Scrutinizing changes in the water demand behavior

Time series novelty or anomaly detection refers to automatic identification of novel or abnormal events embedded in normal time series points. In the case of water demand, these anomalies may be originated by external influences (such as climate factors, for example) or by internal causes (bad telemetry lectures, pipe bursts, etc.). This paper will focus on the development of markers of different possible types of anomalies in water demand time series. The goal is to obtain early warning methods to identify, prevent, and mitigate likely damages in the water supply network, and to improve the current prediction model through adaptive processes. Besides, these methods may be used to explain the effects of different dysfunctions of the water network elements and to identify zones especially sensitive to leakage and other problematic areas, with the aim to include them in reliability plans. In this paper, we use a classical Support Vector Machine (SVM) algorithm to discriminate between nominal and anomalous data. SVM algorithms for classification project low-dimensional training data into a higher dimensional feature space, where data separation is easier. Next, we adapt a causal learning algorithm, based on the reproduction of kernel Hilbert spaces (RKHS), to look for possible causes of the detected anomalies. This last algorithm and the SVM's projection are achieved by using kernel functions, which are necessarily symmetric and positive definite functions