## 4 New Classification of Methods for the Detection of Water Network Operating Conditions
### Software Methods (Indirect)
#### 4.2.3 Flow Rate and Pressure Signal Processing  
The limitations of methods analyzing acoustic signals mobilize the scientific community to select newer techniques of the processing and use of time series of parameters of the state of network operations--the flow rate and/or pressure. One of them is flow rate and pressure signal processing. The analyses performed under laboratory and field conditions are presented in Appendix A. Tables 1 and 2 summarize the more important publications presenting the results of studies in which software analyses of controlled signals were applied for the purpose of assessing the operating conditions of water supply networks.  
to the influence of hourly, daily, weekly, and seasonal variability of water consumption, these solutions require long-term measurements. Methods that use archival measurements to estimate their future distributions are called autoregressive integrated moving average (ARIMA) [49] or autoregressive integrated moving average with exogenous variables ARIMAX) models. The significant role of seasonal variability in the application of predictive methods was demonstrated by [PERSON] and [PERSON] [50] in their analyses of water flow rates. It was proved that the omission of seasonal variation can generate false alarms. The main disadvantages of the developed failure detection method are the omission of already existing leaks in the network and the initial assumption of their absence. Moreover, the failure information is provided to the network manager with a time delay.  
The CUSUM algorithm, compared to heuristic methods, was also implemented in the study of [PERSON] et al. [19]. The created solution was tested with nine real water supply network failures and compared to the results obtained by heuristic methods. The model created by the authors was able to forecast water consumption volumes for the next 48 h with a 15 min time step. Each difference between the predicted value and the observed one was treated as a failure (taking into account the 5% error boundary).  
The future of anomalous condition detection combined with predictive methods is the water demand forecasting model (WDFM) based on the hydraulic model of the water supply network and parameter estimation through, among others, the Kalman Filter [51]. The WDFM is updated with actual inventoried measurements with a 15 min time step and is subject to multiple linear regression (MLR) [52]. The results show that the WDFM system identified the most leakage (80-100%) for the largest failures.  
There are also a number of solutions based on historical water flow rates recorded during real failures. Cluster analysis is used to interpret them [53]. By knowing the coordinates of the position of hydraulic parameters during failures in space, the level of risk of uncontrolled leaks in the future can be determined. [PERSON] et al. [53] demonstrated that cluster analysis can be applied to pre-process data and locate them in two-dimensional space.  
[PERSON] et al. [54] investigated the flow rates of a selected DMA zone to detect the failure of a water supply network. The methodology used, cluster analysis, allowed for the determination of the distance between the means of the measurements, the Euclidean distance, and the density of the distribution. The results indicated that false positive alarms accounted for 0.41-0.76% of the measurements and true positives accounted for 71.43%.