This paper presents an optimization methodology to calibrate the nodal demand in the model of water supply distribution systems. The matrix analysis has been carried out to get the sensitive coefficients matrix for the model of water distribution systems. Singular value decomposition is applied to calculate search director of optimization by solving the sensitive coefficients matrix, which is more efficient than the finite-difference method. Two cases are used to show the performance of this algorithm. The first case is a hypothetical water distribution network showing the calculation of the optimization vector. The second case is the application of real-life water distribution system in Hangzhou, China, which shows the determination of the cutoff singular value and the search step size in one-dimensional search. The calibrated model has been also validated using the measured data. The results have shown that the proposed algorithm is reliable and effective in real-time system.

Leak detection techniques based on Machine Learning (ML) models can assist or even replace manual work in leak detection operations in water distribution systems (WDSs). However, studies on leakage detection based on on-site leak signals are limited compared to studies on lab-scale leak detection. The on-site leak signals have stronger interference and randomness, while leak signals in the laboratory are relatively simpler. To better assist on-site leak detection operations, the present paper develops and compares three ML-based models. For this purpose, many on-site tests were carried out, and tens of thousands of sets of on-site leak detection signals were collected. More than 6000 sets of these signals were marked and the signal features were extracted and analyzed from a statistical point of view. It was found that features such as the main frequency, the spectral roll-off rate, the spectral flatness, and one-dimensional (1-D) Mel Frequency Cepstrum Coefficient (MFCC) could well distinguish the leakage signals from non-leakage signals. After training the decision tree model, the performances of the random forest and Adaboost models were thoroughly compared. It was found that the false positive rates of the three models were 9.80%, 8.27% and 7.35%, all lower than 10%. In particular, the Adaboost model had the lowest false positive rate of 7.35%. The recall rate of the random forest and Adaboost models were 100% and 99.52%.

Pipe bursting is a serious problem for water supply systems. We propose a two-step burst detection and localization method for a long-distance water transportation pipeline. First, we use the Dempster–Shafer theory, an effective inference method for processing uncertain information, and combine two risk functions to identify a pipe burst. Then we identify the location of the burst point using a hydraulic model. The method is prototyped on a transportation pipeline in Guangzhou, China and tested with one-year historical records. The detection system correctly identified all the bursts and the alarm rate is acceptable for the system inspectors (average: two alarms/month). The burst location is identified within the acceptable limits of accuracy.

The leakage detection of a water distribution system (WDS) needs the support of a large number of field data. This paper collected over 6800 leak detection signals from cast iron pipelines used in a WDS. We found that 3280 signals indicated leakage, and the remaining indicated no leakage. The characteristics of the signals were extracted and analyzed from three perspectives: the central frequency of the power spectrum, the spectral roll-off rate, and the spectral flatness. Significant statistical distributions were found. The central frequencies of the leakage signals followed the normal distribution, and their spectral roll-off rates demonstrated the Burr distribution; the Birnbaum–Saunders distribution could describe the spectral flatness of the signals. Based on these characteristics, the recognition rate of the ML model for leak detection was improved. The Random Forest model was used to classify the leakage detection signals. The recall rate was 100%, and the false positive rate was 8.27%.

The true principal factors for the diurnal water-demand pattern of urban water are often difficult to identify using traditional rough-set algorithms because the demand pattern is usually affected by many factors that are uncertain and hard to quantify. An improved attribute-reduction algorithm based on the cumulative weighting coefficient was proposed to solve this problem. The weighting coefficient was determined by the result of the variable precision rough-set algorithm. To discuss the consecutive curves with mathematical tools, an improved fuzzy c-mean (FCM) algorithm was proposed to discretize the diurnal water-demand pattern spatially. The proposed algorithms were then used to analyze the principal factors of the diurnal water-demand pattern in the city of Hangzhou, China. The results show that the improved attribute-reduction algorithm is capable of distinguishing the false attribute from the dynamic reduction sets, and the fuzzy c-mean algorithm is an effective and feasible method of solv...

Water level simulation for complex water river networks is complex, and existing forecasting models are mainly used for single-channel rivers. In this paper, we present a new data assimilation model based on the ensemble Kalman filter (EnKF) for accurate water level simulation in complex river networks. The EnKF-based data model was tested on simulated water level data from a river network hydrodynamic model and optimized through parameter analysis. It was then applied to a real mountainous single-channel river and plain river network and compared with a data assimilation model based on the extended Kalman filter (EKF). The results showed that the EnKF-based model, with a medium ensemble sample size of 100–150, normal observation noise of 0.0001–0.01 m, and a high standard deviation of 0.01–0.1 m, outperformed the EKF-based model, with a 49% reduction in simulation errors, a 45% reduction in calculation cost, and a 43% reduction in filtering time. Furthermore, the EnKF-based data assimilation model predicted the water level in the plain river network better than the mountainous single-channel river. Around 5 to 8 h were required for data assimilation; afterwards, the model could make accurate predictions covering 20 to 30 h. The EnKF-based data assimilation model offers a potential solution for water level predictions in river networks.