Electrical tomography sensors have been widely used for pipeline parameter detection and estimation. Before they can be used in formal applications, the sensors must be calibrated using enough labeled data. However, due to the high complexity of actual measuring environments, the calibrated sensors are inaccurate since the labeling data may be uncertain, inconsistent, incomplete, or even invalid. Alternatively, it is always possible to obtain partial data with accurate labels, which can form mandatory constraints to correct errors in other labeling data. In this paper, a semi-supervised fuzzy clustering algorithm is proposed, and the fuzzy membership degree in the algorithm leads to a set of mandatory constraints to correct these inaccurate labels. Experiments in a dredger validate the proposed algorithm in terms of its accuracy and stability. This new fuzzy clustering algorithm can generally decrease the error of labeling data in any sensor calibration process.

Given a set of data objects, the fuzzy c-means (FCM) partitional clustering algorithm is favored due to easy implementation, rapid response, and feasible optimization. However, FCM fails to reflect either the importance degree of the individual data objects or that of the clusters. Numerous variants of FCM have been proposed to address these issues. However, most of them cannot effectively apply the available information on data objects or clusters. In this paper, a double-constraint fuzzy clustering algorithm is proposed to reflect the importance degrees of both individual data objects and clusters. By incorporating double constraints into each data object and cluster, the objective function of FCM is reformulated and its realization equation is mathematically conducted. Consequently, the clustering accuracy of FCM is improved by applying the available information on both data objects and clusters. Especially, the proposed algorithm effectively addresses the limitations inherent in the existing variants of FCM. The experimental results validate the effectiveness, implementation, and robustness of the new fuzzy clustering algorithm.

As an advanced visualization technique, electrical impedance tomography (EIT) can reconstruct the distribution of electrical parameters and thereby visually show object distribution within a detection field. The quality of EIT reconstruction greatly depends on a selected sensitivity matrix, while various matrices can lead to very different EIT reconstruction results. A large number of efforts to improve the sensitivity matrix have been made to enhance EIT reconstruction quality, but how to construct and select a better matrix in a general and feasible way remains unsolved to date. In this paper, we use the matrix transformation method to address the issue, and two types of symmetric and diagonally dominant matrices are optimally selected to multiply the sensitivity matrix on the left and right, respectively. Therefore, EIT reconstruction quality can generally be improved. The feasibility and robustness of the proposed method have been theoretically demonstrated for both Gaussian kernel-based and power function-based matrices. Experiments validate the proposed method by EIT reconstruction quality.

As an advanced visualization technique, the electrical impendence tomography (EIT) can reconstruct the distribution of electrical parameter and thereby visually show the object distribution within a detection field. The EIT reconstruction quality greatly depends on a selected sensitivity matrix, while various matrixes can lead to very different EIT reconstruction results. A large number of efforts to improve the sensitivity matrix have been made to enhance EIT reconstruction quality, but how to construct and select the best matrix in a generally and feasibly way remains unsolved to date. In this paper, we use the matrix transformation method to address the issue, and two types of symmetric and diagonally dominant matrixes are optimally selected to multiply the sensitivity matrix on left and right, respectively. Therefore, the EIT reconstruction quality can generally be improved. The optimality and generalization of the proposed method have been theoretically demonstrated when specially using either Gaussian kernel-based or power function-based matrices, respectively. Experiments validate the proposed method by the EIT reconstruction quality.