A clustered minimum volume ellipsoid model for event detection in water networks

This study presents a model for detecting abnormal events in water distribution systems using the minimum volume ellipsoid (MVE) clustered into operation modes, is developed and demonstrated. Estimating multivariate location and scatter while maintaining two important properties, equivariance and positive breakdown, has always been difficult. A well-known estimator, which satisfies both properties, is the Minimum Volume Ellipsoid (MVE) Estimator [1]. The minimum volume ellipsoid (MVE) estimator is the smallest volume ellipsoid that covers m of n observations. The MVE could be found by a resampling algorithm. Its low bias makes the MVE especially useful for outlier detection in multivariate observations [2]. Outliers are observations that locate beyond the minimum volume ellipsoid. Detecting events using outliers is well explained in the Methods section. Water distribution systems operation modes have routine changes; thus some parameters may change between one operation mode and another. Consequently, it may be inaccurate to apply all observations in the same ellipsoid. Clustering the data according to operation modes, then constructing an appropriate MVE for each operation mode is the proposed method to increase the MVE model's accuracy and to obtain more convincing results. The model consists of two major steps: event detection and event classification. The main objective of the first step is to detect anomaly using clustered minimum volume ellipsoid according to operation modes. In the second step, detected abnormal events are classified as physical or quality events. The described model is illustrated by a simple water distribution system.