Application of local and global interval embedding algorithms in uncertain system processes

Abstract

The data collected during the fault monitoring of industrial processes are often uncertain because of measurement noise, sensor error, and complex working environments. Currently, most of this uncertainty is transformed into interval-value data for processing. However, the traditional interval fault monitoring method (TIFMM) only considers the global information of the interval-valued data and only rarely considers the local neighborhood information, which can characterize the topological relationship between the interval-valued data points, so that the sample points with some nonlinear relationship still maintain this nonlinear relationship after dimensionality reduction. Therefore, to take into account both local and global information, a new interval-valued data projection algorithm called local and global interval embedding algorithms (LGIEA) is proposed in this paper. First, the measurement error estimation method, based on the principle of reasonable granularity, converts the imprecise variable measurement values into interval-value data that can reflect uncertainty. Then, an interval-matrix feature extraction method based on local and global information fusion, proposed in this paper, extracts process features by minimizing local scattering and maximizing global scattering of interval-valued data. Thereby, it preserves the optimal local neighborhood and global information in low-dimensional space. In addition, four statistical indicators and corresponding variable-contribution graphs have been defined to use online fault monitoring and fault variable identification. Finally, the superiority of the LGIEA was verified using simulation data of the Tennessee Eastman process and actual operating data of a shearer in an inclined-ditch coal mine. The experimental results show that, Compared with TIFMM such as midpoint-radius principal component analysis (PCA), complete information PCA and spectral radius-based interval PCA, proposed method significantly reduces the error alarm rate and the false monitoring rate and improves the accuracy of data classification. It also has better fault identification accuracy and robustness.