Pumping operations represent a major cost for water utilities. The reduction of the pipe cross-sectional area due to defects such as blockages, partially closed valves, changes in wall thickness (bio-films, corrosion, tuberculation, material spalling, and deposition) impacts the pumping costs due to increased energy loss.

Some of our recent works show that the understanding of the phenomenon of wave frequency shifts in the fundamental (resonant) frequencies of the pipe system caused by blockages is an essential factor for improving the success and accuracy of TBDDM. These works also prove that the maximum and minimum frequency shifts are due to the physics of Bragg resonance.

  • Initial stage: the pressure, velocity, and energy of each wave mode are analyzed and the dispersion relations that link the fundamental wave frequencies of the blocked pipe systems to the unknown properties of the blockages (i.e., their number, size, and location) are investigated. Also, the Bragg resonance conditions are derived.

  • Later stage: efficient and robust blockage identification equations based on Bragg resonance conditions are developed. Such conditions provide explicit relations between maximum shift, minimum shift and the location and size of blockage and do not require any optimization procedure. As a result, a large reduction in computational time should be achieved and, at the same time, the problem of uniqueness in the identification solution is addressed.