First- and Second-Order Sensitivities of Steady-State Solutions to Water Distribution Systems
First-order approximations have been used with some success for criticality analysis; sensitivity analysis of physical networks, such as water distribution systems; and uncertainty propagation of model parameters. Certain limitations have been reported regarding the accuracy of the results, particul...
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MDPI AG
2024-09-01
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| Series: | Engineering Proceedings |
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| Online Access: | https://www.mdpi.com/2673-4591/69/1/165 |
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| author | Olivier Piller Sylvan Elhay Jochen W. Deuerlein Angus R. Simpson |
| author_facet | Olivier Piller Sylvan Elhay Jochen W. Deuerlein Angus R. Simpson |
| author_sort | Olivier Piller |
| collection | DOAJ |
| description | First-order approximations have been used with some success for criticality analysis; sensitivity analysis of physical networks, such as water distribution systems; and uncertainty propagation of model parameters. Certain limitations have been reported regarding the accuracy of the results, particularly when non-linearity is dominant. In this paper, we show how to efficiently derive the first- and second-order sensitivities with respect to variation in their parameters. This makes it possible to improve the first-order estimate when necessary. The method is illustrated on a small example system. |
| format | Article |
| id | doaj-art-0b6f6b3c71e94d86b4232ca13cc25c37 |
| institution | OA Journals |
| issn | 2673-4591 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Engineering Proceedings |
| spelling | doaj-art-0b6f6b3c71e94d86b4232ca13cc25c372025-08-20T02:11:13ZengMDPI AGEngineering Proceedings2673-45912024-09-0169116510.3390/engproc2024069165First- and Second-Order Sensitivities of Steady-State Solutions to Water Distribution SystemsOlivier Piller0Sylvan Elhay1Jochen W. Deuerlein2Angus R. Simpson3INRAE, AQUA Division, UR ETTIS, 50 Av. de Verdun, F-33612 Cestas, FranceSchool of Computer and Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, AustraliaSchool of Architecture and Civil Engineering, University of Adelaide, Adelaide, SA 5005, AustraliaSchool of Architecture and Civil Engineering, University of Adelaide, Adelaide, SA 5005, AustraliaFirst-order approximations have been used with some success for criticality analysis; sensitivity analysis of physical networks, such as water distribution systems; and uncertainty propagation of model parameters. Certain limitations have been reported regarding the accuracy of the results, particularly when non-linearity is dominant. In this paper, we show how to efficiently derive the first- and second-order sensitivities with respect to variation in their parameters. This makes it possible to improve the first-order estimate when necessary. The method is illustrated on a small example system.https://www.mdpi.com/2673-4591/69/1/165sensitivitiesSchur complementlinear equationssparse matrixsteady state: demand-driven modelingpressure-driven modeling |
| spellingShingle | Olivier Piller Sylvan Elhay Jochen W. Deuerlein Angus R. Simpson First- and Second-Order Sensitivities of Steady-State Solutions to Water Distribution Systems Engineering Proceedings sensitivities Schur complement linear equations sparse matrix steady state: demand-driven modeling pressure-driven modeling |
| title | First- and Second-Order Sensitivities of Steady-State Solutions to Water Distribution Systems |
| title_full | First- and Second-Order Sensitivities of Steady-State Solutions to Water Distribution Systems |
| title_fullStr | First- and Second-Order Sensitivities of Steady-State Solutions to Water Distribution Systems |
| title_full_unstemmed | First- and Second-Order Sensitivities of Steady-State Solutions to Water Distribution Systems |
| title_short | First- and Second-Order Sensitivities of Steady-State Solutions to Water Distribution Systems |
| title_sort | first and second order sensitivities of steady state solutions to water distribution systems |
| topic | sensitivities Schur complement linear equations sparse matrix steady state: demand-driven modeling pressure-driven modeling |
| url | https://www.mdpi.com/2673-4591/69/1/165 |
| work_keys_str_mv | AT olivierpiller firstandsecondordersensitivitiesofsteadystatesolutionstowaterdistributionsystems AT sylvanelhay firstandsecondordersensitivitiesofsteadystatesolutionstowaterdistributionsystems AT jochenwdeuerlein firstandsecondordersensitivitiesofsteadystatesolutionstowaterdistributionsystems AT angusrsimpson firstandsecondordersensitivitiesofsteadystatesolutionstowaterdistributionsystems |