## 4 New Classification of Methods for the Detection of Water Network Operating Conditions
### Time Domain Analysis  
When a water pipe bursts as a result of a failure, there is a rapid drop in the pressure at a given control point and an increase in flow velocity. The consequence is the phenomenon of hydraulic shock, accompanied by the formation of a wave propagating in both directions from the place of failure, the so-called negative pressure wave NPW). This forms the basis for methods based on the analysis of short-term transients in the time domain. Depending on the pipeline material, foundation conditions, and soil, the propagation velocity of the NPW is between 250-1500 m/s [55]. The wavefront may be well-defined for large faults, or weaker for smaller faults. Solutions based on the analysis of short-term transients (transient phenomenon) include transient analysis TA). Short-term transients are events within the water supply network that are transmitted as a pressure wave or hydraulic shock, resulting in a sudden change in flow velocity. The TA approach is based on the comparison of the pressure distribution under normal network operating conditions with the signal recorded during a failure, which contains information about the transition wave. The methods are implemented by analyzing a forced, short-lived hydraulic shock created by the sudden closing or opening of a valve on an example network installed (typically) under laboratory conditions. The point of the proposed solutions is the detection and localization of failures based on the analysis of the sequence of the passage of the hydraulic shock wavefront, the so-called pressure wavefront tracking. The biggest problem concerns the calibration of the unknown roughness coefficient of the ducts, which reveals the range of the wave attenuation generated by the short transient. The procedure is supposed to lead to the minimization of the objective function, that is, the difference between the measured and estimated values of the hydraulic parameters. Initially, attempts were made to determine the internal roughness of a conduit based on network analysis under steady-state flow conditions, but the significant limitations of this approach did not yield the expected results. Pioneers in this field, [PERSON] and [PERSON] [56], were the first to implement the inverse transient analysis (ITA) method, which consists in estimating the roughness coefficient on the basis of recording pressure values at selected points in the water supply network. Subsequently, [PERSON] and [PERSON] [57] incorporated the formation of short-term transients into the above methodology. TA, in contrast to ITA, consists of estimating the hydraulic parameters of the water supply network based on its characteristics (known roughness coefficients, material and length of pipes). [PERSON], [PERSON], and [PERSON] reversed the meaning of TA; based on known recorded pressures and flow rates, they attempted to determine the internal roughness of the pipelines by implementing an algorithm that minimizes the Levenberg-Marquardt objective function (LM) [58]. [PERSON] et al. [59] were among the first to implement methods based on hydraulic shock transition wave analysis at a semi-technical (rather than laboratory) scale. The propagation speed of the hydraulic shock wave between two sensors was analyzed. The authors implemented the inverse transient solver (ITS), which is an optimization algorithm that minimizes the sum of the squares of the differences between the observed and simulated hydraulic parameter values. The study also used a system for the detection of water main failures along with the estimation of the magnitude of uncontrolled discharge using a machine learning process [60]. The phenomenon of the appearance of the negative pressure wave (NPW) was interpreted using methods such as support vector (SVM), k-nearest neighbors (k-NN), Gaussian mixture model (GMM), and naive Bayes classifier (NBC). They pointed out the problem that too much data is created by traditional methods and is not properly interpreted later because its time-consuming analysis is too expensive.