A mathematical investigation on the invariance problem of some hydraulic indices

Highlights：

• Through mathematics, the paper aims to bring attention to the general problems of invariance in hydraulic engineering.

• Section 3 presents a mathematical-like formalization of a water network and provides the change formulas for the fundamental energy paprameters.

• As an explicit case, considered two widely used resilience indices, they turn out to be non-invariant in a PDA approach.

• In addition to numerical calculations and simulations, the mathematical reasons for their non-invariance are investigated.

• Two new invariant resilience indices, which modify one of those considered, are presented as an example of mathematical solutions in a new specific framework.

摘要

•Through mathematics, the paper aims to bring attention to the general problems of invariance in hydraulic engineering.•Section 3 presents a mathematical-like formalization of a water network and provides the change formulas for the fundamental energy paprameters.•As an explicit case, considered two widely used resilience indices, they turn out to be non-invariant in a PDA approach.•In addition to numerical calculations and simulations, the mathematical reasons for their non-invariance are investigated.•Two new invariant resilience indices, which modify one of those considered, are presented as an example of mathematical solutions in a new specific framework.

论文关键词：Mathematical models,Invariance problems,Linear algebra,Hadamard and scalar product,Water distribution networks,Local performance indices,Resilience indices

论文评审过程：Received 2 April 2020, Revised 25 August 2020, Accepted 5 October 2020, Available online 3 November 2020, Version of Record 11 July 2021.