Water hammer mitigation via PDE-constrained optimization
This paper considers an optimal boundary control problem for fluid pipelines with terminal valve control. The goal is to minimize pressure fluctuation during valve closure, thus mitigating water hammer effects. We model the fluid flow by two coupled hyperbolic PDEs with given initial conditions and...
| Main Authors: | , , , , |
|---|---|
| Format: | Journal Article |
| Published: |
Pergamon
2015
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/42038 |
| _version_ | 1848756308713406464 |
|---|---|
| author | Chen, T. Xu, C. Lin, Qun Loxton, Ryan Teo, Kok Lay |
| author_facet | Chen, T. Xu, C. Lin, Qun Loxton, Ryan Teo, Kok Lay |
| author_sort | Chen, T. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper considers an optimal boundary control problem for fluid pipelines with terminal valve control. The goal is to minimize pressure fluctuation during valve closure, thus mitigating water hammer effects. We model the fluid flow by two coupled hyperbolic PDEs with given initial conditions and a boundary control governing valve actuation. To solve the optimal boundary control problem, we apply the control parameterization method to approximate the time-varying boundary control by a linear combination of basis functions, each of which depends on a set of decision parameters. Then, by using variational principles, we derive formulas for the gradient of the objective function (which measures pressure fluctuation) with respect to the decision parameters. Based on the gradient formulas obtained, we propose a gradient-based optimization method for solving the optimal boundary control problem. Numerical results demonstrate the capability of optimal boundary control to significantly reduce pressure fluctuation. |
| first_indexed | 2025-11-14T09:10:08Z |
| format | Journal Article |
| id | curtin-20.500.11937-42038 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:10:08Z |
| publishDate | 2015 |
| publisher | Pergamon |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-420382017-09-13T16:11:54Z Water hammer mitigation via PDE-constrained optimization Chen, T. Xu, C. Lin, Qun Loxton, Ryan Teo, Kok Lay Hyperbolic PDEs Control parameterization Water hammer Variational method Optimal boundary control Method of lines This paper considers an optimal boundary control problem for fluid pipelines with terminal valve control. The goal is to minimize pressure fluctuation during valve closure, thus mitigating water hammer effects. We model the fluid flow by two coupled hyperbolic PDEs with given initial conditions and a boundary control governing valve actuation. To solve the optimal boundary control problem, we apply the control parameterization method to approximate the time-varying boundary control by a linear combination of basis functions, each of which depends on a set of decision parameters. Then, by using variational principles, we derive formulas for the gradient of the objective function (which measures pressure fluctuation) with respect to the decision parameters. Based on the gradient formulas obtained, we propose a gradient-based optimization method for solving the optimal boundary control problem. Numerical results demonstrate the capability of optimal boundary control to significantly reduce pressure fluctuation. 2015 Journal Article http://hdl.handle.net/20.500.11937/42038 10.1016/j.conengprac.2015.08.008 Pergamon fulltext |
| spellingShingle | Hyperbolic PDEs Control parameterization Water hammer Variational method Optimal boundary control Method of lines Chen, T. Xu, C. Lin, Qun Loxton, Ryan Teo, Kok Lay Water hammer mitigation via PDE-constrained optimization |
| title | Water hammer mitigation via PDE-constrained optimization |
| title_full | Water hammer mitigation via PDE-constrained optimization |
| title_fullStr | Water hammer mitigation via PDE-constrained optimization |
| title_full_unstemmed | Water hammer mitigation via PDE-constrained optimization |
| title_short | Water hammer mitigation via PDE-constrained optimization |
| title_sort | water hammer mitigation via pde-constrained optimization |
| topic | Hyperbolic PDEs Control parameterization Water hammer Variational method Optimal boundary control Method of lines |
| url | http://hdl.handle.net/20.500.11937/42038 |