A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics
We present a parameterized-background data-weak (PBDW) formulation of the variational data assimilation (state estimation) problem for systems modeled by partial differential equations. The main contributions are a constrained optimization weak framework informed by the notion of experimentally obse...
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| Format: | Article |
| Language: | en_US |
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Wiley Blackwell
2015
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| Online Access: | http://hdl.handle.net/1721.1/97702 https://orcid.org/0000-0001-7882-2483 https://orcid.org/0000-0002-8323-9054 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1826193788865871872 |
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| author | Maday, Yvon Patera, Anthony T. Yano, Masayuki Penn, James Douglass |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Maday, Yvon Patera, Anthony T. Yano, Masayuki Penn, James Douglass |
| author_sort | Maday, Yvon |
| collection | MIT |
| description | We present a parameterized-background data-weak (PBDW) formulation of the variational data assimilation (state estimation) problem for systems modeled by partial differential equations. The main contributions are a constrained optimization weak framework informed by the notion of experimentally observable spaces; a priori and a posteriori error estimates for the field and associated linear-functional outputs; weak greedy construction of prior (background) spaces associated with an underlying potentially high-dimensional parametric manifold; stability-informed choice of observation functionals and related sensor locations; and finally, output prediction from the optimality saddle in O(M[superscript 3) operations, where M is the number of experimental observations. We present results for a synthetic Helmholtz acoustics model problem to illustrate the elements of the methodology and confirm the numerical properties suggested by the theory. To conclude, we consider a physical raised-box acoustic resonator chamber: we integrate the PBDW methodology and a Robotic Observation Platform to achieve real-time in situ state estimation of the time-harmonic pressure field; we demonstrate the considerable improvement in prediction provided by the integration of a best-knowledge model and experimental observations; we extract, even from these results with real data, the numerical trends indicated by the theoretical convergence and stability analyses. |
| first_indexed | 2024-09-23T09:45:25Z |
| format | Article |
| id | mit-1721.1/97702 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:45:25Z |
| publishDate | 2015 |
| publisher | Wiley Blackwell |
| record_format | dspace |
| spelling | mit-1721.1/977022022-09-30T16:37:23Z A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics Maday, Yvon Patera, Anthony T. Yano, Masayuki Penn, James Douglass Massachusetts Institute of Technology. Department of Mechanical Engineering Patera, Anthony T. Penn, James Douglass Yano, Masayuki We present a parameterized-background data-weak (PBDW) formulation of the variational data assimilation (state estimation) problem for systems modeled by partial differential equations. The main contributions are a constrained optimization weak framework informed by the notion of experimentally observable spaces; a priori and a posteriori error estimates for the field and associated linear-functional outputs; weak greedy construction of prior (background) spaces associated with an underlying potentially high-dimensional parametric manifold; stability-informed choice of observation functionals and related sensor locations; and finally, output prediction from the optimality saddle in O(M[superscript 3) operations, where M is the number of experimental observations. We present results for a synthetic Helmholtz acoustics model problem to illustrate the elements of the methodology and confirm the numerical properties suggested by the theory. To conclude, we consider a physical raised-box acoustic resonator chamber: we integrate the PBDW methodology and a Robotic Observation Platform to achieve real-time in situ state estimation of the time-harmonic pressure field; we demonstrate the considerable improvement in prediction provided by the integration of a best-knowledge model and experimental observations; we extract, even from these results with real data, the numerical trends indicated by the theoretical convergence and stability analyses. Fondation Sciences Mathematiques de Paris United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613) United States. Office of Naval Research (Grant N00014-11-1-0713) SUTD-MIT International Design Centre 2015-07-07T16:55:48Z 2015-07-07T16:55:48Z 2014-08 2014-06 Article http://purl.org/eprint/type/JournalArticle 00295981 1097-0207 http://hdl.handle.net/1721.1/97702 Maday, Yvon, Anthony T. Patera, James D. Penn, and Masayuki Yano. “A Parameterized-Background Data-Weak Approach to Variational Data Assimilation: Formulation, Analysis, and Application to Acoustics.” Int. J. Numer. Meth. Engng 102, no. 5 (August 15, 2014): 933–965. https://orcid.org/0000-0001-7882-2483 https://orcid.org/0000-0002-8323-9054 https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1002/nme.4747 International Journal for Numerical Methods in Engineering Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Wiley Blackwell MIT web domain |
| spellingShingle | Maday, Yvon Patera, Anthony T. Yano, Masayuki Penn, James Douglass A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics |
| title | A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics |
| title_full | A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics |
| title_fullStr | A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics |
| title_full_unstemmed | A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics |
| title_short | A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics |
| title_sort | parameterized background data weak approach to variational data assimilation formulation analysis and application to acoustics |
| url | http://hdl.handle.net/1721.1/97702 https://orcid.org/0000-0001-7882-2483 https://orcid.org/0000-0002-8323-9054 https://orcid.org/0000-0002-2631-6463 |
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