Electrical resistance tomography (ERT) can reconstruct measured field images non-invasively and is therefore widely used in the field of engineering technology. However, blurred reconstructed images and the lack of detailed features limit the application of electrical tomography. In this paper, a reconstruction method based on a conditional generative adversarial network (CGAN) is proposed to mitigate these problems. CGAN, a deep learning algorithm, can generate images based on condition information, making the generated images more stable and trustable. To adapt the training to the characteristics of ERT, the CGAN structure has been improved. In addition, loss judgement is added to the discriminator training to improve the training efficiency. We further propose a data generation method to simulate various conductivity distributions. The method is tested by using a testing set without repetition data in the training set. The results indicate that the method can effectively improve the sharpness of the reconstructed images and the reconstruction of the image details and reduce reconstructed image error. Using real experimental data for reconstruction, the results also show that this method can effectively improve the quality of reconstruction.

Electrical resistance tomography (ERT) is used to reconstruct the resistance/conductivity distribution. Usually, a uniform distribution is assumed as the initial condition to obtain a generic sensitivity matrix, which may be very different from a theoretical sensitivity matrix, resulting in a large error. The aim of this study is to analyse the difference between a generalized sensitivity matrix and a theoretical sensitivity matrix and to improve image reconstruction. The effect of the generic sensitivity matrix and theoretical sensitivity matrix on image reconstruction is analyzed. The error caused by the use of the generic sensitivity matrix is estimated. To reduce the error, an improved iterative image reconstruction algorithm is proposed, which is based on calculation of the error between the generic sensitivity matrix and the theoretical sensitivity matrix, and a correction coefficient with a penalty. During the iterative process, the resistivity distribution and sensitivity matrix are alternatively corrected. Simulation and experimental results show that the proposed algorithm can improve the quality of images, e.g., of two‐phase distributions.

A novel computationally efficient machine learning (ML) framework has been developed for constructing the turbulent flow field of single-phase or two-phase particle-liquid flow in a mechanically agitated vessel by feeding a very short-term experimental Lagrangian trajectory. Using a supervised k-nearest neighbours regressor learning algorithm coupled with a Gaussian process, the framework predicts the mean flow and turbulent fluctuations by sharing the statistical features learned from experimental data. The capability of the ML framework is evaluated by comparing the flow dynamics of predicted trajectories to extensive Lagrangian particle tracking measurements under various flow conditions. Local velocity distributions, Lagrangian statistical analysis, solid concentration distributions and phase flow numbers show very good agreement between ML-predictions and experiments. Being accurate, efficient and robust, the ML framework is a powerful tool for analysing and modelling multiphase flow systems using a minimal amount of driver data input which can equally be provided from any reliable numerical simulation, thus avoiding costly experimental measurements.

A hybrid learning algorithm consisting of a preprocessor, a k-nearest neighbors regressor, a noise generator, and a particle–wall collision model is introduced for predicting features of turbulent single-phase and particle–liquid flows in a pipe. The hybrid learning algorithm has the ability to learn and predict the behavior of such complex fluid dynamic systems using experimental dynamic databases. Given a small amount of typical training data, the algorithm is able to reliably predict the local liquid and particle velocities as well as the spatial distribution of particle concentration within and without the limits of the range of training data. The algorithm requires an order of magnitude less training data than a typical full set of experimental measurements to give predictions on the same level of accuracy (typically, 20 cf. 100 trajectories for phase velocity distribution and 40 cf. 500 trajectories for phase concentration distribution), thus leading to huge reductions in experimentation and simulation. A feature importance analysis revealed the effects of the different experimental variables on the particle velocity field in a two-phase particulate flow, with particle–liquid density ratio and particle vertical radial position being the most influential and particle concentration the least. The algorithm is amenable to extension by using more complex databanks to address a much more comprehensive range of flow situations.

Machine learning (ML) is used to build a new computationally efficient data-driven dynamical model for single-phase and complex multicomponent particle–liquid turbulent flows in a stirred vessel. By feeding short-term trajectories of flow phases or components acquired experimentally for a given flow condition via a positron emission particle tracking (PEPT) technique, the ML model learns primary flow dynamics from the input driver data and predicts new long-term trajectories pertaining to new flow conditions. The model performance is evaluated over a wide range of flow conditions by comparing ML-predicted flow fields with extensive long-term experimental PEPT data. The ML model predicts the local velocities and spatial distribution of each flow phase and component to a high degree of accuracy, including conditions of impeller speeds, particle loadings and sizes within and without the range of the input driver datasets. A new flow analysis and modeling strategy is thus developed, whereby only short-term experiments (or alternatively high-fidelity simulations) covering a few typical flow situations are sufficient to enable the prediction of complex multiphase flows, significantly reducing experimental and/or simulation costs.

Although electrical resistance tomography has been successfully applied to visualise gas–water two-phase flow in many applications, its capability for the determination of the sharp interfaces between gas bubbles and water is still below engineering expectations, which impedes effective estimation of fluid characteristics and flow regimes. A thresholding value method applied to a tomogram demonstrated a splendid view of most flow regimes, especially of a large bubble, but it may present a challenge with its accuracy in practice since the thresholding value was determined empirically. In this paper, a size projection algorithm is proposed for imaging a large bubble with a distinctive boundary, where the optimal thresholding value is automatically determined by minimising the projection error between measured voltages and computed voltages via a forward numerical solution, which specifically focuses on imaging of large bubbles. The accuracy of imaging a large bubble is evaluated by simulating the typical cross-sectional configurations of common pipeline flow regimes. Experimental results are reported in the paper, which were conducted on both horizontal and vertical pipelines engaged with typical gas–water flow regimes, including stratified, plug, slug and annular flow regimes. The results are also compared with the images obtained from a wire-mesh sensor system and high-speed camera videos recorded through a transparent photo-chamber lined in the test rig.