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Abstract

Many processes utilize statistical process monitoring (SPM) methods in order to ensure that process safety and product quality is maintained. Principal Component Analysis (PCA) is a data-based modeling and fault detection technique that it widely used by the industry [1]. PCA is a dimensionality reduction technique that transforms multivariate data into a new set of variables, called principal components, which capture most of the variations in the data in a small number of variables. This work examines different improved PCA-based monitoring techniques, discusses their advantages and drawbacks, and also provides solutions to address the issues faced by these techniques. Most data based monitoring techniques are known to rely on three fundamental assumptions: that fault-free data are not contaminated with excessive noise, are decorrelated (independent), and follow a normal distribution [2]. However, in reality, most processes may violate one or more of these assumptions. Multiscale wavelet-based data representation is a powerful data analysis tool that utilizes wavelet coefficients which are known to possess characteristics that are inherently able to satisfy these assumptions as they are able to denoise data, force data to follow a normal distribution and be decorrelated at multiple scales. Multiscale representation has been utilized to develop a multiscale principal component analysis (MSPCA) method for improved fault detection [3]. In a previous work, we also analyzed the performance of multiscale charts under violation of the main assumptions, demonstrating that multiscale methods do provide lower missed detection rates, and ARL1 values when compared to conventional charts, with comparable false alarm rates [2]. The choice of wavelet to use, the choice of decomposition depth, and Gibb's phenomenon are a few issues faced by multiscale representation, and these will be discussed in this work. Another common drawback of most conventional monitoring techniques used in the industry is that they are only capable of efficiently handling linear data [4]. The kernel principal component analysis (KPCA) method is a simple improvement to the PCA model that enables nonlinear data to be handled. KPCA relies on transforming data from the time domain to a higher dimensional space where linear relationships can be drawn, making PCA applicable [5]. From a fault detection standpoint KPCA suffers from a few issues that require discussion, i.e., the importance of the choice of kernel utilized, the kernel parameters, and the procedures required to bring the data back to the time domain, also known as the pre-image problem in literature [6]. Therefore, this work also provides a discussion on these concerns. Recently, literature has shown hypothesis testing methods, such as the Generalized Likelihood Ratio (GLR) charts can provide improved fault detection performance [7]. This is accomplished by utilizing a window length of previous observations in order to compute the maximum likelihood estimates (MLEs) for the mean and variance, which are then utilized to maximize the likelihood functions in order to detect shifts in the mean and variance [8], [9]. Although, utilizing a larger window length of data to compute the MLEs has shown to reduce the missed detection rate, and ARL1 values, the larger window length increases both the false alarm rate and the computational time required for the GLR statistic. Therefore, an approach to select the window length parameter keeping all fault detection criterion in mind is required, which will be presented and discussed. The individual techniques described above have their own advantages and limitations. Another goal of this work is to develop new algorithms, through the efficient combination of the different SPM techniques, to improve fault detection performances. Illustrative examples using real world applications will be presented in order to demonstrate the performances of the developed techniques as well as their applicability in practice. References [1] I. T. Joliffe, Principal Component Analysis, 2nd ed. New York, NY: Springer-Verlag, 2002. [2] M. Z. Sheriff and M. N. Nounou, “Improved fault detection and process safety using multiscale Shewhart charts,” J. Chem. Eng. Process Technol., vol. 8, no. 2, pp. 1–16, 2017. [3] B. Bakshi, “Multiscale PCA with application to multivariate statistical process monitoring,” AIChE J., vol. 44, no. 7, pp. 1596–1610, Jul. 1998. [4] M. Z. Sheriff, C. Botre, M. Mansouri, H. Nounou, M. Nounou, and M. N. Karim, “Process Monitoring Using Data-Based Fault Detection Techniques: Comparative Studies,” in Fault Diagnosis and Detection, InTech, 2017. [5] J.-M. Lee, C. Yoo, S. W. Choi, P. a. Vanrolleghem, and I.-B. Lee, “Nonlinear process monitoring using kernel principal component analysis,” Chem. Eng. Sci., vol. 59, no. 1, pp. 223–234, 2004. [6] G. H. BakIr, J. Weston, and B. Schölkopf, “Learning to Find Pre-Images,” Adv. neural Inf. Process. Syst. 16, no. iii, pp. 449–456, 2004. [7] M. Z. Sheriff, M. Mansouri, M. N. Karim, H. Nounou, and M. Nounou, “Fault detection using multiscale PCA-based moving window GLRT,” J. Process Control, vol. 54, pp. 47–64, Jun. 2017. [8] M. R. Reynolds and J. Y. Lou, “An Evaluation of a GLR Control Chart for Monitoring the Process Mean,” J. Qual. Technol., vol. 42, no. 3, pp. 287–310, 2010. [9] M. R. Reynolds, J. Lou, J. Lee, and S. A. I. Wang, “The Design of GLR Control Charts for Monitoring the Process Mean and Variance,” vol. 45, no. 1, pp. 34–60, 2013.

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/content/papers/10.5339/qfarc.2018.ICTPD864
2018-03-15
2020-02-22
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