Electrical Capacitance Tomography Research Articles

Research on electrical capacitance tomography (ECT) detection of cerebral hemorrhage based on symmetrical cancellation method

Currently, there is an urgent need for a fast and portable intracerebral hemorrhage (ICH) detection technology for pre-hospital emergency scenarios. Owing to the disproportionately elevated permittivity of blood compared to other brain tissues, Electrical Capacitance Tomography (ECT) offers a viable modality for mapping the spatial distribution of permittivity within the brain, thus facilitating the imaging-based identification of ICH. Currently, ECT is confined to time-differential imaging due to limited sensitivity, and this methodology requires non-hemorrhagic measurements for comparison, data that are frequently inaccessible in clinical contexts. To overcome this limitation, in accordance with the natural bilateral symmetry of the cerebral hemispheres, a symmetrical cancellation scheme is introduced. In this method, electrodes are uniformly arrayed around the cranial periphery and strategically positioned in a symmetrical manner relative to the sagittal suture. Subsequently, the measured capacitances for each electrode pair are subtracted from those of their symmetrical counterparts aligned with the sagittal suture. As a result, this process isolates the capacitance attributable solely to hemorrhagic events within a given hemisphere, permitting the absolute imaging of ICH. To assess the feasibility of this method, simulation and empirical imaging were conducted respectively on a numerical hemorrhage model and three physical models (a water-wrapped hemorrhage model, an isolated porcine fat-wrapped hemorrhage model, and an isolated porcine brain tissue-wrapped hemorrhage model). Traditional absolute imaging, time-differential imaging and symmetrical cancellation imaging were performed on all models. The results substantiate that the proposed imaging modality is capable of obtaining absolute imaging of ICH. But a mirrored artifact, symmetrical to the site of the actual hemorrhage image appeared in each of the imaging results. This mirror artifact was characterized by identical dimensions and an inverted pixel-value schema, an intrinsic consequence of the symmetrical cancellation imaging algorithm. The real image of hemorrhage can be ascertained through pre-judgment with the symptoms of the patient. Additionally, the quality of this imaging is seriously dependent on the precise alignment between the electrodes and the sagittal suture of the brain; even a minor deviation in symmetry could introduce excessive noises. Thus, the complicated operational procedures remain as challenges for practical application.

A permittivity imaging method in the polar coordinates: Electrical capacitance tomography based on the electromagnetic momentum

Electrical capacitance tomography (ECT) is widely used in petroleum, chemical, and other industrial detection. The ECT equations are nonlinear, and their corresponding inverse problems are ill-posed, so the imaging resolution is low. The ECT technique detects scalar data. The permittivity imaging method based on the electromagnetic momentum reciprocity theorem detects vector data, which carries more information than scalar data. To improve the ability of the imaging system to recognise permittivity boundaries, we propose a permittivity imaging method in the polar coordinate system, which is centred on electrical capacitance tomography based on the electromagnetic momentum (ECT-EMM). ECT-EMM principle with the electrodes-moving scheme and the object-moving scheme is proposed. We reconstruct the permittivity gradient from the capacitance gradient. We adopt the object-moving scheme and use the Tikhonov regularisation algorithm to reconstruct the permittivity through the permittivity gradient. The image reconstruction results and image evaluation metrics show that the proposed method clearly recognises the object boundaries compared to ECT. The proposed method performs better when using threshold filtering.

Noninvasive Detection and Quantitative Characterization of Flashback in a Bluff-Body-Stabilized Flame Under Acoustic Excitation by Electrical Capacitance Tomography

Noninvasive Detection and Quantitative Characterization of Flashback in a Bluff-Body-Stabilized Flame Under Acoustic Excitation by Electrical Capacitance Tomography

PECT Composite Defect Detection Algorithm Based on DualGAN

To address the problems of insufficient accuracy and slow reconstruction speed of Planar Electrical Capacitance Tomography (PECT) detection of damaged specimens, a Dual Generative Adversarial Networks (DualGAN)-based PECT image defect detection method is proposed in this paper. The improved particle swarm algorithm with adaptive particle number and L2-norm is used to optimize the sensitivity field, combined with the parallel Landweber algorithm to solve the PECT inverse problem to obtain the dielectric constant distribution map. In the DualGAN network, the Unet generator utilizes an Adam-based local attention mechanism to adjust module weights, facilitating feature extraction and the generation of high-quality transformation images of the Landweber dielectric constant distribution. A PatchGAN discriminator is employed to distinguish between transformation images and real images, using the generated transformation images as target images. Experimental results demonstrate that the sensitivity field, enhanced by the improved particle swarm algorithm and L2-norm normalization, achieves better balance. Furthermore, the addition of a network transformation using the Adam-based local attention weight mechanism on the DualGAN network reduces artifacts in the reconstructed images, resulting in more accurate PECT reconstructions. The PECT image defect detection method, integrating DualGAN, an improved particle swarm optimization algorithm, and a local attention mechanism, has made significant strides in addressing challenges related to image reconstruction accuracy and speed. This technological advancement has enhanced the precision and efficiency of defect detection in carbon fiber composite materials, thereby fostering the broader utilization of planar capacitance tomography technology in industrial damage detection and material defect analysis.

Efficient Jacobian Computations for Complex ECT/EIT Imaging

The reconstruction of the spatial complex conductivity σ+jωε0εr from complex valued impedance measurements forms the inverse problem of complex electrical impedance tomography or complex electrical capacitance tomography. Regularized Gauß-Newton schemes have been proposed for their solution. However, the necessary computation of the Jacobian is known to be computationally expensive, as standard techniques such as adjoint field methods require additional simulations. In this work, we show a more efficient way to computationally access the Jacobian matrix. In particular, the presented techniques do not require additional simulations, making the use of the Jacobian, free of additional computational costs.

DEVELOPMENT OF IMAGE RECONSTRUCTION FOR DETECTING STATIC OIL-GAS REGIMES USING INVASIVE ELECTRICAL CAPACITANCE TOMOGRAPHY IN STEEL PIPE APPLICATION – AN INITIAL STUDY An Initial Study

Electrical Capacitance Tomography (ECT) is a well-known technique for identifying two-phase regimes when a non-conducting medium is the main medium inside a pipe. However, the common non-invasive techniques of ECT are not suitable for monitoring non-conducting systems that use steel pipes. This is because the placement of the common ECT sensor is outside of the pipe and thus cannot penetrate the conducting pipe. Therefore, this paper presents the development of image reconstruction techniques for invasive Electrical Capacitance Tomography (ECT) in steel pipe applications. The study uses eight electrodes for invasive ECT that are independently designed for easy replacement. The shield guard of each electrode is individually designed, unlike the common sensor of ECT. Moreover, it produces a sensitivity map in the forward problem by modeling the geometry to mimic the real hardware of invasive ECT in Comsol Multiphysics livelink with MATLAB. The data from real hardware is exported offline and a linear back projection algorithm is used as the inverse problem. The phantom of gas-oil with different sizes, positions, and multiple phantoms from the range of 20mm, 25 mm and 33mm are tested. The tomograms of the region of interest can be obtained as a result. The paper concludes that the developed image reconstruction techniques for invasive ECT in steel pipe applications can provide acceptable and reliable results. This study can be useful for researchers and practitioners in the field of ECT and steel pipe applications.

A fusion algorithm for mass flow rate measurement based on neural network and electrical capacitance tomography

The process tomography has received a noticeable attention in industry due to non-invasive and non-intrusive characterise. To asses the potential of electrical capacitance tomography for gravity-fallen mass flow rate measurement, a fusion algorithm based on neural network is designed and implemented. The hardware of instrument is composed of a pipe as circular phantom with 200 mm internal diameter and the front-end electronics. The specially programmed software, runs five well-known, non-iterative reconstruction algorithms (LBP, Tikhonov, SVD, ART and SIRT) and fusions the results in a MLP-NN. The sensor experimentally evaluated by wheat grains. Five implemented algorithms, and the fusion NN are compared using RMSE and concentration error parameters. According to evaluated results in whole of tests, the fusion algorithm reduces RMSE and concentration error by approximately 2–3 and 7–10 folds respectively. Since these five algorithms are completely independent, running the program in parallel by Multi-Thread mode, do not adds run-time.

ECT image reconstruction based on sensitive field expansion and optimization

Electrical capacitance tomography (ECT) is an efficient method for addressing the issue of two-phase flow monitoring. Most current methods result in low image reconstruction accuracy due to soft field issues. This paper propose an ECT image reconstruction method based on sensitive field expansion and optimization, which improve reconstruction efficiency and accuracy. Firstly, a sensitivity field optimization method based on flow pattern identification was proposed. The flow pattern recognition determines the flow pattern to which the input signal belongs and selects the sensitive field for the corresponding flow pattern. Secondly, a sensitive field expansion method based on feature extraction is proposed. The ECT image is modeled as a finite rate of innovation signal, sampled using an exponential reproducing kernel. Feature information is extracted from the input signal for data fusion, and the optimized sensitive field is expanded into a new sensitive field distribution matrix by zero-padding and random reorganization. Then, based on optimized and expanded sensitive fields, a sparse image reconstruction method is proposed. Image reconstruction by constructing comprehensive observation equation to obtain the original permittivity distribution vector of the ECT system using the sparsity of the sensitivity matrix and capacitance signal. Finally, the ECT hardware system and the upper computer measurement and imaging integration software are designed. The experimental results show that the method outperforms other existing algorithms in terms of imaging indexes, has better imaging results.

Influence of Frictional Stress Models on Simulation Results of High-Pressure Dense-Phase Pneumatic Conveying in Horizontal Pipe

Based on the two-fluid model, a three-zone drag model was developed, and the kinetic theory of granular flows and the Schneiderbauer solids wall boundary model were modified to establish a new three-dimensional (3D) unsteady mathematical model for high-pressure dense-phase pneumatic conveying in horizontal pipe. With this mathematical model, the influence of the three frictional stress models, namely Dartevelle frictional stress model, Srivastava and Sundaresan frictional stress model, and the modified Berzi frictional stress model, on the simulation result was explored. The simulation results showed that the three frictional stress models accurately predicted the pressure drop and its variations with supplementary gas in the horizontal pipe, with relative errors ranging from −4.91% to +7.60%. Moreover, the predicted solids volume fraction distribution in the cross-section of the horizontal pipe using these frictional stress models exhibited good agreement with the electrical capacitance tomography (ECT) images. Notably, the influence of the three frictional stress models on the simulation results was predominantly observed in the transition region and deposited region. In the deposited region, stronger frictional stress resulting in lower solids volume fraction and a higher pressure drop in the horizontal pipe were observed. Among the three frictional stress models, the simulation results with the modified Berzi frictional stress model aligned better with the experimental data. Therefore, the modified Berzi frictional stress model is deemed more suitable for simulating high-pressure dense-phase pneumatic conveying in horizontal pipe.

Investigation of spatial resolution of electrical capacitance tomography based on the electromagnetic momentum (ECT-EMM)

Electrical capacitance tomography (ECT) is a permittivity imaging method widely used in industrial inspection. The equations described by the ECT technique are nonlinear and ill-posed, which results in low image resolution. ECT can be considered an imaging method based on the Green’s reciprocity theorem, an energetic reciprocity theorem. ECT detects scalars, i.e. capacitances. Electromagnetic fields have both ‘energy’ and ‘momentum.’ In recent years, the electromagnetic momentum reciprocity theorem has enriched the electromagnetic reciprocity theorem. The electromagnetic momentum reciprocity theorem is an imaging method that detects vectors, i.e. capacitance gradients. Vectors contain richer information than scalars; thus, electrical capacitance tomography based on electromagnetic momentum (ECT-EMM) methods is expected to improve the resolution of permittivity imaging. This paper briefly describes the principle of the ECT-EMM technique for image reconstruction using sensitivity matrix gradient and capacitance gradient. Tikhonov regularisation algorithm is applied. The two methods, with and without capacitance measurements, are used to evaluate imaging resolution. Under different numbers of pixels and electrodes, typical permittivity distributions are used for reconstruction, and correlation coefficients are calculated. Simulations and experiments show that the ECT-EMM technique recognises object boundaries more clearly with high noise immunity. Five quality measures are used to evaluate the performance of the point spread function without capacitance measurements. Compared to ECT, the ECT-EMM technique is more sensitive to the central region away from the electrodes, recognises smaller minimum objects, and has smaller shape deformation.

Data and measurement mechanism integrated imaging method for electrical capacitance tomography

This study presents a new imaging paradigm for overcoming the challenges limiting the improvement of the imaging quality in the electrical capacitance technique. The new imaging model enables the integration of measurement physics, sparsity-induced prior and physics-informed multi-fidelity learning prior (PIMFLP), as well as the synergy between data-driven and measurement physics modeling paradigms. The transformed L1 norm is used to model the PIMFLP, and the maximum correntropy criterion is used as a data misfit term to restrict the adverse impact of noises or outliers. The PIMFLP is learned from data and characterizes the structural details of imaging targets. The half-quadratic optimization method is developed to overcome computational challenges in solving the novel imaging model. A new physics-informed multi-fidelity learning method is developed to predict PIMFLP by synergizing deep convolutional neural network with measurement physics, and a new bilevel optimization model solved by a new nested algorithm that merges the genetic algorithm and the split Bregman method is proposed for training. Comparisons with other popular reconstruction algorithms confirm that the new imaging method leads to the improved reconstruction accuracy and noise immunity, and opens up new possibilities for unlocking the potential of the measurement technology.

CGAN-ECT: Reconstruction of Electrical Capacitance Tomography images from capacitance measurements using Conditional Generative Adversarial Networks

Due to the rapid growth of applications of Electrical Capacitance Tomography (ECT) across diverse industrial sectors, there is a pressing demand for swift and high-fidelity methodologies for image reconstruction from raw capacitance measurements. Deep learning, as an effective non-linear mapping tool for complicated functions, has been going viral in many fields including electrical tomography. This paper introduces a pioneering contribution by proposing a Conditional Generative Adversarial Network (CGAN) model explicitly tailored for the purpose of reconstructing ECT images from capacitance measurements. We propose a novel modulator to transform the raw input capacitance measurements into a 2D image. To the best of our knowledge, this is the first time to represent the capacitance measurements in an image form. We have created a new massive ECT dataset of synthetic image-measurements pairs for training and testing purposes of the proposed model. This extensive ECT dataset comprises 320,000 synthetic image-measurement pairs. It forms the basis for evaluating the feasibility and generalizability of the CGAN-ECT model, with assessments conducted on testing data, contaminated data, and flow patterns which are intentionally excluded from the model’s training phase. The evaluation results prove the efficacy of the proposed CGAN model in generating ECT images with heightened accuracy compared to traditional methods and alternative deep learning-based image reconstruction algorithms. The CGAN-ECT model has succeeded in a achieving an average image correlation coefficient exceeding 99.3%, coupled with an average relative image error of approximately 0.07.

Efficient super-resolution image reconstruction of electrical capacitance tomography for gas–solid fluidized bed measurement

Electrical capacitance tomography (ECT) has been widely used to investigate the flow dynamics of the gas–solid fluidized bed. Deep learning-based tomographic imaging of ECT is of great potential to reconstruct the particle concentration distribution with compatible image quality and reconstruction speed. However, it suffers from low model construction efficiency as numerous data samples need to be collected for training the deep neural network. Here a super-resolution (SR) imaging model based on a two-stage imaging network is proposed to improve the model construction efficiency. A low-resolution (LR) imaging network is used to reconstruct the LR image with the measured capacitance matrix while a subsequent high-resolution (HR) network calculates the HR image with the reconstructed LR image. The imaging performance, construction efficiency, and generalization ability of the trained SR imaging model are evaluated by reconstructing the samples in the test set and the unseen typical flow patterns. Considering the training set includes 100,000 data samples, the time consumption of numerically collecting the dataset for training the SR imaging model is 2.70 h, 2.2 % of that for a conventional deep learning-based imaging model of ECT, and the overall model construction time is only 4.44 h when the grid numbers of the LR and HR images are 246 and 8053, respectively. Experimental measurements are further carried out on a fluidized bed and the preliminary results show good prediction and generality of the trained model for reconstructing the particle concentration distribution.

Research on ECT image reconstruction method based on Long Short-Term Memory Network (LSTM)

In order to solve the problem of low image reconstruction accuracy of electrical capacitance tomography (ECT), this paper proposes an ECT image reconstruction method based on Long Short-Term Memory Network (LSTM). Based on the analysis and research of LSTM and ECT image reconstruction problems, the image reconstruction problem is transformed into a time series problem that LSTM can handle. Firstly, this paper proposes an image based encoding method of “rows” and “columns”, which organizes the images into N*M matrices according to “rows” and “columns” respectively. These N rows are considered as output “time series” with time steps. Then, according to the above method, the reconstructed images obtained using the Landweber method and setting images are encoded separately. Thus, the input and output sample libraries of the neural network are obtained. At the same time, the LSTM model was constructed and trained according to the “row” and “column” encoding methods. The above trained models are respectively used for inference, and the inference results are post-processed and fused, and the fusion results are used as the final ECT reconstruction image. Finally, simulation experiments were conducted. The experimental results have shown that the image error and correlation coefficient of the reconstructed image proposed in this paper are superior to Landweber algorithm, Tikhonov algorithm and convolutional neural network (CNN). This also provides a new approach and means for ECT image reconstruction algorithms.

Learnable bilevel optimization method for electrical capacitance tomography

The positive role of electrical capacitance tomography technology depends on high-precision tomographic images. Despite its success, one of the main barriers is the low-quality tomogram. A new learnable bilevel optimization imaging method is proposed to address this problem in this study, in which the image prior and model parameters can be learned from the collected datasets. The upper level optimization problem learns the regularization parameter under the constraint of the lower level optimization problem that implements image reconstruction. A new lower level optimization problem with the introduced machine learning prior is built, which leverages the prior knowledge from collected datasets, imaging targets and imaging mechanisms. The machine learning prior is learned through extreme learning machine, and the training is reformulated into a fractional optimization problem with the physical mechanisms of imaging as a constraint. A new optimizer is proposed to solve the learnable bilevel optimization imaging problem. The effectiveness has been demonstrated by the reconstruction of higher precision images and better noise immunity in comparison with advanced imaging techniques. The new imaging method unifies imaging mechanisms and machine learning, and promotes the complementarity of image priors, which offers new opportunities to unlock the potential of the measurement technique.

Flight-ready Electrical Capacitance Tomography SMARTTS tank for use with cryogenics

The Atout SMARTTS (SMART Tanks for Space) system allows the propellant mass distribution in a storage vessel to be measured accurately under several motion and gravity conditions and at any fill level. Based on Electrical Capacitance Tomography (ECT), SMARTTS systems incorporate electrodes on the inside of the tank, electrical connections to these electrodes, and capacitance measurements. Interpretation of the capacitance measurements is done through the Atout software, providing live images, fill levels and center of mass measurement of the propellant within the tank. The main objective of this work is to demonstrate the successful operation of a flight-ready aluminum tank with integrated SMARTTS electrodes and feedthroughs at cryogenic temperatures. The experiments presented herein consist of three submersion cycles in which the tank is lowered into an open-top dewar filled with liquid nitrogen. During the cycle, the tank is filled with liquid nitrogen when lowered into the dewar, then drained as it is lifted out. Successful operation of the SMARTTS system has been proven via live images of the fluid in the tank, as well as measured fill volume and center of mass of fluid. The materials and sensors have performed satisfactorily with no failures or post-experiment signs of damage.

A Novel Computational Imaging Algorithm for Electrical Capacitance Tomography

High-precision images enable electrical capacitance tomography (ECT) to obtain more reliable measurement results, meaning that the reconstruction algorithm is particularly important. Some excellent numerical algorithms have successfully solved the inverse problem for ECT imaging, but their imaging quality is relatively low. To solve this problem, this paper proposes a new reconstruction algorithm based on regularized extreme learning machines (RELMs). The implementation of the algorithm is mainly divided into two steps: (1) according to a large number of training samples, the RELM model can be obtained by the iterative split Bregman (ISB) algorithm, which can describe the mapping relationship between the capacitance correlation coefficient and the imaging target well, and (2) the capacitance correlation coefficient is calculated, which is then used as input to the RELM model to predict the final imaging. Both simulation and experimental results show that the RELM algorithm achieves greater improvement in imaging quality and robustness, and provides new development ideas for the ECT.

Fractional Optimization With the Learnable Prior for Electrical Capacitance Tomography

Fractional Optimization With the Learnable Prior for Electrical Capacitance Tomography

Study on detection of intracerebral hemorrhage based on frequency difference of permittivity

Introduction: Current detection of intracerebral hemorrhage (ICH), whether employing Electrical Capacitance Tomography (ECT) or other electrical imaging techniques, rely on time-difference measurements. The time-difference methods necessitate baseline measurements from the patient in a non-hemorrhagic state, which is impractical to obtain, rendering rapid detection of ICH unfeasible.Methods: This study introduces a novel approach that capitalizes on the distinct dispersion characteristics of the permittivity in brain tissue and the spectral variance of the permittivity between blood and other brain components. Specifically, the frequency-dependent variations in the permittivity are employed to achieve absolute detection of ICH, thereby eliminating the need for non-hemorrhagic baseline data. The methodology entails identification of two frequency points that the frequency-dependent variation in the permittivity at these two frequency points manifest the maximal difference between blood and other brain tissues. Subsequently, this permittivity differential at the two identified frequency points is utilized for hemorrhage detection. Experimental measurements were conducted using an impedance analyzer and a parallel plate capacitor to capture the capacitance in four single-component substances—distilled water, sheep blood, isolated pig fat, and isolated pig brain—as well as three mixed blood compounds—distilled water enveloping sheep blood, pig fat encapsulating sheep blood, and pig brain surrounding sheep blood—across a frequency range of 10 kHz to 20 MHz.Results: The results show that in different frequency bands, it is indeed possible to distinguish single-component substances from mixed substances by the frequency difference of capacitance variation. Comparative analysis reveals that the 1 MHz to 5 MHz frequency range is most effective for detecting blood in distilled water. For blood detection in pig fat, a 10 kHz to 1 MHz frequency range is identified as optimal, while a 10 kHz to 0.5 MHz frequency range is advantageous for blood detection in pig brain tissue.Discussion: The findings confirm that absolute detection of ICH is achievable through frequency-dependent variations in the permittivity. However, this necessitates the identification of the frequency band manifesting the largest difference of frequency-dependent variation between single-component and mixed substances. The study acknowledges limitations primarily due to the use of anticoagulant-altered sheep blood, which exhibits permittivity divergent from those of natural blood. Additionally, the in vitro pig fat and pig brain samples, having been subjected to freeze-thaw cycles, also demonstrate permittivity unrepresentative of in vivo tissue.

The use of an LSTM-based autoencoder for measurement denoising in process tomography

The main problem with any tomography is the transformation of measurements into images. It is the so-called “inverse problem”, which, due to its indeterminacy, can never be solved perfectly. An additional factor contributing to the deterioration of the quality of tomograms is measurement noise. This article shows how to denoise electrical capacitance tomography measurements using the LSTM autoencoder. The presented model is two-staged. First, the autoencoder is trained using very noisy measurements. Then, the decoder autoencoder generates a training set to using activations ofe the latent layer. In the second stage, the LSTM network is trained, which has encoder latent layer activations at the input and pattern images at the output. The results of the experiments show that using an autoencoder to denoise the measurements improves the reconstruction quality.