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Comparison of global and local sensitivity techniques for rate constants determined using complex reaction mechanisms
Author(s) -
Scire James J.,
Dryer Frederick L.,
Yetter Richard A.
Publication year - 2001
Publication title -
international journal of chemical kinetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.341
H-Index - 68
eISSN - 1097-4601
pISSN - 0538-8066
DOI - 10.1002/kin.10001
Subject(s) - monte carlo method , sensitivity (control systems) , nonlinear system , polynomial , nonlinear regression , statistics , mathematics , statistical physics , chemistry , regression analysis , mathematical analysis , physics , quantum mechanics , electronic engineering , engineering
Many rate constant measurements, including some “direct” measurements, involve fitting a complex reaction mechanism to experimental data. Two techniques for estimating the error in such measurements were compared. In the first technique, local first‐order elementary sensitivities were used to rapidly estimate the sensitivity of the fitted rate constants to the remaining mechanism parameters. Our group and others have used this technique for error estimation and experimental design. However, the nonlinearity and strong coupling found in reaction mechanisms make verification against globally valid results desirable. Here, the local results were compared with analogous importance‐sampled Monte Carlo calculations in which the parameter values were distributed according to their uncertainties. Two of our published rate measurements were examined. The local uncertainty estimates were compared with Monte Carlo confidence intervals. The local sensitivity coefficients were compared with coefficients from first and second‐degree polynomial regressions over the whole parameter space. The first‐order uncertainty estimates were found to be sufficiently accurate for experimental design, but were subject to error in the presence of higher order sensitivities. In addition, global uncertainty estimates were found to narrow when the quality of the fit was used to weight the randomly distributed points. For final results, the global technique was found to provide efficient, accurate values without the assumptions inherent in the local analysis. The rigorous error estimates derived in this way were used to address literature criticism of one of the studies discussed here. Given its efficiency and the variety of problems it can detect, the global technique could also be used to check local results during the experimental design phase. The global routine, coded using SENKIN, can easily be extended to different types of data, and therefore can serve as a valuable tool for assessing error in rate constants determined using complex mechanisms. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 784–802, 2001