Ultrasound tomography (UT) of bubbly two-phase flows using machine learning (ML) was investigated by performing two-dimensional ultrasound numerical simulations using a finite element method simulator. Studies on UT for two-phase flow measurements have been conducted only for some bubbles. However, in an actual bubbly flow, numerous bubbles are complexly distributed in the cross-section of the flow channel. This limitation of previous studies originates from the transmission characteristics of ultrasound waves through a medium. The transmission characteristics of ultrasound waves differ from those of other probe signals, such as radiation, electrical, and optical signals. This study evaluated the feasibility of combining UT with ML for predicting dense bubble distributions with up to 20 bubbles (cross-sectional average void fraction of approximately 0.29). We investigated the effects of the temporal length of the received waveform and the number of sensors to optimize the system on the prediction performance of the bubble distribution. The simultaneous driving of the installed sensors was simulated to reduce the measurement time for the entire cross-section and verify the method's applicability. Thus, it was confirmed that UT using ML has sufficient prediction performance, even for a complex bubble distribution with many bubbles, and that the cross-sectional average void fraction can be predicted with high accuracy. 

A numerical study on machine-learning-based ultrasound tomography of bubbly two-phase flows

Electrical impedance tomography (EIT) is a nondestructive testing technique, which has great potential to be used for the detection of the cross-sectional gas-holdup ratio (CGR) of gas–liquid two-phase flow. Due to the nonlinear and ill-posed characteristics of the EIT image reconstruction, the accuracy of image-based CGR estimation methods is poor. To improve the detection accuracy, a learning-based direct CGR estimation method is proposed in this study, which applies a novel multiscale attention network (MSA-Net) to directly estimate the CGR from the voltage measurements. Multiscale feature extraction and residual structure are introduced into MSA-Net to fully extract the features, and attention unit (AU) is also used to capture high-frequency features. As a result, accurate and robust CGR estimation can be realized by MSA-Net. ResNet18 and single-scale attention network (SSA-Net) are selected for comparison. The simulation results indicate that the relative error (RE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\text {CG}}{)}$ </tex-math></inline-formula> of CGR estimated by the learning-based direct CGR estimation method is far lower than that of the image-based CGR estimation methods. Compared with ResNet18 and SSA-Net, the RECG of the CGR estimated by MSA-Net is lower, and the range is 0.07%–0.36%. Moreover, MSA-Net shows good noise robustness simultaneously. The experiment is also set to test MSA-Net. The range of RECG is 0.1%–1.12%, which further verifies the practicability of the proposed learning-based direct CGR estimation method. 

An MSA-Net Algorithm for Direct Estimation of Gas Holdup Based on Electrical Impedance Tomography System

Electrical impedance tomography (EIT) is a nondestructive testing technique, which has great potential to be used for the detection of the cross-sectional gas-holdup ratio (CGR) of gas–liquid two-phase flow. Due to the nonlinear and ill-posed characteristics of the EIT image reconstruction, the accuracy of image-based CGR estimation methods is poor. To improve the detection accuracy, a learning-based direct CGR estimation method is proposed in this study, which applies a novel multiscale attention network (MSA-Net) to directly estimate the CGR from the voltage measurements. Multiscale feature extraction and residual structure are introduced into MSA-Net to fully extract the features, and attention unit (AU) is also used to capture high-frequency features. As a result, accurate and robust CGR estimation can be realized by MSA-Net. ResNet18 and single-scale attention network (SSA-Net) are selected for comparison. The simulation results indicate that the relative error (RE $_{\text {CG}}{)}$ of CGR estimated by the learning-based direct CGR estimation method is far lower than that of the image-based CGR estimation methods. Compared with ResNet18 and SSA-Net, the RECG of the CGR estimated by MSA-Net is lower, and the range is 0.07%–0.36%. Moreover, MSA-Net shows good noise robustness simultaneously. The experiment is also set to test MSA-Net. The range of RECG is 0.1%–1.12%, which further verifies the practicability of the proposed learning-based direct CGR estimation method.

This Special Feature provides a cross-section of measurement innovation from the International Society for Industrial Process Tomography (ISIPT) 10th World Congress in industrial Process Tomography (WCIPT). Although scheduled for September 2020 this was postponed by one year due to the Covid pandemic and held as a Global, Virtual event in September 2021. The scope of the WCIPT is to share innovative and radical advances in 3 themes: (A) tomographic (and related) measurement in industrial processes; (B) transformational enhancements to existing methods, and (C) application case studies for new areas and processes. The 10th WCIPT also celebrated 20 + years of WCIPT reporting of global developments in Industrial Process Tomography (IPT), and 30 + years since its inception as a viable process measurement technology. Early research focussed on basic concepts. A landmark project c1990 created the first real-time instrument able to operate at a viable resolution and frame rate ( ∼ 100 fps) for an oil/gas pipeline flow, and interpret resulting cross-sectional data to derive flow rates. This integrated electrical capacitance tomography (ECT) sensing (from University of Manchester, UK) with 16 element parallel-processing for data-acquisition, reconstruction and interpretation (from University of Leeds, UK) [1]. Proving trials on a large inclinable flow-loop at a Schlumberger laboratory demonstrated viability within accuracy bounds of the integral plant instrumentation. This 1st generation (fixed excitation mode and energy/frequency) ECT design was commercialised and widely deployed. It was followed by an analogous electrical resistance tomography (ERT) sensing design, deploying early microcomputer processing, suited to slower processes such as stirred tank mixers; also commercialised c1995 as the first of a range of now globally deployed ERT products. IPT addresses a wide range of processes. Unlike medical tomography, internal images

Special issue on the 10th world congress on industrial process tomography

Abstract Multiphase flow systems, crucial in fields like chemical, petroleum, and biology, often involve challenging gas-liquid flows with variable interfaces. Ultrasonic Tomography (UT) helps visualize these flows by using array sensors to create two-dimensional images.&amp;#xD;However, issues arise in assessing the cross-section gas-holding ratio (CGR) with UT, as original images usually need filter processing and multi-dimensional evaluations can be contradictory. This study introduces a comprehensive evaluation method for UT image quality, leveraging the entropy evaluation method. It uses ultrasonic data and algorithms like&amp;#xD;SLBP, Landweber, and Tikhonov for image reconstruction. Evaluation focuses on three aspects: Pearson correlation coefficient, image position error, and reconstruction area error, offering a thorough assessment of image accuracy. The entropy evaluation method balances contradictory indicators and aligns with most indicator distribution laws, proving effective in assessing UT image reconstruction quality.&amp;#xD; 

Comprehensive quality evaluation method of ultrasound tomography algorithms based on entropy method

Ultrasonic transmission tomography is an effective non-intrusive method for detecting gas–liquid two-phase flow patterns. A specific interest is the many processes whose reaction utilizes a bubble column, where the fast estimation of cross-sectional gas-holdup ratio is important for monitoring and control. In this study reference indirect image-based estimates were obtained from reconstructed tomographic data. Direct (non-image) estimation of the gas holdup ratio was also obtained using trained neural processing networks. Two forms were trialled: a generalized regression neural network (GRNN); and a long short-term memory (LSTM) network. Comparison trials were carried out for single-bubble, dual-bubble, circulation and laminar flows. Relative cross-sectional gas holdup error was selected for evaluation. For the image-based indirect trials the Tikhonov regularization algorithm had the lowest error range: 2.15%–15.64%. For direct methods the LSTM network had the lowest error range: 0.41%–9.63%, giving better performance than the image-based methods. The experimental data were used to verify the effectiveness of the network. The root-mean-square error of the test metrics for GRNN and LSTM network were 6.4260 and 5.4282, respectively, indicating that LSTM network has higher performance in processing the data in this paper.

Direct estimation of gas holdup in gas–liquid bubble column reactors using ultrasonic transmission tomography and artificial neural processing

Ultrasonic tomography (UT) technology is a typical industrial process tomography (IPT) technology and an effective method for the cross-sectional visualization of a gas–liquid two-phase flow pipeline. For typical noniterative or iterative algorithms, the design of sensitivity maps is an important aspect for imaging results of UT. The construction of sensitivity maps is often based on the assumption of wave propagation theory; therefore, a sharp edge in a sensitive map (SESM) seems difficult to avoid, which produces a low quality of reconstructed images when the sensing objects appear on the edge. This article proposes the multilevel slope reduction methods to improve image quality via changing the effects of SESM. The multilevel slope reduction method is used to create a gradient slope and to eliminate the SESM effect. The Pearson correlation coefficient (PCC), position error (PE), and area error (AE) are selected as image quality evaluation criteria. The simulation and experimental results show that the proposed method can reduce the AE of the reconstruction results by approximately 0.1. The multilevel slope reduction method can increase the PCCs of the simulation and experimental reconstruction results by 0.02 and 0.06, respectively.

A Sensitivity Map Deformation Method for Image Quality Improvement of Ultrasonic Tomography

As a typical industrial process tomography (IPT) technology, ultrasonic transmission tomography (UTT) is an effective method for cross-section visualization of the gas-liquid two-phase flow pipeline. The quality of the reconstructed image is necessary to evaluate the performance of the method. Sector-diffusion-matrix linear back-projection algorithm (SLBP) algorithm with two filtering algorithms, Hybrid Reconstruction (HR) algorithm and Adaptive Threshold Filtering (ATF) algorithm, were used to reconstruct and post-process the image of the sensing area. A single bubble flow pattern is discussed in this article. Three variables including the thickness of the tube wall, the position of the gas bubble, and the area of the bubble are involved. Image correlation coefficient (ICC), position error (PE), shape distortion (SD), and area resolution (AR) indexes are selected as evaluation criteria of the imaging quality to evaluate the influence of the variables on the imaging quality. ICC was mainly affected by the area of the bubble, and the fluctuation reached 0.5. The relationship between image quality and the three factors was nonlinear. But overall, the thicker the wall, the larger the distance or area, the greater the PE. SD and AR were affected by the bubble area. The larger the area, the smaller the SD. The relationship between image quality and bubble area was also nonlinear. When the bubble area was 314mm2, AR was the smallest, 0.03. When the wall thickness was 3mm, the bubble was located at (-10, 10), and the bubble area was 707mm2, the quality of the reconstructed image was the best, ICC=0.58, PE=0.72, SD=0.96, AR=0.05. The simulation results analyze the influence of the thickness of the pipe wall, the location and area of the reconstruction target on the reconstructed image, and this conclusion has the potential to be applied to industrial processes.

Simulation Study on Influencing Factors of Image Reconstruction Quality Based on UT System

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Papers

Direct estimation of gas holdup in gas–liquid bubble column reactors using ultrasonic transmission tomography and artificial neural processing

A Sensitivity Map Deformation Method for Image Quality Improvement of Ultrasonic Tomography

An MSA-Net Algorithm for Direct Estimation of Gas Holdup Based on Electrical Impedance Tomography System

Simulation Study on Influencing Factors of Image Reconstruction Quality Based on UT System