(333a) Visualization and Analysis of Periodic Process Data

The operation of periodic processes differs significantly from that of continuous processes and batch processes: the well-defined operating state is replaced by a limit cycle, which can in principle repeat an infinite number of times. Typical examples include adsorption-based separation systems (e.g., pressure or temperature swing adsorption); however, the periodic operation of, e.g., chemical reactors and biological systems 1, 2 has also been explored. Research efforts have also been expended on fast simulation of periodic processes3.
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.

References
Sowa, S. W., Baldea, M., & Contreras, L. M. (2014). Optimizing metabolite production using periodic oscillations. PLoS Comput Biol, 10(6), e1003658.
Sterman, L. E., & Ydstie, B. E. (1990). The steady-state process with periodic perturbations. Chemical Engineering Science, 45(3), 721-736.
Pattison, R.C., Schmal, P., & Pantelides, C. (2015). Efficient Computation of Cyclic Steady States in Periodic Adsorption Processes Using the JFNK Method. 2015 AIChE Annual Meeting, 431146
Wang, R. C., Edgar, T. F., Baldea, M., Nixon, M., Wojsznis, W., & Dunia, R. (2015). Process fault detection using time�explicit Kiviat diagrams. AIChE Journal, 61(12), 4277-4293
Wang, R., Baldea, M., & Edgar, T.F. (2015). Visualization and Data-Driven Monitoring of Batch Processes. 2015 AIChE Annual Meeting, 418567