Since the 1990s, pressure waves propagating in pressurized pipes during a transient event have been re-evaluated both in the laboratory and in real systems as a way to obtain information about location and size of leaks. However, a systematic analysis of the obtained results has not been offered yet in the literature. In this paper, a review of the available experimental data concerning the use of transient tests for leak identification in pressurized pipe systems is presented. The selected data are examined with regard to the main features (categories) influencing the transient response of a leaky pipe system: layout, modality of transient generation, material, diameter, pre-transient pressure and flow condition, inserted pressure wave, and leak characteristics. Moreover, for each of such categories, possible specific issues to address for future research are proposed.

Stable and accurate reconstruction of pollutant transport is a crucial and challenging problem, including the inverse problem of identifying pollution sources and physical coefficients and the forward problem of inferring pollutant transport. Governed by advection, diffusion, and reaction processes, this transport phenomenon can be represented by the advection–diffusion–reaction (ADR) equation. In this paper, the physics-informed neural networks (PINNs) are applied to solve the forward and inverse ADR problems. To further enhance the stability and accuracy of the original PINN, two improvements are developed. The first adjusts the orthogonal grid (OG) point selection method and the other suggests adding an additional regulation function, namely, first derivative constraint (FDC). The new method is referred to as OG-PINN with FDC. To verify the effectiveness of the proposed method, five forward and inverse ADR problems are solved, and the results are compared with the analytical and reference solutions. For forward problems, the improved method can solve various ADR problems accurately and stably. For inverse problems, the ability of the OG-PINN for model parameter learning and initial distribution prediction is demonstrated and analyzed. The former gives the missed physical information in the ADR equation from the data, and the latter is used to trace the source of pollutants. The proposed method is quantitatively reliable for investigating various advection–diffusion–reaction processes.

This paper addresses leak detection in the presence of measurement noise using the inverse transient method (ITM). The unknown leak parameters are determined by optimizing a merit function, which fits the numerically modeled pressures to measurements. Traditionally, the fitting is accomplished by a least-square (LS) objective function that minimizes the L2 distance between the model and data. However, in practical problems where the environment is noisy, the minimum L2 distance may result in some fictitious leaks. This paper proposes an alternative objective function, known as matched-filter (MF) in the literature, which is expected to produce a more robust localization in a noisy environment because it maximizes the signal-to-noise ratio (SNR). This function is then compared with the conventional LS approach by assessment of leak-detection accuracy. It was proved that the MF estimator has smaller mean square error of leak localization than LS when signals have high noise level ($\mathrm{SNR}\le 3\mathrm{dB}$ ). For a low noise level, the two estimators converge to the same results. The conclusions were supported by numerical and experimental case studies.