Fault diagnosis statistical

This chapter provides a complementary perspective to that provided by Kramer and Mah (1994). Whereas they emphasize the statistical aspects of the three primary process monitoring tasks, data rectification, fault detection, and fault diagnosis, we focus on the theory, development, and performance of approaches that combine data analysis and data interpretation into an automated mechanism via feature extraction and label assignment. 

As concerns the former, statistical tests on the measured data are usually adopted to detect any abnormal behavior. In other words, an industrial process is considered as a stochastic system and the measured data are considered as different realizations of the stochastic process. The distribution of the observations in normal operating conditions is different from those related to the faulty process. Early statistical approaches are based on univariate statistical techniques, i.e., the distribution of a monitored variable is taken into account. For instance, if the monitored variable follows a normal distribution, the parameters of interest are the mean and standard deviation that, in faulty conditions, may deviate from their nominal values. Therefore, fault diagnosis can be reformulated as the problem of detecting changes in the parameters of a stochastic variable [3, 30],... 

S. Yoon and J.F. MacGregor. Fault diagnosis with multivariate statistical models part I using steady state fault signature. Journal of Process Control, 11 387-400, 2001. 

One of the most influential books on the subject of PCA was by I.T. Jolliffe [128] who published recently a new edition [129] of his book. The book by Smilde et al. [276] is the most recent contribution to the literature on multivariate statistics, with special emphasis on chemical systems. Two books coauthored by R. Braatz [38, 260] review a number of fault detection and diagnosis techniques for chemical processes. Cinar [41] coauthored a book on monitoring of batch fermentation and fault diagnosis in batch process operations. 

Contribution plots presented in Section 7.4 provide an indirect approach to fault diagnosis by first determining process variables that have inflated the detection statistics. These variables are then related to equipment and disturbances. A direct approach would associate the trends in process data to faults explicitly. HMMs discussed in the first three sections of this chapter is one way of implementing this approach. Use of statistical discriminant analysis and classification techniques discussed in this section and in Section 7.6 provides alternative methods for implementing direct fault diagnosis. 

Quality control, production monitoring, fault diagnosis, and production statistics are important supplementary functions for the shop-floor control and management system to be operated efficiently and effectively. 

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