Fault diagnosis using contribution plots

When or SPE charts exceed their control limits to signal abnormal process operation, variable contributions can be analyzed to determine which variable (s) caused the inflation of the monitoring statistic and initiated the alarm. The variables identified provide valuable information to plant personnel who are responsible for associating these process variables with process equipment or external disturbances that will influence these variables, and diagnosing the source causes for the abnormal plant behavior. The procedure and equations for developing the contribution plots was p-resented in Section 3.4. 

The decomposition technique given in [146] can be extended to the and SPEn values of state variables. The state variables are calculated by Eq. 4.67 in which the past data vector is used. When the or SPE chart of the state variables gives an out-of-control signal, contribution plots can be inspected to find the responsible variable for that signal. 

The contribution of output (process) variable yj on state variable Xj at time k is 

TRAN is used to calculate state variable vector x by utilizing which is composed of K past values of the process variables. Based on Eq. 4.67, matrix TRAN is given as 

The computed values of the contributions of each process variable and its past values on all the state variables are plotted on a bar chart. The procedure is repeated for all process variables j = 1. p). Their contributions are plotted on the same bar plot to decide which variable(s) caused the out-of-control alarm in the multivariate chart of state variables. Use of state variables in SPM and their contribution plots are introduced and illustrated in [211] and [219], respectively. 

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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. 

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