Monitoring functional anomalies in cyclical water treatment processes

Fault detection in water treatment (WT) facilities is important to maintain system operation. Batch processes and backwashes within these systems create cyclical data, allowing for the application of functional data techniques. Previously, a limited number of functional fault detection methods have been applied to real data whose faults have unknown start and endpoints. In this article, we use simulations and case studies of cyclical WT data to compare different process monitoring approaches for different types of faults. First, we introduce a new method based on measures of directional outlyingness, and we compare this with three competing methods: (i & ii) Shewhart control charts with and without data preprocessing and (iii) T2 and SPE charts based on functional principal components. A simulation study generating functional data compares the performance of these methods, and then an extensive set of case studies is used to evaluate their real-world behavior. These case studies are unique in that the faults are introduced deliberately, so their start and end times are known. We demonstrate the importance of accounting for expected changing global behavior in WT systems when performing fault detection, as well as the circumstances under which a given fault detection method would be appropriate.