Geometric fault detection using 3D Kiviat plots and their applications

The surge in large-scale data being collected through various social and economic systems comes along with the ever-increasing need to understand and gain insight from the data being collected. This has spurred on the development and advent of big data analytics in many different areas such as healthcare, e-commerce, and group-sharing applications. This applies also to the process industry as well, as the development of more complex processes, which in turn require increased monitoring, mean that a larger amount of data are being collected than previously seen. This data is not only high in volume (measurements taken with a high sampling frequency), but also high in dimensionality (many sensors set up throughout the process). Process monitoring requires the continuous observation of such high dimensional and high volume data, but current visualization techniques do not lend themselves to do doing so. Furthermore, parallel to process monitoring is the desire for fault detection capability -- to detect faults as soon as they occur or predict them before they occur. For that reason it is ideal if there is a visualization technique that also contributes to fault detection efforts, so that both process monitoring and fault detection is satisfied. To that end, in this dissertation the development of three-dimensional (3D) Kiviat diagrams and its use in fault detection is explored in great detail. In Kiviat diagrams, axes are laid out radially around a center point, in contrast to axes being perpendicular to one another in traditional score plots, or in parallel to one another as seen in parallel coordinates. This theoretically allows for an infinite number of axes, and therefore high dimensional data, to be plotted on one figure at once. Due to the time-explicit nature of process data, the addition of a third axis normal to the Kiviat diagram is proposed as well. In the Kiviat diagram representation, each sample forms a polygon on the plot. This is taken advantage of for fault detection purposes by condensing each polygon into its centroid. By doing so the state of the process at every point in time can be represented by its centroid -- this allows for multivariate fault detection to be performed. Using these centroids, a variety of fault detection mechanisms are proposed specific to the types of processes the data is obtained from. The mechanisms are developed for 3 process types commonly seen in industry -- continuous processes, batch processes, and periodic processes. For each process type the fault detection mechanism is detailed and case studies are laid out, demonstrating the application of the method.