General Semi-Nonnegative Matrix Factorization and Its Application for Statistical Process Monitoring

As an effective feature extraction and dimensionality reduction technique, nonnegative matrix factorization (NMF) has been widely applied in fault detection in recent years. The requirement for vectorization of samples causes NMF to disrupt the inherent structure of matrix data, making subsequent fault isolation and localization unachievable. In addition, existing statistical metrics used for fault detection are distance-based. Due to additional terms or other constraints, the data distribution in low-dimensional space deviates from the origin, resulting in excessively large decision boundaries and reduced fault detection performance. To directly utilize matrix data and address the issue of excessively large decision boundaries, a new method, named general semi-nonnegative matrix factorization, is proposed for statistical process monitoring. Its novelties include the following. First, the common features among the samples are extracted within a lower dimensional space, concurrently preserving the special features of the data. Second, by constructing two new statistical metrics, the latent variables extracted by GSNMF are combined with process monitoring techniques for fault detection. Third, the algorithm relieves the nonnegative restriction for original data, and allows samples to be input as vectors or matrices. On this basis, an abnormal variable isolation method named generic reconstruction-based contribution, which is suitable for matrix and variable data, is proposed for statistical process. The effectiveness of the proposed fault detection and abnormal variable isolation methods are verified on the benchmark dataset and the practical electrical-fused magnesia furnace process.