(325d) Visual Data Mining and Fault Detection in Radial Coordinates
The monitoring of chemical plant operations usually requires displaying numerous variables at any given point in time. These variables are frequently tracked using score plots, which can only show up to 2 variables per plot, one for each axis. For n number of variables, n(n-1)/2 number of plots must be used to fully visualize plant operations . The use of parallel coordinates permits the presentation of a significant number of process variables on one plot, allowing for easy visualization of the entire process operations. In this work, we introduce 3D radial plots (3DRP) as an extension of parallel coordinate systems. In a 3DRP, an additional axis normal to the 2D plane of a radial plot is used to represent time. In this manner, the data collected at one sample instant become a data “slice” in a 3DRP. 3DRPs remedy one of the main shortcomings of parallel coordinate representations, i.e., the lack of a clear time dimension.
This contribution shows that 3DRPs can provide a new means for data mining and visualization, and additional insight for real-time monitoring of plant operations. Furthermore, we introduce a novel approach for process fault detection based on convex hulls. Specifically, we define the inner and outer convex hulls of a 3DRP as the curves in the radial coordinate space that enclose, respectively, the minimum and maximum values of each variable during a pre-defined period of steady-state operation. We define a faulty process state as a state whose corresponding data slice lies partially outside the annular region defined by the inner and outer hulls. Subsequently, we use geometric arguments to define fault signatures that support the fault isolation component of the proposed framework.
The incorporation of principal component analysis (PCA) into the 3DRP representation avoids cluttering of the radial plots as it reduces the required number of variables for process monitoring. By focusing on the variance in the dataset, the PCA radial plots method allows for detection of some faults that might otherwise be missed.
We present two applications of the proposed method. First, we analyze a complement of industrial datasets collected from a multi-stage compressor subject to surge events. This application shows that 3DRP is capable of anticipating the onset of surge. Subsequently, we consider the operation of the Tennessee Eastman Challenge Process . In this case, the proposed technique performs comparably and sometimes better than other methods proposed in the literature using the Tennessee Eastman benchmark. In effect, 3DRP is able to detect some of the faults listed in the original paper  that are missed by well known fault detection methods.
 Dunia, R., Edgar, T. F., & Nixon, M. (2013). Process monitoring using principal components in parallel coordinates. AIChE J., 59(2), 445–456
 Downs, J. J., & Vogel, E. F. (1993). A plant-wide industrial process control problem. Comput. Chem. Eng., 17(3), 245-255.