Inverse Transient Analysis in Pipe Networks

TLDR

Modern monitoring devices can cheaply extract large amounts of pressure and flow data from water‑distribution systems, enabling transient analysis, time‑lagged calculations, inverse calculations, and event detection, with inverse calculations providing calibration and leak or unauthorized‑use detection. Efficient inverse calculations rely on an adjoint solution that yields gradient and Jacobian data, from which a Hessian is derived for Levenberg‑Marquardt parameter adjustment to minimize head discrepancies, while also providing sensitivities to assess solution quality.

Abstract

Modern monitoring devices can inexpensively extract a huge amount of data from water‐distribution systems through measurements of pressure (and sometimes flows). These data can be used in algorithms for transient analysis, time‐lagged calculations, inverse calculations, and event detection to continuously determine the calibration and the general state of health of the distribution system. The last three calculations depend on the first. The most useful of those three is the inverse calculation, which can calibrate while determining leaks or unauthorized use. A key to efficient calculation is the adjoint solution of the system (generally easier than the transient analysis) to find gradient data and a Jacobian matrix. These are used to find a Hessian matrix, which is used in the Levenberg‐Marquardt method to adjust parameters so as to minimize the difference between calculated and measured heads. The adjoint method is also used to compute sensitivities, which are valuable in judging the quality of the solution.