Automating adjoint sensitivity analysis for multidisciplinary models involving partial differential equations Article Swipe
Ru Xiang
,
Sebastiaan P. C. van Schie
,
Luca Scotzniovsky
,
Jiayao Yan
,
David Kamensky
,
John T. Hwang
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.21203/rs.3.rs-4265983/v1
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.21203/rs.3.rs-4265983/v1
We present a general framework for incorporating partial differential equation (PDE)- based models into gradient-based optimization of multidisciplinary systems by integrating FEniCSx with the recently-developed Computational System Design Language (CSDL). CSDL is a domain specific language designed to facilitate adjoint sensitivity analysis multidisciplinary design optimization (MDO). We use CSDL’s abstractions to link together sub-models representing different disciplines, not all of which are necessarily modeled by PDEs. For the subsystems which are modeled by PDEs, we use FEniCSx to compute partial derivatives of problem residuals, which CSDL can combine with derivatives from other disciplines using the chain rule and the adjoint method. The development of this framework is motivated by the problem of optimizing designs of electric vertical takeoff and landing (eVTOL) aircraft where, due to the relative novelty of this class of vehicle, there is currently a large, unexplored design space. Predicting the performance of eVTOL aircraft requires PDE-based modeling of various sub-problems, including electric motors, composite shell structures, and thermoelasticity and electrochemistry of battery packs. For system-level analysis and optimization, these must be coupled to non-PDE components, such as low-fidelity aerodynamic models, geometric design tools, and lumped-parameter battery and circuit models. In this work, we demonstrate the modeling flexibility and efficiency of this framework through classic optimal control and topology optimization problems with known solutions, and also challenging eVTOL-related applications including shape optimization of an electric motor, and aeroelastic coupling for gust response of an eVTOL wing. Given the generality of this framework, we expect it to facilitate research on a wide-range of PDEconstrained MDO problems beyond eVTOL applications.
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- Type
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- Language
- en
- Landing Page
- https://doi.org/10.21203/rs.3.rs-4265983/v1
- OA Status
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- References
- 41
- Related Works
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- OpenAlex ID
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https://openalex.org/W4400344728Canonical identifier for this work in OpenAlex
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https://doi.org/10.21203/rs.3.rs-4265983/v1Digital Object Identifier
- Title
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Automating adjoint sensitivity analysis for multidisciplinary models involving partial differential equationsWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
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2024-07-03Full publication date if available
- Authors
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Ru Xiang, Sebastiaan P. C. van Schie, Luca Scotzniovsky, Jiayao Yan, David Kamensky, John T. HwangList of authors in order
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https://doi.org/10.21203/rs.3.rs-4265983/v1Publisher landing page
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goldOpen access status per OpenAlex
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https://doi.org/10.21203/rs.3.rs-4265983/v1Direct OA link when available
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Sensitivity (control systems), Multidisciplinary approach, Partial differential equation, Applied mathematics, Computer science, Mathematics, Mathematical optimization, Mathematical analysis, Engineering, Political science, Electronic engineering, LawTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.and | 98, 119, 160, 162, 170, 187, 190, 201, 210, 217, 229 |
| abstract_inverted_index.are | 62, 71 |
| abstract_inverted_index.can | 87 |
| abstract_inverted_index.due | 124 |
| abstract_inverted_index.for | 6, 232 |
| abstract_inverted_index.not | 58 |
| abstract_inverted_index.the | 24, 68, 95, 99, 110, 126, 143, 198, 240 |
| abstract_inverted_index.use | 48, 76 |
| abstract_inverted_index.CSDL | 31, 86 |
| abstract_inverted_index.also | 218 |
| abstract_inverted_index.from | 91 |
| abstract_inverted_index.gust | 233 |
| abstract_inverted_index.into | 14 |
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| abstract_inverted_index.rule | 97 |
| abstract_inverted_index.such | 179 |
| abstract_inverted_index.this | 105, 130, 194, 204, 243 |
| abstract_inverted_index.with | 23, 89, 214 |
| abstract_inverted_index.Given | 239 |
| abstract_inverted_index.PDEs, | 74 |
| abstract_inverted_index.PDEs. | 66 |
| abstract_inverted_index.based | 12 |
| abstract_inverted_index.chain | 96 |
| abstract_inverted_index.class | 131 |
| abstract_inverted_index.eVTOL | 146, 237, 259 |
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| abstract_inverted_index.shape | 223 |
| abstract_inverted_index.shell | 158 |
| abstract_inverted_index.there | 134 |
| abstract_inverted_index.these | 172 |
| abstract_inverted_index.using | 94 |
| abstract_inverted_index.which | 61, 70, 85 |
| abstract_inverted_index.wing. | 238 |
| abstract_inverted_index.work, | 195 |
| abstract_inverted_index.(MDO). | 46 |
| abstract_inverted_index.(PDE)- | 11 |
| abstract_inverted_index.Design | 28 |
| abstract_inverted_index.System | 27 |
| abstract_inverted_index.beyond | 258 |
| abstract_inverted_index.design | 44, 140, 185 |
| abstract_inverted_index.domain | 34 |
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| abstract_inverted_index.large, | 138 |
| abstract_inverted_index.models | 13 |
| abstract_inverted_index.motor, | 228 |
| abstract_inverted_index.packs. | 166 |
| abstract_inverted_index.space. | 141 |
| abstract_inverted_index.tools, | 186 |
| abstract_inverted_index.where, | 123 |
| abstract_inverted_index.(CSDL). | 30 |
| abstract_inverted_index.(eVTOL) | 121 |
| abstract_inverted_index.FEniCSx | 22, 77 |
| abstract_inverted_index.adjoint | 40, 100 |
| abstract_inverted_index.battery | 165, 189 |
| abstract_inverted_index.circuit | 191 |
| abstract_inverted_index.classic | 207 |
| abstract_inverted_index.combine | 88 |
| abstract_inverted_index.compute | 79 |
| abstract_inverted_index.control | 209 |
| abstract_inverted_index.coupled | 175 |
| abstract_inverted_index.designs | 114 |
| abstract_inverted_index.general | 4 |
| abstract_inverted_index.landing | 120 |
| abstract_inverted_index.method. | 101 |
| abstract_inverted_index.modeled | 64, 72 |
| abstract_inverted_index.models, | 183 |
| abstract_inverted_index.models. | 192 |
| abstract_inverted_index.motors, | 156 |
| abstract_inverted_index.non-PDE | 177 |
| abstract_inverted_index.novelty | 128 |
| abstract_inverted_index.optimal | 208 |
| abstract_inverted_index.partial | 8, 80 |
| abstract_inverted_index.present | 2 |
| abstract_inverted_index.problem | 83, 111 |
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| abstract_inverted_index.takeoff | 118 |
| abstract_inverted_index.through | 206 |
| abstract_inverted_index.various | 152 |
| abstract_inverted_index.CSDL’s | 49 |
| abstract_inverted_index.Language | 29 |
| abstract_inverted_index.aircraft | 122, 147 |
| abstract_inverted_index.analysis | 42, 169 |
| abstract_inverted_index.coupling | 231 |
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| abstract_inverted_index.electric | 116, 155, 227 |
| abstract_inverted_index.equation | 10 |
| abstract_inverted_index.language | 36 |
| abstract_inverted_index.modeling | 150, 199 |
| abstract_inverted_index.problems | 213, 257 |
| abstract_inverted_index.relative | 127 |
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| abstract_inverted_index.research | 250 |
| abstract_inverted_index.response | 234 |
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| abstract_inverted_index.topology | 211 |
| abstract_inverted_index.vehicle, | 133 |
| abstract_inverted_index.vertical | 117 |
| abstract_inverted_index.PDE-based | 149 |
| abstract_inverted_index.composite | 157 |
| abstract_inverted_index.currently | 136 |
| abstract_inverted_index.different | 56 |
| abstract_inverted_index.framework | 5, 106, 205 |
| abstract_inverted_index.geometric | 184 |
| abstract_inverted_index.including | 154, 222 |
| abstract_inverted_index.motivated | 108 |
| abstract_inverted_index.Predicting | 142 |
| abstract_inverted_index.efficiency | 202 |
| abstract_inverted_index.facilitate | 39, 249 |
| abstract_inverted_index.framework, | 244 |
| abstract_inverted_index.generality | 241 |
| abstract_inverted_index.optimizing | 113 |
| abstract_inverted_index.residuals, | 84 |
| abstract_inverted_index.solutions, | 216 |
| abstract_inverted_index.sub-models | 54 |
| abstract_inverted_index.subsystems | 69 |
| abstract_inverted_index.unexplored | 139 |
| abstract_inverted_index.wide-range | 253 |
| abstract_inverted_index.aerodynamic | 182 |
| abstract_inverted_index.aeroelastic | 230 |
| abstract_inverted_index.challenging | 219 |
| abstract_inverted_index.components, | 178 |
| abstract_inverted_index.demonstrate | 197 |
| abstract_inverted_index.derivatives | 81, 90 |
| abstract_inverted_index.development | 103 |
| abstract_inverted_index.disciplines | 93 |
| abstract_inverted_index.flexibility | 200 |
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| abstract_inverted_index.sensitivity | 41 |
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| abstract_inverted_index.abstractions | 50 |
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| abstract_inverted_index.differential | 9 |
| abstract_inverted_index.disciplines, | 57 |
| abstract_inverted_index.low-fidelity | 181 |
| abstract_inverted_index.optimization | 16, 45, 212, 224 |
| abstract_inverted_index.representing | 55 |
| abstract_inverted_index.system-level | 168 |
| abstract_inverted_index.Computational | 26 |
| abstract_inverted_index.applications. | 260 |
| abstract_inverted_index.eVTOL-related | 220 |
| abstract_inverted_index.incorporating | 7 |
| abstract_inverted_index.optimization, | 171 |
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| abstract_inverted_index.electrochemistry | 163 |
| abstract_inverted_index.lumped-parameter | 188 |
| abstract_inverted_index.thermoelasticity | 161 |
| abstract_inverted_index.multidisciplinary | 18, 43 |
| abstract_inverted_index.recently-developed | 25 |
| abstract_inverted_index.<title>Abstract</title> | 0 |
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| corresponding_author_ids | https://openalex.org/A5098876107 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 6 |
| corresponding_institution_ids | https://openalex.org/I36258959 |
| citation_normalized_percentile.value | 0.22389084 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |