Geodesic
Numerical leak detection in a pipeline network of complex structure with unsteady flow
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12, pp. 1966-1982

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An inverse problem for a pipeline network of complex loopback structure is solved numerically. The problem is to determine the locations and amounts of leaks from unsteady flow characteristics measured at some pipeline points. The features of the problem include impulse functions involved in a system of hyperbolic differential equations, the absence of classical initial conditions, and boundary conditions specified as nonseparated relations between the states at the endpoints of adjacent pipeline segments. The problem is reduced to a parametric optimal control problem without initial conditions, but with nonseparated boundary conditions. The latter problem is solved by applying first-order optimization methods. Results of numerical experiments are presented. 
@article{ZVMMF_2017_57_12_a3,
     author = {K. R. Aida-zade and Y. R. Ashrafova},
     title = {Numerical leak detection in a pipeline network of complex structure with unsteady flow},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1966--1982},
     publisher = {mathdoc},
     volume = {57},
     number = {12},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_12_a3/}
}
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K. R. Aida-zade; Y. R. Ashrafova. Numerical leak detection in a pipeline network of complex structure with unsteady flow. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12, pp. 1966-1982. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_12_a3/