Traditional multivariate statistical process monitoring techniques usually assume measurements follow a multivariate Gaussian distribution so that T2 can be used for monitoring. The assumption usually does not hold in practice. Many efforts have been spent on redefining a proper boundary of control region for non-Gaussian distributed processes. These efforts lead to new models such as independent component analysis (ICA), statistical pattern analysis (SPA), and new techniques such as kernel density estimation (KDE), support vector data description (SVDD). However, it has not been stated clearly how a latent structure will affect monitoring performance. In this paper, most of main stream methods for non-Gaussian process monitoring are recalled and categorized. The essential problem formulation of process monitoring is summarized from a general case and then explained in both Gaussian and non-Gaussian distribution, respectively. According to this formulation, KDE and SVDD methods are effective but time-consuming to extract proper control region of non-Gaussian distributed processes. Dimension reduction models are more beneficial to overcome the curse of dimensionality, rather than extracting non-Gaussian data structure. Besides, the monitoring of non-Gaussian processes can be converted into the monitoring of Gaussian processes according to central limitation theorem.
Bibliographical noteThis work was supported by members of Texas-Wisconsin-California Control Consortium (TWCCC), and Center for Interactive Smart Oilfield Technologies (Cisoft). It was also supported by NSFC under grants (61020106003, 61490704, 61333005, 61273173, 61473002, 61673032 and 61473033 ), the SAPI Fundamental Research of Northeastern University of China (2013ZCX02-01).
- Gaussian mixture model
- Independent component analysis
- Kernel density estimation
- Neyman Pearson lemma
- Non-Gaussian distribution
- Statistical pattern analysis
- Support vector data description