The two-phase flow is widely used in industrial production, and the phenomenon of pipe blocking often occurs in pipeline transportation. It affects the efficiency and stability of production. At this time, it is very important to detect the process parameters of two-phase flow. To realize the detection of two-phase flow parameters without causing damage to the distribution in the measurement area, process tomography (PT) has been developed. As a kind of PT technology, electrical capacitance tomography (ECT) has the advantages of fast imaging speed, simple structure, non-invasive, and high safety performance. It has gradually become a hot spot of research in the development of visualization detection technology. The problem of image reconstruction is at the heart of ECT technology. Due to the serious nonlinearity, under characterization, and soft-field characteristics of ECT systems, ECT image reconstruction cannot be well matched with the corresponding application scenarios. ECT image reconstruction method based on fuzzy mode and sensitive field optimization has better advantages in terms of imaging effects and imaging performance indicators. 1) The sensitivity field distribution matrix corresponding to the flow pattern is selected by fuzzy pattern flow pattern identification. It greatly improves the sensitivity of different flow patterns to changes in the sensitivity field. 2) The sensitive field matrix corresponding to the flow pattern is further expanded by the sensitive field expansion method under feature extraction. It better mitigates the effect of soft field characteristics. In addition, the optimization direction of the existing ECT image reconstruction algorithms is mainly to improve the solution accuracy of the inversion problem, and it is less involved in the optimization of the reconstruction process of the sensitive field matrix and the distribution vector of the dielectric constant in the ECT image reconstruction system. Therefore, the method has good feasibility and applicability and provides a method and idea to optimize the effect of an algorithm for image reconstruction.

We propose an ECT image reconstruction method based on fuzzy pattern recognition and sensitive field optimization for the impact of the soft field characteristics of ECT on the quality of image reconstruction. This approach aims to optimize the reconstruction process of sensitive field matrices and dielectric constant distribution vectors in ECT image reconstruction systems. Firstly, the sensitivity matrix corresponding to the flow pattern attributes is selected by fuzzy pattern flow pattern identification. In this way, the sensitive field has been optimized. Secondly, feature information is extracted from the initial image reconstruction signal for data fusion. Expansion of the optimized sensitive field into a new sensitive field distribution matrix is realized by means of zero-padding and stochastic reorganization. Finally, the synthesized observation equations are constructed for image reconstruction to accurately reconstruct the permittivity distribution vector of the ECT system. In verifying the performance of the method, this method is compared with four selected image reconstruction optimization algorithms (Landweber, Tikhonov, Kalman, CGLS) in terms of imaging effectiveness and imaging metrics.

We model the 3D ECT system using COMSOL software (Fig. 6) to obtain the measured capacitance data used for the simulation experiments and the sensitive field distribution matrices corresponding to different flow patterns (Fig. 2). The proposed method is shown in the results of fuzzy pattern-based ECT flow pattern identification (Table 1). The average recognition accuracies are 100%, 99.75%, and 98.75% under no noise, 60 dB and 40 dB Gaussian white noise, respectively. This shows that the method has high recognition accuracy and robustness against noise. Six common flow patterns are imaged under 40 dB Gaussian white noise to compare the method of this paper with four optimized algorithms in terms of imaging effect and imaging performance metrics (Fig. 8). This method has a clear image with distinct edges and no serious blurring effect in the imaging effect as seen from the results of the relative errors (Table 3, Fig. 9) and correlation coefficients (Table 4, Fig. 10) of the reconstructed images. The method in this paper has the lowest correlation error and the highest correlation coefficient compared to the other 4 algorithms. This shows that the method substantially improves the image reconstruction accuracy and comes closest to the dielectric constant distribution of the original flow pattern.

To improve the accuracy of capacitive tomography image reconstruction, this paper proposes an ECT image reconstruction method based on fuzzy pattern recognition and sensitive field optimization. This method combines the optimization of sensitive fields into the image reconstruction process. The sensitive field of the flow pattern is selected by fuzzy pattern recognition. The feature information is extracted from the approximate solution for data fusion, and zero filling and random recombination are carried out to extend the matrix distribution of the sensitive field and the vector distribution of the measured capacitance. The comprehensive observation equation is constructed to solve the dielectric constant distribution vector. In addition, COMSOL software is used to build a 3D simulation model of ECT to obtain the sensitive field matrix and measure the capacitance vector. It carries out flow pattern identification experiments, simulation image reconstruction experiments, and imaging performance index calculation. The flow pattern identification results show that the method has high recognition accuracy and robustness against noise. This shows the effectiveness of the fuzzy model-based ECT flow pattern identification method. The results from the image reconstruction and imaging performance metrics show that the method proposed in this paper can obtain better ECT image reconstruction quality under the same experimental conditions. It provides a method and idea to maximize the effect of the image reconstruction optimization algorithm.