A Graphical Calibration Method for a Water Quality Model Considering Process Variability Versus Delay Time: Theory and a Case Study

Process Variability (PV) is a significant water quality time-series measurement. It is a critical element in detecting abnormality. Typically, the quality control system should raise an alert if the PV exceeds its normal value after a proper delay time (DT). The literature does not address the relation between the extended process variability and the time delay for a warning. The current paper shows a graphical method for calibrating a Water Quality Model based on these two parameters. The amount of variability is calculated based on the Euclidean distance between records in a dataset. Typically, each multivariable process has some relation between the variability and the time delay. In the case of a short period (a few minutes), the PV may be high. However, as the relevant DT is longer, it is expected to see the PV converge to some steady state. The current paper examines a method for estimating the relationship between the two measurements (PV and DT) as a detection tool for abnormality. Given the user’s classification of the actual event for true and false events, the method shows how to build a graphical map that helps the user select the best thresholds for the model. The last section of the paper offers an implementation of the method using real-world data.