Inverse Transient Method for Model Calibration and Leak Detection in a Polymeric Laboratory Pipe by a Nelder-mead Algorithm

This paper presents a technique for detecting leaks in polymeric pipelines, by combining the Inverse Transient Analysis (ITA) and Reflected Wave Method (RWM). The proposed method uses transient pressure waves, generated by a sudden closure of a valve, to locate and size a leak. The performance of the proposed algorithm has been tested on a High Density Polyethylene (HDPE) pipe installed at the Water Engineering Laboratory of the University of Perugia, Italy. Transient model takes into account the viscoelastic behavior of the pipe using the generalized Kelvin–Voigt model. Nelder-Mead algorithm has been used for the model calibration: the viscoelastic parameters as well as the unsteady friction decay coefficient have been determined by minimizing the differences between simulated pressure heads and experimental data in the case of intact pipe. The described procedure has been also applied to locate and size the leak in the case of a damaged pipe. The results show that ITA is reliable for leak sizing with a mean relative error of 5%; however, the leak location highly depends on the initial guess. For this reason, the ITA has been combined with RWM for localizing the leak: the actual position of the leak has been identified with a mean relative error of 7%.