In this paper, a new fault monitoring method based on adaptive partitioning non-negative matrix factorization (APNMF) is presented for non-Gaussian processes. Non-negative matrix factorization (NMF) is a new dimension reduction technique, which can effectively deal with Gaussian and non-Gaussian data. However, the NMF model of traditional fault monitoring method is time-invariant and cannot provide fault warning for the slowly changing industrial process. Therefore, this paper proposes an adaptive partition NMF algorithm with non-fixed sub-block NMF models. First, the process variables under different operating conditions of the system are divided into several sub-variable spaces adaptively by the complete linkage algorithm. Then, the global variables space and each sub-variable space are modeled by the NMF method. Finally, the kernel density estimation (KDE) method is adapted to calculate the control limits of the defined statistical metrics. The proposed method makes full use of intra-block local information and inter-block global information, which improves diagnostic performance. The experimental results of a numerical process and the Tennessee Eastman (TE) benchmark process show that the proposed method improves the accuracy of fault monitoring compared with the existing algorithms. INDEX TERMS Fault monitoring, adaptive partitioning, non-negative matrix factorization, non-Gaussian processes, kernel density estimation.
Non-negative matrix factorization (NMF) is a novel technique for dimensionreduction, which can be used to process data of non-Gaussian and Gaussian efficiently. A global NMF model is inappropriate for the whole process, since it neglects the local information and monitoring results are often hard to be interpreted. On the basis of adaptive partition non-negative matrix factorization (APNMF) and Bayesian inference, a multi-block NMF model for non-Gaussian process monitoring is put forward to detect and isolate the faults effectively. Using APNMF method, the original variables in different fault states can be adaptively divided into multiple sub-blocks, and on this basis, the NMF monitoring model of each sub-block is formed. Then, two new statistics are constructed by Bayesian inference to supply an intuitive display. Finally, a weighted reconstruction-based contribution (RBC) plot method is presented to reduce the smearing effect and find out the main causes of these faults. This method makes full use of the local and global information of process data and improves the effectiveness of process monitoring. The validity and feasibility of the proposed method will be proved by an example of a numerical process, a Tennessee Eastman (TE) benchmark process and a continuous stirred-tank reactor (CSTR) process.
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