Difference between revisions of "Sensitivity Analysis"
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where ''c'' is the ''n''-vector of species concentrations, ''α'' is the ''m''-vector of systems parameters (which can include the initial conditions ''c''<sup>0</sup>), and ''t'' (time) is the variable of integration. | where ''c'' is the ''n''-vector of species concentrations, ''α'' is the ''m''-vector of systems parameters (which can include the initial conditions ''c''<sup>0</sup>), and ''t'' (time) is the variable of integration. | ||
| − | The local sensitivities ∂''c''/∂''α<sub>j</sub>'' are calculated via finite difference approximations | + | The local unscaled sensitivities ∂''c''/∂''α<sub>j</sub>'' are calculated via finite difference approximations |
:: [[File:DAE-models-Sensitivity-Analysis-sa2.png]] | :: [[File:DAE-models-Sensitivity-Analysis-sa2.png]] | ||
where ''c<sub>ss</sub>''(''α<sub>j</sub>'') and ''c<sub>ss</sub>''(''α<sub>j</sub>''+Δ''α<sub>j</sub>'') correspond to the solutions of the algebraic systems ''f''(''c'', ''α<sub>j</sub>'') = 0 and ''f''(''c'', ''α<sub>j</sub>''+Δ''α<sub>j</sub>'') = 0 respectively. | where ''c<sub>ss</sub>''(''α<sub>j</sub>'') and ''c<sub>ss</sub>''(''α<sub>j</sub>''+Δ''α<sub>j</sub>'') correspond to the solutions of the algebraic systems ''f''(''c'', ''α<sub>j</sub>'') = 0 and ''f''(''c'', ''α<sub>j</sub>''+Δ''α<sub>j</sub>'') = 0 respectively. | ||
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| + | The matrix of scaled sensitivities is calculated by multiplying ∂''c''/∂''α<sub>j</sub>'' and the normalization factor ''α<sub>j</sub>''/''c<sub>ss</sub>''(''α<sub>j</sub>''). | ||
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==== References ==== | ==== References ==== | ||
Revision as of 16:32, 12 March 2019
- Analysis title
Sensitivity Analysis
- Provider
- Institute of Systems Biology
- Class
SensitivityAnalysis- Plugin
- biouml.plugins.modelreduction (Model reduction plug-in)
Description
The method calculates sensitivities associated with the steady state of the purely temporal system
where c is the n-vector of species concentrations, α is the m-vector of systems parameters (which can include the initial conditions c0), and t (time) is the variable of integration.
The local unscaled sensitivities ∂c/∂αj are calculated via finite difference approximations
where css(αj) and css(αj+Δαj) correspond to the solutions of the algebraic systems f(c, αj) = 0 and f(c, αj+Δαj) = 0 respectively.
The matrix of scaled sensitivities is calculated by multiplying ∂c/∂αj and the normalization factor αj/css(αj).
References
- H Rabitz, M Kramer, D Dacol, "Sensitivity analysis in chemical kinetics". Annu. Rev. of Phys. Chem., 34:419-461.
