An extended Marquardt-type procedure for fitting error-in-variables models
The paper presents a simple derivation of the method of fitting nonlinear algebraic models where all variables are subject to error and improves the numerical efficiency of the algorithm. Including a known procedure for equilibrating balance equations and factorizing the weighting matrix, the classi...
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| Published in | Computers & chemical engineering Vol. 11; no. 1; pp. 37 - 43 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Elsevier Ltd
1987
Elsevier |
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| Abstract | The paper presents a simple derivation of the method of fitting nonlinear algebraic models where all variables are subject to error and improves the numerical efficiency of the algorithm. Including a known procedure for equilibrating balance equations and factorizing the weighting matrix, the classical Gauss-Marquardt method of estimating parameters in nonlinear models is shown to handle also the error-in-variables model, thereby extending the efficiency and robustness of Marquardt's compromise to this slightly more involved case. |
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| AbstractList | The paper presents a simple derivation of the method of fitting nonlinear algebraic models where all variables are subject to error and improves the numerical efficiency of the algorithm. Including a known procedure for equilibrating balance equations and factorizing the weighting matrix, the classical Gauss-Marquardt method of estimating parameters in nonlinear models is shown to handle also the error-in-variables model, thereby extending the efficiency and robustness of Marquardt's compromise to this slightly more involved case. |
| Author | Valkó, P. Vajda, S. |
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| Cites_doi | 10.1002/aic.690280519 10.2307/1267784 10.2307/1270208 10.1002/kin.550170107 10.1002/aic.690260208 10.1016/0009-2509(81)80061-9 10.2307/1267519 10.2307/1266919 10.1137/0707011 10.1002/aic.690280409 10.1016/0009-2509(80)85096-2 10.2307/1266984 10.2307/1270465 |
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| Keywords | Non linear equation Algebraic equation Error Parameter estimation Mathematical model Chemical engineering |
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| References_xml | – volume: 15 start-page: 233 year: 1973 end-page: 241 ident: BIB4 article-title: The estimation of parameters in nonlinear implicit models publication-title: Technometrics – volume: 7 start-page: 157 year: 1970 end-page: 186 ident: BIB8 article-title: Comparison of gradient methods for the solution of nonlinear parameter estimation problems publication-title: SIAM Jl numer. Analysis – volume: 2 year: 1973 ident: BIB1 publication-title: The Advanced Theory of Statistics – year: 1977 ident: BIB18 publication-title: The Properties of Gases and Liquids – volume: 14 start-page: 71 year: 1972 end-page: 76 ident: BIB7 article-title: On an iterative procedure for estimating functions when both variables are subject to error publication-title: Technometrics – reference: L. 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Engng Sci. doi: 10.1016/0009-2509(81)80061-9 – year: 1977 ident: 10.1016/0098-1354(87)80004-2_BIB18 – volume: 2 year: 1973 ident: 10.1016/0098-1354(87)80004-2_BIB1 – volume: 18 start-page: 161 year: 1976 ident: 10.1016/0098-1354(87)80004-2_BIB12 article-title: Implicit multifunctional nonlinear regression analysis publication-title: Technometric doi: 10.2307/1267519 – ident: 10.1016/0098-1354(87)80004-2_BIB19 – volume: 61 start-page: 8 issue: 55 year: 1965 ident: 10.1016/0098-1354(87)80004-2_BIB6 article-title: Adjustment of experimental data publication-title: Chem. Engng Prog. Symp. Ser. – volume: 14 start-page: 71 year: 1972 ident: 10.1016/0098-1354(87)80004-2_BIB7 article-title: On an iterative procedure for estimating functions when both variables are subject to error publication-title: Technometrics doi: 10.2307/1266919 – volume: 7 start-page: 157 year: 1970 ident: 10.1016/0098-1354(87)80004-2_BIB8 article-title: Comparison of gradient methods for the solution of nonlinear parameter estimation problems publication-title: SIAM Jl numer. Analysis doi: 10.1137/0707011 – year: 1974 ident: 10.1016/0098-1354(87)80004-2_BIB9 – volume: 28 start-page: 580 year: 1982 ident: 10.1016/0098-1354(87)80004-2_BIB17 article-title: Statistical estimation of parameters in vapor—liquid equilibrium publication-title: AIChE Jl doi: 10.1002/aic.690280409 – volume: 38 start-page: 1067 year: 1980 ident: 10.1016/0098-1354(87)80004-2_BIB20 article-title: On the rectification of measurement errors for complex chemical plants publication-title: Chem. Engng Sci. doi: 10.1016/0009-2509(80)85096-2 – volume: 15 start-page: 233 year: 1973 ident: 10.1016/0098-1354(87)80004-2_BIB4 article-title: The estimation of parameters in nonlinear implicit models publication-title: Technometrics doi: 10.2307/1266984 – volume: 57 start-page: 44 year: 1961 ident: 10.1016/0098-1354(87)80004-2_BIB5 article-title: Computer control II publication-title: Chem. Engng Prog. – year: 1970 ident: 10.1016/0098-1354(87)80004-2_BIB10 – volume: 27 start-page: 17 year: 1985 ident: 10.1016/0098-1354(87)80004-2_BIB14 article-title: Numerical methods for estimating parameters in nonlinear models with errors in variables publication-title: Technometrics doi: 10.2307/1270465 |
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| SubjectTerms | Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization Applied sciences Chemical engineering Exact sciences and technology |
| Title | An extended Marquardt-type procedure for fitting error-in-variables models |
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