to the actual results.
(a)
(b)
(c)
3. Experiment
In this paper, a series of experiments are designed to verify the accuracy of the proposed method, and some factors affecting the reconstruction results are discussed. The experiments are summarized in Table 1.

3.1. Experimental Platform Design
In this paper, an experimental platform is designed to test and verify the metal conductivity tomography imaging system's central performance, which leads to ascertaining the proposed method's feasibility in this paper. The total surface area of the electrode in contact with the medium is 19.63 mm^{2} square. The measured dimensions of the experimental material are shown in Table 2.

The experimental platform is shown in Figure 8. The excitation unit provides a sinusoidal AC voltage value signal rated at 75 Hz to excite the electrodes sequentially. A voltagecurrent evaluation method and current excitation voltage measurements were chosen for the experiments, and the electrodes cycled through this acquisition process sequentially and recorded data frames [44]. The data acquisition and processing unit acquire the voltage signal at a frequency of 1 kHz. The voltage signal data is transmitted to a computer via a serial line connection and used to reconstruct still images.
(a)
(b)
(c)
3.2. Influencing Factors and Discussion
3.2.1. Data Noise Reduction
The voltage signal received by the data acquisition module contains many interference signals that directly affect the collected voltage signal, including those with industrial frequency interference, radio interference, etc., thus causing severe interference to the experimental results [45]. Therefore, this paper arranges two steps to solve the data noise reduction problem. First, the excitation source provides a single frequency sinusoidal AC signal to complete the excitation. The excitation signal imparts a frequency signature. Figure 9 shows the excitation sensitive field potential map, where a is the electric field distribution and b is the local electrode potential line distribution.
(a)
(b)
Then, according to the frequency characteristics of the collected data, wavelet analysis is used to extract the single frequency excitation information and complete the noise reduction of the mixedsignal data.
Figure 10 shows the noise reduction results of the 16electrode disc. The results show that the simulation is closer to the actual situation as the degree of noise reduction deepens. The effect of noise reduction on the data using the Shannon wavelet is apparent and provides a reliable basis for image reconstruction.
3.2.2. Relationship between the Number of Electrodes and Measurement Data
The number of sensitive field boundary electrodes is a critical factor in determining the accuracy of the data collected. The greater the number of electrodes, the greater the amount of voltage value data obtained. The more information provided in the image reconstruction, the more accurate the calculation of the resistivity distribution in the field [45]. Figure 11 shows a twodimensional model diagram, in which a is the 8electrode 2D model diagram and b is the 16electrode 2D model diagram.
(a)
(b)
Figure 12 shows a graph of the measurement data of the electrode perforated disc. Figure 12(a) shows the diagram of measurement data of the 8electrode perforated disc, and Figure 12(b) shows the graph of measurement data of the 16electrode perforated disc. The voltage signal data plots for the two cases of the number of excitation electrodes are compared and analyzed. After the electrodes finished excitation, the measured voltage data showed a “U” curve distribution, which was consistent with the theoretical curve of voltage signal distribution of the sensitive field electrode array arrangement.
(a)
(b)
According to the results, 16 electrodes can obtain more measurement data than eight with the same excitation pattern and medium distribution. The data are smoother and have fewer outliers, which is conducive to improving the reconstruction image quality. Moreover, the 16electrode model has less noise and better spatial recognition of the medium distribution than the 8electrode model. Therefore, the number of 16 electrodes selected in this paper has a good consistency and is more suitable for metal conductivity tomography imaging systems.
3.2.3. Relationship between Incentive Measurement Mode and Measurement Data
The excitation measurement mode is a crucial factor affecting the reliability of the voltage signal data of the metal structure and determines the quality of the reconstructed image. Figure 13 shows the schematic diagram of the excitation and measurement modes. Among them, Figure 13(a) is the schematic diagram of adjacent excitation adjacent measurement; Figure 13(b) is the schematic diagram of interval excitation reference measurement. A mode of excitation current mostly passes through the field’s boundary only, and the distribution of equipotential lines in the sensitive area is not uniform. B mode of excitation current passes through the centre of the field, the uniformity of current distribution is enhanced, and the amplitude of voltage value change is more significant, which is beneficial to measure the voltage signal and improve the quality of inversion imaging.
The adjacent excitation mode is defined as Mode1. Depending on the number of spaced electrodes, the spaced excitation mode is defined as Mode2Mode8 in that order.
Table 3 shows the amount of measurement data for each excitation and measurement mode. The table shows that the reference measurement mode in the metal perforated disc measurement mode has significantly more data volume than the adjacent measurement mode. The amount of independent data is more favourable when Mode 2 to 7 interval excitation mode is used for the excitation mode. Mode1 contiguous excitation mode is the second; Mode8 relative excitation mode has the least amount of data and should be avoided as much as possible.

Figure 14 shows the measurement data plot of the perforated disc for the interval excitation reference measurement mode, and Figure 12(b) shows the measurement data plot for the adjacent excitation adjacent measurement mode. The RMS voltage data collected during the two different excitation measurement methods are compared and analyzed. Because the measurement method in Figure 14 is a reference measurement, the measurement data graph is presented as an inverted “U” shape.
Figure 15 shows the electric field diagram for each excitation mode. The figure shows that the electric field distribution is uniform as the number of electrodes spaced between the excitation electrodes increases.
According to the above results, the combination mode of Mode7 and reference measurement selected for this system can measure higher voltage values than adjacent modes. The absolute value of the measured value is significant, the current distribution is uniform, and the signal data fluctuation is slightly more stable, which is conducive to improving the resolution of the inversion reconstruction image. In summary, the adjacent excitation and reference measurement mode selected in this paper is better than other excitation measurement methods and is more reasonable in practical applications.
3.2.4. Comparative Analysis of ERT SuperResolution Reconstructed Images
To address the low resolution of the reconstructed image, this paper takes the lowresolution image reconstructed by the conventional Gaussian Newton algorithm as the reference basis. It uses a larger magnification of the traditional array of pixels to extract feature information. Then, the highresolution images are reconstructed by multiple iterations to improve the quality of the reconstructed images.
Figure 16 shows the superresolution reconstruction of the perforated disc. The results show that the Gaussian Newton method has a low similarity and is unsuitable for detecting complex, sensitive fields. The ghosting and noise of the superresolution reconstructed image are significantly reduced. The resolution of the reconstructed image is improved considerably with the application of the superresolution reconstruction technique, which can achieve accurate reproduction of the medium shape, size, and spatial orientation of the sensitive field fields. The following experiments will use the superresolution method to complete the reconstructed images of 304 stainless steel temperature experiments.
3.3. Results and Discussion
In this paper, metal disc temperature experiments demonstrate the feasibility of the proposed research method and the designed ERT system in a complex environment.
Figure 17 shows the experimental test diagram. Figure 17(a) shows the experimental platform; Figure 17(b) shows the graph of the measured data of the heated disc. The ERT data acquisition unit is connected to the nonporous disc and heated at a fixed position chosen by the 304 stainless steel disc to simulate and analyze the change of resistivity distribution caused by the temperature. The actual atomic vibrations inside the metal are proportional to the temperature. When the temperature increases, the chance of collision between free electrons and real atomic increases, leading to fluctuations in the resistivity distribution, which indirectly affects the boundary voltage. The results show that the voltage near the heated region shows significant volatility relative to the specific area. The measured data follow the pattern, which verifies the feasibility of the ERT imaging system in terms of actual voltage data.
(a)
(b)
Figure 18 shows the temperature experiment disc reconstruction diagram. As shown in the figure, the red area indicates the heating interface. The other parts of the colour indicate the regular metal plate, which gradually expands around the red zone. On the other hand, when the heated area is close to the excitation electrode pair, the current lines pass through the site, and thus the potential values are more affected. The current line “bypasses” the heated area through the outer ring in the area of the distant electrode pair so that the resistivity of the more distant area is less affected by temperature. The location and size of the heated area shown in the figure are generally consistent with the actual situation, which verifies the feasibility of the ERT imaging system in terms of location and size.
4. Discussion
The conductivity tomography imaging device for metal materials developed in this paper can accurately resolve the conductivity distribution of metals with high image quality accuracy. It is assumed that the accuracy of data acquisition is improved. In this case, microlevel metal conductivity distribution detection will be realized, which is essential for preventing industrial accidents. Therefore, in this paper, future research can be conducted regarding data acquisition and processing units in the ERT system to improve the data acquisition accuracy. This research result can be applied to the crystal structure analysis of metal materials in the future, which has some commercial research value.
5. Conclusions
In this paper, a highprecision method for conductivity tomography imaging of metallic materials is proposed. At the same time, the performance of the designed metal conductivity tomography imaging equipment is thoroughly investigated in this paper, and the relationship between data noise reduction, number of electrodes, excitation measurement mode, superresolution reconstruction method, and measurement data is discussed in detail. The research in this paper reveals the principle of excitation source to give single frequency sinusoidal AC feature signal, which provides the theoretical basis for Shannon wavelet to extract feature signal. The data noise reduction results show that the simulation effect is closer to the actual situation than the noise reduction depth. The experimental results of the number of electrodes show that 16 electrodes can obtain more measurement data. The data are smoother and with fewer outliers, conducive to improving the reconstructed image quality, and more suitable for metal conductivity tomography imaging system. The experimental results of the excitation measurement mode show that the combination mode of Mode7 and reference measurement selected for this system can measure higher voltage values than the adjacent modes. The absolute value of the measured value is significant, the current distribution is uniform, and the signal data fluctuation is slightly more stable, which is conducive to improving the resolution of the inverse reconstructed image. The superresolution image reconstruction method takes the lowresolution image reconstructed by the traditional Gaussian Newton algorithm as the reference basis. It then reconstructs the highresolution image by multiple iterations. The experimental results of superresolution reconstructed images show that the ghosting and noise of superresolution reconstructed images are significantly reduced, which effectively solves the low resolution of reconstructed images of conductivity distribution of metal materials. Finally, the temperature experiment verifies the feasibility of the highprecision laminar imaging method for metallic materials proposed in this paper. The results show that the voltage near the heated region shows significant voltage fluctuations compared to the specific area. The measured data are by the pattern, which verifies the feasibility of the ERT imaging system in terms of the actual voltage data. The location and size of the heated area shown in the figure are generally consistent with the actual situation, which verifies the feasibility of the ERT imaging system in terms of location and size.
In conclusion, based on a series of experiments, it can be concluded that the experimental platform built in this paper can detect and visualize the electrical conductivity distribution of metals. The proposed method of metal conductivity detection can be used as a reference for the study of metal processing. Studying the relationship between crystal structure changes and electrical conductivity has good application prospects for improving the processing process. In conclusion, this study can be applied to structural defect detection and conductivity analysis of large metal parts and lays the foundation for using resistive tomography in the direction of metallic materials.
Data Availability
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to restrictions, e.g., privacy or ethical.
Disclosure
The funding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
Conflicts of Interest
The authors declare no conflicts of interest.
Acknowledgments
This research was funded by Shaanxi Provincial Key Research and Development Program, Grant no. 2020ZDLGY0406, and by Shaanxi Provincial Key Research and Development Program, Grant no. 2019ZDLGY030902. The work was also supported by the Natural Science Foundation of Shaanxi Province, Grant no. 2020JM529, and the Natural Science Foundation of Shaanxi Province Shaanxi Coal Joint Fund Project, Grant no. 2021JLM08.
References
 H. Mao, X. Yi, H. Mao et al., “Fatigue damage detection and location of metal materials by electrical impedance tomography,” Results in Physics, vol. 15, Article ID 102664, 2019. View at: Publisher Site  Google Scholar
 T. d. C. Martins, A. K. Sato, F. S. d. Moura et al., “A review of electrical impedance tomography in lung applications: Theory and algorithms for absolute images,” Annual Reviews in Control, vol. 48, pp. 442–471, 2019. View at: Publisher Site  Google Scholar
 K. C. Mandal, J. W. Kleppinger, and S. K. Chaudhuri, “Advances in highresolution radiation detection using 4HSiC epitaxial layer devices,” Micromachines, vol. 11, no. 3, p. 254, 2020. View at: Publisher Site  Google Scholar
 J. M. Milne and P. Carter, “A transient thermal method of measuring the depths of subsurface flaws in metals,” British Journal of Nondestructive Testing, vol. 30, no. 5, pp. 333–336, 1988. View at: Google Scholar
 S. Zhao, M. Wei, C. Zhang, W. Guo, and Z. Lu, “Coal mine inclined shaft advanced detection method and physical model test based on shield cutterhead moving array electrodes,” Energies, vol. 12, no. 9, p. 1671, 2019. View at: Publisher Site  Google Scholar
 Z. Xing, S. Zhao, W. Guo, X. Guo, and Y. Wang, “Processing laser point cloud in fully mechanized mining face based on DGCNN,” ISPRS International Journal of GeoInformation, vol. 10, no. 7, p. 482, 2021. View at: Publisher Site  Google Scholar
 Q. Wang, J. He, J. Wang et al., “An image reconstruction algorithm for electrical impedance tomography using Symkaczmarz based on structured sparse representation,” Transactions of the Institute of Measurement and Control, vol. 41, no. 10, pp. 2803–2815, 2019. View at: Publisher Site  Google Scholar
 R. Saad, M. N. M. Nawawi, and E. T. Mohamad, “Groundwater detection in alluvium using 2D electrical resistivity tomography (ERT),” Electronic Journal of Geotechnical Engineering, vol. 17, pp. 369–376, 2012. View at: Google Scholar
 T. Rymarczyk, P. Adamkiewicz, K. Duda, J. Szumowski, and J. Sikora, “New electrical tomographic method to determine dampness in historical buildings[J],” Archives of Electrical Engineering, vol. 65, no. 2, pp. 273–283, 2016. View at: Publisher Site  Google Scholar
 A. Kemna, J. Vanderborght, B. Kulessa, and H. Vereecken, “Imaging and characterisation of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models,” Journal of Hydrology, vol. 267, no. 34, pp. 125–146, 2002. View at: Publisher Site  Google Scholar
 J. Koestel, A. Kemna, M. Javaux, A. Binley, and H. Vereecken, “Quantitative imaging of solute transport in an unsaturated and undisturbed soil monolith with 3‐D ERT and TDR,” Water Resources Research, vol. 44, no. 12, 2008. View at: Publisher Site  Google Scholar
 M. Sharifi and B. Young, “Electrical resistance tomography (ERT) applications to chemical engineering,” Chemical Engineering Research and Design, vol. 91, no. 9, pp. 1625–1645, 2013. View at: Publisher Site  Google Scholar
 Z. J. Yang and G. Yan, Detection of Impact Damage for Composite Structure by Electrical Impedance Tomography, Springer, New York, NY, USA, 2020.
 H. Ghaednia, C. E. Owens, R. Roberts, T. N. Tallman, A. J. Hart, and K. M. Varadarajan, “Interfacial load monitoring and failure detection in total joint replacements via piezoresistive bone cement and electrical impedance tomography,” Smart Materials and Structures, vol. 29, no. 8, Article ID 085039, 2020. View at: Publisher Site  Google Scholar
 Y. Zhu and Z. Wang, “Measurement of soil resistivity based on FFT DC component,” Optics and Precision Engineering, vol. 21, no. 1, pp. 115–123, 2013. View at: Publisher Site  Google Scholar
 K. Karhunen, A. Seppänen, A. Lehikoinen, P. J. M. Monteiro, and J. P. Kaipio, “Electrical resistance tomography imaging of concrete,” Cement and Concrete Research, vol. 40, no. 1, pp. 137–145, 2010. View at: Publisher Site  Google Scholar
 G. Rao, M. A. Sattar, R. Wajman, and L. JackowskaStrumillo, “Application of the 2DERT to evaluate phantom circumscribed regions in various sucrose solution concentrations,” in Proceedings of the 2019 International Interdisciplinary PhD Workshop (IIPhDW), pp. 34–38, IEEE, Wismar, Germany, May 2019. View at: Google Scholar
 G. Rao, S. Aghajanian, T. Koiranen, R. Wajman, and L. JackowskaStrumiłło, “Process monitoring of antisolvent based crystallization in low conductivity solutions using electrical impedance spectroscopy and 2D electrical resistance tomography,” Applied Sciences, vol. 10, no. 11, p. 3903, 2020. View at: Publisher Site  Google Scholar
 L. Boulanger, “Observations on variations in electrical conductivity of pure demineralized water: modification (“activation”) of conductivity by lowfrequency, lowlevel alternativing electric fields,” International Journal of Biometeorology, vol. 41, no. 3, pp. 137–140, 1998. View at: Publisher Site  Google Scholar
 K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks, vol. 2, no. 5, pp. 359–366, 1989. View at: Publisher Site  Google Scholar
 V. Kolehmainen, M. Lassas, M. Lassas, P. Ola, and S. Siltanen, “Recovering boundary shape and conductivity in electrical impedance tomography,” Inverse Problems and Imaging, vol. 7, no. 1, pp. 217–242, 2013. View at: Publisher Site  Google Scholar
 S. Ciulli, M. K. Pidcock, and C. Sebu, “An integral equation method for the inverse conductivity problem,” Physics Letters A, vol. 325, no. 34, pp. 253–267, 2004. View at: Publisher Site  Google Scholar
 J. Santana Martins, C. Stein Moura, and R. M. Figueiró Vargas, “Avaliação de 3 diferentes aproximações para a solução do problema direto da tomografia de impedância elétrica,” Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, vol. 31, no. 1, pp. 42–49, 2015. View at: Publisher Site  Google Scholar
 M. Zhang and M. Soleimani, “Imaging floating metals and dielectric objects using electrical capacitance tomography,” Measurement, vol. 74, pp. 143–149, 2015. View at: Publisher Site  Google Scholar
 L. Xiao, H. Wang, and X. Xu, “Improved Newtonraphson algorithm for electrical resistance tomography image reconstruction. Zhongguo dianji gongcheng xuebao (proceedings of the Chinese society of electrical engineering),” Chinese Society for Electrical Engineering, vol. 32, no. 8, pp. 91–97, 2012. View at: Google Scholar
 M. Sharifi and B. Young, “Electrical resistance tomography (ERT) for flow and velocity profile measurement of a single phase liquid in a horizontal pipe,” Chemical Engineering Research and Design, vol. 91, no. 7, pp. 1235–1244, 2013. View at: Publisher Site  Google Scholar
 O. Dorn, E. L. Miller, and C. M. Rappaport, “A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets,” Inverse Problems, vol. 16, no. 5, pp. 1119–1156, 2000. View at: Publisher Site  Google Scholar
 J. Wu, “The applied technology of time resolved ultrasonic flow meter,” SciTech & Development of EnterPrise, vol. 2, pp. 16–20, 2010. View at: Google Scholar
 T. De Castro Martins, E. D. L. Bueno de Camargo, R. Gonzalez Lima, M. B. P. Amato, and M. de Sales Guerra Tsuzuki, “Image reconstruction using interval simulated annealing in electrical impedance tomography,” IEEE Transactions on Biomedical Engineering, vol. 59, no. 7, pp. 1861–1870, 2012. View at: Publisher Site  Google Scholar
 Z. Huang, D. Xie, H. Zhang, and H. Li, “Gas–oil twophase flow measurement using an electrical capacitance tomography system and a Venturi meter,” Flow Measurement and Instrumentation, vol. 16, no. 23, pp. 177–182, 2005. View at: Publisher Site  Google Scholar
 M. Wang and X. Zhong, “Applied research on time difference method in ultrasonic gas flow meter,” Instrument Technique and Sensor, vol. 7, pp. 26–28, 2013. View at: Google Scholar
 K. S. KuoSheng Cheng, D. Isaacson, J. C. Newell, and D. G. Gisser, “Electrode models for electric current computed tomography,” IEEE Transactions on Biomedical Engineering, vol. 36, no. 9, pp. 918–924, 1989. View at: Publisher Site  Google Scholar
 J. Ye, H. Wang, and W. Yang, “A sparsity reconstruction algorithm for electrical capacitance tomography based on modified Landweber iteration,” Measurement Science and Technology, vol. 25, no. 11, Article ID 115402, 2014. View at: Publisher Site  Google Scholar
 C. W. Groetsch and C. W. Groetsch, Inverse Problems in the Mathematical Sciences, Vieweg, Braunschweig, Germany, 1993.
 B. S. Kim, S. Kim, and K. Y. Kim, “Image reconstruction with prior information in electrical resistance tomography,” Journal of IKEEE, vol. 18, no. 1, pp. 8–18, 2014. View at: Publisher Site  Google Scholar
 W. ChuanLei and Y. ShiHong, “New selection methods of regularization parameter for electrical resistance tomography image reconstruction,” in Proceedings of the 2016 IEEE International Instrumentation and Measurement Technology Conference Proceedings, pp. 1–5, IEEE, Taipei, Taiwan, May 2016. View at: Google Scholar
 F. Dickin and M. Wang, “Electrical resistance tomography for process applications,” Measurement Science and Technology, vol. 7, no. 3, pp. 247–260, 1996. View at: Publisher Site  Google Scholar
 B. S. Kim, A. K. Khambampati, S. Kim, and K. Y. Kim, “Image reconstruction with an adaptive threshold technique in electrical resistance tomography,” Measurement Science and Technology, vol. 22, no. 10, Article ID 104009, 2011. View at: Publisher Site  Google Scholar
 M. Vauhkonen, W. R. B. Lionheart, L. M. Heikkinen, P. J. Vauhkonen, and J. P. Kaipio, “A MATLAB package for the EIDORS project to reconstruct twodimensional EIT images,” Physiological Measurement, vol. 22, no. 1, pp. 107–111, 2001. View at: Publisher Site  Google Scholar
 A. Adler and W. R. B. Lionheart, “Uses and abuses of EIDORS: an extensible software base for EIT,” Physiological Measurement, vol. 27, no. 5, pp. S25–S42, 2006. View at: Publisher Site  Google Scholar
 N. Polydorides and W. R. B. Lionheart, “A Matlab toolkit for threedimensional electrical impedance tomography: a contribution to the Electrical Impedance and Diffuse Optical Reconstruction Software project,” Measurement Science and Technology, vol. 13, no. 12, pp. 1871–1883, 2002. View at: Publisher Site  Google Scholar
 P. Yan and Y. Mo, “Imaging the complex conductivity distribution in electrical impedance tomography,” IFAC Proceedings Volumes, vol. 36, no. 15, pp. 73–76, 2003. View at: Publisher Site  Google Scholar
 B. S. Kim, A. K. Khambampati, Y. J. Jang, K. Y. Kim, and S. Kim, “Image reconstruction using voltagecurrent system in electrical impedance tomography,” Nuclear Engineering and Design, vol. 278, pp. 134–140, 2014. View at: Publisher Site  Google Scholar
 M. Soleimani, W. R. B. Lionheart, and O. Dorn, “Level set reconstruction of conductivity and permittivity from boundary electrical measurements using experimental data,” Inverse Problems in Science and Engineering, vol. 14, no. 2, pp. 193–210, 2006. View at: Publisher Site  Google Scholar
 C. Luo, W. He, and X. Dong, “Driven patterns with fixed excitation in electrical impedance tomography,” Chinese Journal of Biomedical Engineering, vol. 28, no. 6, pp. 949–953, 2009. View at: Google Scholar
Copyright
Copyright © 2022 Shuanfeng Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.