Off-line 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. One of the fundamental problems in data-based knowledge acquisition and decision support is the comparison of time-series data. Many signal comparison methods require signals that are of the same length and are synchronized. In this paper, we propose a robust method for univariate signal synchronization, based on dynamic time warping (DTW). The high computational complexity of DTW, which deters its widespread adoption, is significantly reduced by exploiting landmarks (such as extreme values and sharp changes in the data) called singular points. Singular points are used to segment the process signal into regions (called episodes) with homogeneous properties. The comparison of signals is based on linking their singular points or episodes using dynamic programming. Time-warping methods are used to match the corresponding episodes of the two signals. This two-step comparison approach leads to significant improvements in the speed, memory requirement, and efficacy of signal comparison. Another important advantage of the proposed approach is that, because the singular points have physical meaning (such as the beginning or ending of a process event), they can be directly used for state identification, monitoring, and supervision. These applications of the proposed approach are illustrated using three different case studies: (i) identifying operating states in a simulated fiuidized catalytic cracking unit, (ii) differentiating among operating modes in the Tennessee Eastman process simulation, and (iii) identifying the occurrence of transitions in a laboratoryscale fed-batch fermentation process. © 2005 American Chemical Society.