Statistical Monitoring of Dynamic Multivariate Processes Part 1. Modeling Autocorrelation and Cross-correlation

Abstract

The work summarized in this paper represents the first part of a two-paper analysis of statistical monitoring of complex dynamic multivariate processes. Motivated by recent research highlighting the difficulties of monitoring autocorrelated variables, this first paper revisits the impact of autocorrelation and cross-correlation upon the significance level for hypothesis testing in monitoring statistics. The presented analysis shows that both correlations lead to profound alterations of the significance level, which can manifest themselves in the production of false alarms or an insensitive monitoring scheme. In the research literature on statistical process monitoring, however, only the issue of autocorrelation has received attention thus far. To improve process monitoring of autocorrelated and cross-correlated variables, this article proposes the use of Kalman innovation models to remove these correlations. The utility of this improvement is demonstrated using an application to the Tennessee Eastman simulator and the analysis of recorded data from an industrial distillation unit.

Fault detection in non-Gaussian vibration systems using dynamic statistical-based approaches

“…The subsequent analysis of the SVDD approach yielded that the parameters C = 2 and s=0.01 produced a 99% confidence limit for the transformed ICs. Next, for determining a subspace identification model, the application of the AIC cost function, as proposed in reference [18], suggested the selection of 14 state variables. Fig.…”

“…To address these issues, this paper proposes two approaches that can monitor correlated vibration signals which are non-Gaussian. Proposed work on dynamic MSPC [17,18] showed that an incorrect data model can affect the number of Type I and II errors, whilst the same effect is noticeable for assuming an incorrect distribution function for the vibration signals [19][20][21].…”

“…Although a number of research studies have been carried out on these two aspects separately, such as dynamic PCA (DPCA) [17,18,22], improved dynamic PCA [23], subspace model identification (SMI) [18,24,25] for the dynamic issue, and independent component analysis (ICA) [17,19,20], support vector machine (SVM) [21], support vector data description (SVDD) [26] for the non-Gaussian issue, the research literature has not offered a comprehensive treatment that considered both dynamic and non-Gaussian behavior.…”

On reducing false alarms in multivariate statistical process control

“…For example, the application of PCA is based the assumption that the process data is independent and identically Gaussian distributed. However in practice the process variables tend to be auto-correlated, necessitating time-series modelling approaches to reduce the resultant false alarms (Alabi et al, 2005;Kruger et al, 2004;Xie et al, 2006). Furthermore, in some situations the multivariate Gaussian distribution may be an inadequate approximation to the real process variables, and thus more advanced semi-parametric and non-parametric distributions are required to characterize the process normal behaviour accurately, including kernel density estimation (Martin and Morris, 1996), wavelet based density estimation (Safavi et al, 1997), and more recently the Gaussian mixture model (Chen and Sun, 2009;Choi et al, 2004;Thissen et al, 2005).…”

Sensor Fault Detection and Isolation by Robust Principal Component Analysis

“…Thirdly, Kruger et al (2004) have shown that DPCA produces correlated scores which lead to an undesired impact upon the fault detection ability in the representation subspace (production of false alarms). Xie et al (2006) have then proposed to filter the principal scores obtained by DPCA by a Kalman innovation filter to remove the correlation between them. These points being outside the scope of this chapter, for the sake of simplicity, in the following, only classic PCA is considered in the following.…”