Dynamic Analysis and Shape Sensing of Pipes Subjected to Water Hammer by the Inverse Finite Element Method

Pipe structures are commonly employed in modern industries. However, the transient pressure induced by water hammer leads to a high risk of structural damage, highlighting the importance of Structural Health Monitoring (SHM). The inverse Finite Element Method (iFEM) offers a way to reverse structural deformations based on a set of discrete strain data. In this paper, the water hammer phenomenon in a Reservoir-Pipe-Valve (RPV) system is investigated. The element iQS4 is adopted to reconstruct dynamic deformations for the pipe using iFEM. The water hammer resulting from an instantaneous closure of the valve can generate significant fluid pressure, leading to severe pipe vibrations. The vibration deformations can be monitored by iFEM. The maximum error of the pipe nodal displacement is below 3 % and the average error is below 2 % in the proposed several sensor location cases, even the mesh of iFEM is coarser than the FE model. Among the sparse sensor location cases, the X path which is suitable for Fiber Bragg Grating (FBG) sensors has the highest accuracy of the displacement reconstruction. The results reveal a promising prospect in the real-time monitoring based on iFEM for pipes.