(333a) Visualization and Analysis of Periodic Process Data
While the design, operation and simulation of periodic processes have received some attention in the literature, periodic process monitoring remains an open question. In this presentation, we discuss a novel geometric method for data-driven monitoring of periodic processes. Our work is an extension of the time-explicit Kiviat (radial) plot visualization and fault detection frameworks that were previously developed for both continuous processes4 as well as batch processes5. In this framework, each sample data point of the multivariate time-series collected from process operations is represented in a radial plot. These plots are stacked vertically in the order they were acquired, resulting in a time-explicit representation of the multivariate time series. The geometric properties of this setup allow for the process state at a given time to be represented as a single point, the centroid of the corresponding plot in radial coordinates.
To extend these ideas to periodic processes, we propose a two-step monitoring and fault detection algorithm. In the first step, we conduct inter-cycle fault detection by defining a centroid for each cycle and identifying problematic cycles. Based on the principles developed for fault detection in continuous processes, this is done by using several normal operating cycles to obtain a confidence ellipse for the centroids of cycles represented in radial coordinates â?? any cycles whose centroids falls outside of this region is deemed to be a problematic or faulty cycle.
After the problematic cycles are determined, it is often desirable to determine the timing of a fault within a cycle. Thus, in the second step, we conduct intra-cycle fault detection. In this application, we build x confidence ellipses for normal operating cycles that have a period of x. The samples in the problematic cycle are then compared on a sample-by-sample basis with these confidence ellipses to identify when the deviations begin.
We also introduce ancillary mechanisms for determining the period of operation of the process and for defining the normal operating state, and discuss a strategy for online implementation. We demonstrate our methodology on two simulation case studies â?? a CSTR simulation with oscillatory set points, and a pressure-swing adsorption (PSA) system.
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