## 4 New Classification of Methods for the Detection of Water Network Operating Conditions
### Time Domain Analysis
Therefore, they focused on processing the information at the point of acquisition. The machine learning and inference module is \"asleep\" under normal network operating conditions and is only stimulated when a potential failure occurs. The naive NBC had the highest accuracy (94.8%) in the failure detection situation. This study debuted the combination of WNS sensors with optimization methods and classifiers that process data in situ. Frequency Domain Analysis  
Methods based on the analysis of short-term transients in the frequency domain, that is, the frequency response method (FRM), consist of the analysis of the pressure transition waveform distribution in the frequency domain. These solutions are reduced to the observation of dominant frequencies, which are included in the failure time series. Results obtained via FRM depend largely on the shape of the generated waveform and the location of the sensor. The need to remove measurement noise from signals recorded during short transients was demonstrated by [PERSON] et al. [61]. In their study, the authors determined the so-called adaptive threshold, which defines the boundary between the normal and failure operation of the water supply network. To obtain the de-noised time series, wavelet transform was used, which gives satisfactory results when processing a signal loaded with the white noise of Gaussian distribution. The mean squared error (MSE) between the estimated values and the estimators was analyzed. The TSWA algorithm was compared with the back-propagation neural network BPNN) method based on the LM algorithm. Finally, the smallest MSE error was obtained for the proposed solution (at 0.01097). [PERSON] [16] demonstrated the usefulness of analyzing the pressure signal in the frequency domain using Hilbert transform (HT) and Hilbert-Huang transform (HHT). The process of locating the failure was done using the decomposition of the signal into empirical modes, known as empirical mode decomposition (EMD). HT and HHT allowedfor the analysis of the instantaneous nature of the pressure wave for experimental and model data. Successively, the data were filtered through EMD. The signal analysis approach of an artificially created transition wave in the FRM frequency domain was implemented in the study by [PERSON] et al. [62]. They mainly interpreted the wavelet coefficient and Lipschitz exponent, which contain information about the nature of the signal and can be useful for classification processes. When a leakage occurs, the analysis of the extremes of the wavelet of the hydraulic shock transition can be detected by applying a bandpass filter. It is observable when it is possible to change the frequency of a given signal. However, this methodology is effectively applicable when the signal is isolated and free of noise. Identification of a failure signal allows for the observation of changes in the values of the wavelet coefficients at each step of its decomposition. The feature extraction (FE) method for evaluating the occurrence of a water supply network failure from a pressure signal was applied by [PERSON] et al. [63]. The time series were clustered into two groups--failure measurements (LEAK) and normal measurements (NOLEAK). The results showed that during uncontrolled water outflow, a more frequent occurrence of low frequencies for energy and high frequencies for enthalpy can be observed. The zero crossing count (ZCC) for the emergency signal is characterized by fewer transitions through zero. In analyzing the distribution of the decomposed signal, it can be seen that low frequencies reach samples mainly in the absence of leakage. [PERSON] et al. [64] dealt with factors affecting the shape and weakening of pressure transition waves, thus proving that dynamic friction and gas cavitation phenomena are the most common causes. Modeling transition wave processes is a complex activity, even for simple duct sections.