# A Multi-Leak Identification Scheme Using Multi-Classification for Water Distribution Infrastructure
## 1 Introduction
By integrating CNN-SVM and graph-based localization algorithms, the proposed leakage detection scheme in paper [18] achieved more than 90% detection accuracy and positioning accuracy within less than 3 m.  
Most of the aforementioned leakage detection schemes and algorithms showed relatively high detection accuracy in experimental settings or a certain part of WDI. Nevertheless, these methodologies would reveal certain limitations in flexibility and adaptiveness whenever water distribution infrastructure is modified or expanded. In general, WDIs inevitably undergo modification or expansion due to urban reconstruction or pipeline system optimization. When a new pipe branch is added to the existing system, most of the above detection algorithms need to be reconfigured to apply to the new pipeline architecture, which increases the complexity of operation. In addition, different hydraulic behaviors in various pipeline conditions are not considered in these algorithms. These hydraulic behaviors greatly impact the accuracy of detection. For instance, water pressure decreases gradually as the distance from the water pump increases. The corresponding water pressure due to leakage would also drop. Hence, it is necessary to assign different levels of importance to different hydraulic behaviors to ensure leak detection accuracy for each pipeline. Further, whether these detection methods are applicable to multiple leaks remains to be investigated. This paper aims at developing a multi-leak identification (MLI) system for WDI. At this point in time, the real challenges in leak detection and the related research consist of the following: (i) lack of systematic design for automated leak detection systems; (ii) low practicability limited by inhomogeneous operating environments, i.e., the MLI system might perform differently in different parts of WDI; and (iii) lack of adaptiveness to modifications of WDI (referred to as the addition/removal/repair/replacement of pipelines). In view of the need for an MLI system, a multi-classification MLI system (MC-MLI) for WDI is developed in this paper. An adaptive kernel (AK), which is the core of classification, is designed to incorporate the weighting vector into the extracted feature vector. The weighting vector revealing the features' importance levels will improve the overall detection performance. The problem of inhomogeneous working environments is always critical, and now it will be solved by the proposed multi-classification (MC) scheme. The MC scheme is composed of multiple unique classifiers assigned to the specific pipe sections. The classifiers are configured by different classifier scenarios, which are subject to feature combinations, feature weighting vector, and performance weighting vector. Every scenario has different detection performance, and will be chosen to meet certain requirements (e.g., sensitivity > detection time > cost). Thus, the proposed MC scheme can adapt to inhomogeneous working environments and system requirements. High system flexibility to the modification of WDI is another crucial advantage attributed to the MC scheme. When WDI is modified, only several affected classifiers will be re-trained, or new classifiers will be trained for new pipe sections. This mechanism significantly improves system feasibility. The novelty of this study is as follows. A new multi-leak detection scheme, namely multi-classification-based multi-leak identification (MC-MLI), is developed for WDI. In this scheme, an adaptive kernel (AK) and a multi-classification (MC) algorithm are developed to adapt to inhomogeneous working environments and maintain high detection accuracy.