Deviation Contribution Plots of Multivariate Statistics

As data analytic techniques evolve and the accessibility of process measurements improves, data-driven process monitoring has enjoyed a quick development in both theoretical and application perspectives recently. Although abundant process measurements will facilitate data-driven process monitoring and lead to better monitoring indexes, it becomes difficult to identify the underlying variables that are responsible for a fault directly with the monitoring indexes as the scope of measured variables is getting broader. To restrain the scope and identify the source of fault, contribution plots are commonly used in fault diagnosis in order to quantify the influence of process variables in presence of fault. Nevertheless, as sophisticated monitoring techniques become more and more complicated, deriving corresponding contribution plots is challenging. The concept of deviation contribution plots is proposed to address this issue. By extending the original definition of contribution for linear processes, the deviation contribution is defined to quantify the contribution of deviations in originally measured variables to the deviation of monitoring indexes. The ability of the proposed deviation contribution plots to identify influential variables in monitoring algorithms based on nonlinear feature extractions is verified by both numerical simulation and the Tennessee Eastman process benchmark case study.