One class classifiers for process monitoring illustrated by the application to online HPLC of a continuous process

Abstract

In process monitoring, a representative out-of-control class of samples cannot be generated. Here, it is assumed that it is possible to obtain a representative subset of samples from a single 'in-control class' and one class classifiers namely Q and D statistics (respectively the residual distance to the disjoint PC model and the Mahalanobis distance to the centre of the QDA model in the projected PC space), as well as support vector domain description (SVDD) are applied to disjoint PC models of the normal operating conditions (NOC) region, to categorise whether the process is in-control or out-of-control. To define the NOC region, the cumulative relative standard deviation (CRSD) and a test of multivariate normality are described and used as joint criteria. These calculations were based on the application of window principal components analysis (WPCA) which can be used to define a NOC region. The D and Q statistics and SVDD models were calculated for the NOC region and percentage predictive ability (%PA), percentage model stability (%MS) and percentage correctly classified (%CC) obtained to determine the quality of models from 100 training/test set splits. Q, D and SVDD control charts were obtained, and 90% confidence limits set up based on multivariate normality (D and Q) or SVDD D value (which does not require assumptions of normality). We introduce a method for finding an optimal radial basis function for the SVDD model and two new indices of percentage classification index (%CI) and percentage predictive index (%PI) for non-NOC samples are also defined. The methods in this paper are exemplified by a continuous process studied over 105.11 h using online HPLC.

Combined generative topographic mapping and graph theory unsupervised approach for nonlinear fault identification

“…Despite its linear nature, extensions were developed to overcome this issue and deal with non‐linear systems, such as kernel PCA . Other methods also tackle nonlinearity from scratch, such as support vector machines, Gaussian Mixture Models, generative topographic mapping (GTM), and even the use of inferential models …”

Data density-based fault detection and diagnosis with nonlinearities between variables and multimodal data distributions

“…When there is a nonlinear relationship between the process variables and the data distribution is multimodal, nonlinear MSPC methods [11] contribution plot for KPLS to identify faulty process variables [16]. A one-class support vector machine (OCSVM) can be applied to the domain description problem, enabling us to estimate domains in which the data density is high [17][18][19]. The k-nearest neighbors (k-NN) algorithm can also be applied to estimate the data density [20].…”

Multivariate Statistical Process Control Method Including Soft Sensors for Both Early and Accurate Fault Detection

“…13,14 ICA was combined with PCA 15 and applied to dissimilarity 16 and the hidden Markov model. 17 In addition, nonlinearity in processes can be considered with nonlinear MSPC methods such as kernel PCA 18,19 and support vector machines (SVMs), 20,21 and multivariate multimodal distributions in process data can be handled with the Gaussian mixture model (GMM) 22 and adaptive GMM. 23 However, the traditional MSPC methods cannot detect faults that relate to process variables that are difficult to measure online because the values of these variables cannot be obtained in real time and the variables cannot be used as input variables for the fault detection model.…”