(187h) Process Monitoring Using a PCA-Based Exponentially Weighted Generalized Likelihood Ratio Chart

Most industrial processes are multivariate in nature and can be highly dimensional and complex. These processes require continuous monitoring in order to ensure that they run safely, while maintaining consistent product quality and minimizing pollution to the environment. A critical part of process monitoring methods is fault detection. Process history or data based methods are frequently used to carry out process monitoring, as they do not do require the process model to be explicitly defined. A popular input-based process monitoring technique is the principal component analysis (PCA) method [1].

PCA is a linear dimensionality reduction technique that is widely utilized to monitor a broad range of industrial processes. PCA functions by applying an orthogonal transformation to a set of highly correlated variables in order to produce a set of uncorrelated values, where the largest principal component is in the direction that accounts for the greatest degree of correlation between two variables. The dimensionality of a process is then reduced by only retaining the principal components that account for a majority of correlation between variables in the process (95-99%). Numerous authors have produced extensions of the conventional PCA method. However, many of these extensions have not been implemented in practice, as most techniques only offer marginal improvement in results and may increase computational time, which is an important factor since most industrial processes require quick detection.

The hypothesis testing method, the generalized likelihood ratio (GLR) method has recently been incorporated with the PCA model in order to further enhance its performance [2]. However, the conventional GLR method only utilizes a single observation to compute the detection statistic. Results have demonstrated that the utilization of a moving window when implementing the GLR statistic can improve the performance of the technique even further [3], [4]. However, since the moving window GLR method only utilizes a mean filter when computing the detection statistic, it is possible to improve the results further. The exponentially weighted moving average (EWMA) is a method contains process memory, and is known to show improved performance over a simple moving average technique. Therefore, a control chart that integrates the advantages of the GLR test with those of the EWMA method should provide improved performance, as it utilizes exponential weights with decaying memory in order to compute the GLR statistic [5].

This work focuses on extending the conventional PCA model, to one that utilizes an exponentially weighted GLR chart, in order to provide enhanced results. The fault detection performance of PCA-based EW-GLR chart will be demonstrated through illustrative examples using real-world applications, including chemical processes, and will be evaluated using the three main fault detection criteria: missed detection rate, false alarm rate, and out-of-control average run length (ARL₁). This work will also demonstrate that the PCA-based EW-GLR algorithm is relatively easy to implement, and therefore encourages its application in practice for process monitoring purposes.

[1] D. C. Montgomery, Introduction to Statistical Quality Control, 7th ed. Hoboken, NJ: John Wiley & Sons, 2013.

[2] F. Harrou, M. N. Nounou, H. N. Nounou, and M. Madakyaru, “Statistical fault detection using PCA-based GLR hypothesis testing,” J. Loss Prev. Process Ind., vol. 26, no. 1, pp. 129–139, 2013.

[3] 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.

[4] 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.

[5] J. Zhang, C. Zou, and Z. Wang, “A control chart based on likelihood ratio test for monitoring process mean and variability,” Qual. Reliab. Eng. Int., vol. 26, no. 1, pp. 63–73, 2010.