Identification of Bayesian posteriors for coefficients of chaos expansions
This article is concerned with the identification of probabilistic characterizations of random variables and fields from experimental data. The data used for the identification consist of measurements of several realizations of the uncertain quantities that must be characterized. The random variable...
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| Veröffentlicht in: | Journal of computational physics 2010-05, Vol.229 (9), p.3134-3154 |
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| container_title | Journal of computational physics |
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| creator | Arnst, M. Ghanem, R. Soize, C. |
| description | This article is concerned with the identification of probabilistic characterizations of random variables and fields from experimental data. The data used for the identification consist of measurements of several realizations of the uncertain quantities that must be characterized. The random variables and fields are approximated by a polynomial chaos expansion, and the coefficients of this expansion are viewed as unknown parameters to be identified. It is shown how the Bayesian paradigm can be applied to formulate and solve the inverse problem. The estimated polynomial chaos coefficients are hereby themselves characterized as random variables whose probability density function is the Bayesian posterior. This allows to quantify the impact of missing experimental information on the accuracy of the identified coefficients, as well as on subsequent predictions. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed methodology. |
| doi_str_mv | 10.1016/j.jcp.2009.12.033 |
| format | Article |
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The data used for the identification consist of measurements of several realizations of the uncertain quantities that must be characterized. The random variables and fields are approximated by a polynomial chaos expansion, and the coefficients of this expansion are viewed as unknown parameters to be identified. It is shown how the Bayesian paradigm can be applied to formulate and solve the inverse problem. The estimated polynomial chaos coefficients are hereby themselves characterized as random variables whose probability density function is the Bayesian posterior. This allows to quantify the impact of missing experimental information on the accuracy of the identified coefficients, as well as on subsequent predictions. 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The data used for the identification consist of measurements of several realizations of the uncertain quantities that must be characterized. The random variables and fields are approximated by a polynomial chaos expansion, and the coefficients of this expansion are viewed as unknown parameters to be identified. It is shown how the Bayesian paradigm can be applied to formulate and solve the inverse problem. The estimated polynomial chaos coefficients are hereby themselves characterized as random variables whose probability density function is the Bayesian posterior. This allows to quantify the impact of missing experimental information on the accuracy of the identified coefficients, as well as on subsequent predictions. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed methodology.</description><subject>Aeroelastic stability</subject><subject>Approximation</subject><subject>Bayesian</subject><subject>Bayesian analysis</subject><subject>CHAOS THEORY</subject><subject>Computational techniques</subject><subject>Engineering Sciences</subject><subject>Engineering, computing & technology</subject><subject>Exact sciences and technology</subject><subject>Identification</subject><subject>Ingénierie mécanique</subject><subject>Ingénierie, informatique & technologie</subject><subject>Inverse problems</subject><subject>MATHEMATICAL METHODS AND COMPUTING</subject><subject>Mathematical methods in physics</subject><subject>Mathematics</subject><subject>Maximum likelihood</subject><subject>MAXIMUM-LIKELIHOOD FIT</subject><subject>Mechanical engineering</subject><subject>Mechanics</subject><subject>Physics</subject><subject>Polynomial chaos</subject><subject>POLYNOMIALS</subject><subject>PROBABILISTIC ESTIMATION</subject><subject>Probability</subject><subject>PROBABILITY DENSITY FUNCTIONS</subject><subject>Probability theory</subject><subject>Random variables</subject><subject>RANDOMNESS</subject><subject>Statistics</subject><subject>Stochastic inversion</subject><subject>STOCHASTIC PROCESSES</subject><subject>Uncertainty quantification</subject><subject>Validation</subject><issn>0021-9991</issn><issn>1090-2716</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kU9v1DAUxCMEEkvhA3CLhJDgkPCenX8Wp7YCWrQSFzhbzstz16s0DnZ2Rb89Dql65GTL-s14NJNlbxFKBGw-HcsjzaUAUCWKEqR8lu0QFBSixeZ5tgMQWCil8GX2KsYjAHR11e2y77cDT4uzjszi_JR7m1-ZB47OTPns48LB-RBz60NOnm3iXOLjytHB-Jjzn9lMMUnj6-yFNWPkN4_nRfbr65ef1zfF_se32-vLfUE1qKWoWtsTDiwVN31t64FYNW1bt8ZarkTdATLWUpm2byklNmQ6NfQGamRCK-RF9m7zTfGcjuQWpgP5aWJatEApparaRMmNGh3fsfahd_ostDduu5_GO21I96yFaDqNIDrRJNXHTXUwo56Duzfh4Z_m5nKv1zeApqsktmdM7IeNnYP_feK46HsXicfRTOxPUWPTopAoqiqhuKEUfIyB7ZM3gl7300ed9tPrfhqFTvslzftHexPJjDaYiVx8EqbUKAHqxH3eOE6dnx2HtRKeiAcX1kYG7_7zy1_wNK6z</recordid><startdate>20100501</startdate><enddate>20100501</enddate><creator>Arnst, M.</creator><creator>Ghanem, R.</creator><creator>Soize, C.</creator><general>Elsevier Inc</general><general>Elsevier</general><general>Academic Press</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><scope>VOOES</scope><scope>Q33</scope><scope>OTOTI</scope><orcidid>https://orcid.org/0000-0002-1083-6771</orcidid></search><sort><creationdate>20100501</creationdate><title>Identification of Bayesian posteriors for coefficients of chaos expansions</title><author>Arnst, M. ; Ghanem, R. ; Soize, C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c509t-47fbc1de39e6b5f5dce967757affe425801e1539a7b7c999aca89dba051ec1f23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Aeroelastic stability</topic><topic>Approximation</topic><topic>Bayesian</topic><topic>Bayesian analysis</topic><topic>CHAOS THEORY</topic><topic>Computational techniques</topic><topic>Engineering Sciences</topic><topic>Engineering, computing & technology</topic><topic>Exact sciences and technology</topic><topic>Identification</topic><topic>Ingénierie mécanique</topic><topic>Ingénierie, informatique & technologie</topic><topic>Inverse problems</topic><topic>MATHEMATICAL METHODS AND COMPUTING</topic><topic>Mathematical methods in physics</topic><topic>Mathematics</topic><topic>Maximum likelihood</topic><topic>MAXIMUM-LIKELIHOOD FIT</topic><topic>Mechanical engineering</topic><topic>Mechanics</topic><topic>Physics</topic><topic>Polynomial chaos</topic><topic>POLYNOMIALS</topic><topic>PROBABILISTIC ESTIMATION</topic><topic>Probability</topic><topic>PROBABILITY DENSITY FUNCTIONS</topic><topic>Probability theory</topic><topic>Random variables</topic><topic>RANDOMNESS</topic><topic>Statistics</topic><topic>Stochastic inversion</topic><topic>STOCHASTIC PROCESSES</topic><topic>Uncertainty quantification</topic><topic>Validation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Arnst, M.</creatorcontrib><creatorcontrib>Ghanem, R.</creatorcontrib><creatorcontrib>Soize, C.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><collection>Université de Liège - Open Repository and Bibliography (ORBI)</collection><collection>OSTI.GOV</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Arnst, M.</au><au>Ghanem, R.</au><au>Soize, C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Identification of Bayesian posteriors for coefficients of chaos expansions</atitle><jtitle>Journal of computational physics</jtitle><date>2010-05-01</date><risdate>2010</risdate><volume>229</volume><issue>9</issue><spage>3134</spage><epage>3154</epage><pages>3134-3154</pages><issn>0021-9991</issn><issn>1090-2716</issn><eissn>1090-2716</eissn><coden>JCTPAH</coden><abstract>This article is concerned with the identification of probabilistic characterizations of random variables and fields from experimental data. 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| subjects | Aeroelastic stability Approximation Bayesian Bayesian analysis CHAOS THEORY Computational techniques Engineering Sciences Engineering, computing & technology Exact sciences and technology Identification Ingénierie mécanique Ingénierie, informatique & technologie Inverse problems MATHEMATICAL METHODS AND COMPUTING Mathematical methods in physics Mathematics Maximum likelihood MAXIMUM-LIKELIHOOD FIT Mechanical engineering Mechanics Physics Polynomial chaos POLYNOMIALS PROBABILISTIC ESTIMATION Probability PROBABILITY DENSITY FUNCTIONS Probability theory Random variables RANDOMNESS Statistics Stochastic inversion STOCHASTIC PROCESSES Uncertainty quantification Validation |
| title | Identification of Bayesian posteriors for coefficients of chaos expansions |
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