Qualitative path estimation: A fast and reliable algorithm for qualitative trend analysis

Fault detection and identification is challenged by a lack of detailed understanding of process dynamics under anomalous circumstances as well as a lack of historical data concerning rare events in a typical process. Qualitative trend analysis (QTA) techniques provide a way out by focusing on a coarse-grained representation of time series data. Such qualitative representations are valid in a larger set of operating conditions and thus provide a robust way to handle the detection and identification of rare events. Unfortunately, available methods fail when faced with moderate noise levels or result in rather large computational efforts. For this reason, this article provides a novel method for QTA. This leads to dramatic improvements in computational efficiency compared to the previously established shape constrained splines method while the accuracy remains high.