Online Temporal Signal Comparison Using Singular Points Augmented Time Warping

Abstract

Advances in instrumentation and data storage technologies have allowed the process industries to collect extensive operating data which can be used to extract information about the underlying process and provide online decision support. One of the fundamental problems in data-based decision support is comparison of time-series data. Many signal comparison methods require signals that are of the same length and synchronized. Synchronization of varying length signals is usually achieved using dynamic time warping (DTW). Major limitations of DTW include computational cost and the tendency to link operationally different points. Previously, we proposed singular points augmented time warping to overcome these shortcomings during offline signal comparison (Srinivasan and Qian Ind. Eng. Chem. Res. 2005, 44, 4697). Landmarks in process data such as extreme values and sharp changes, called singular points, are used to segment a signal into regions with homogeneous properties, called episodes. Singular points of two signals are linked by dynamic programming; time warping is used to synchronize the episodes. A locally optimal equivalent of DTW called extrapolative time warping (XTW) with better computational performance was also proposed. In this paper, we present the extension of this approach to online signal comparison. The online signal comparison problem is a generalization of the offline problem and has two additional challenges: (1) the reference signal for comparison is not known a priori and has to be selected from a library, and (2) the starting point of the reference and real-time signal would not coincide in general, and the corresponding points have to be identified. The approach proposed here addresses these by extending dynamic locus analysis (Srinivasan and Qian Chem. Eng. Sci. 2006, 61, 6109) and singular point augmented XTW using anchoring and flanking strategies. The application of the proposed approach is illustrated using two different case studies: online operating mode identification in the Tennessee Eastman process and online fault identification in a lab-scale distillation column. The results show that the proposed approach is robust, efficient, and suitable for online signal comparison.