Difference between revisions of "Sensitivity Analysis"

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;Analysis title
 
;Analysis title
:[[File:DAE-models-Sensitivity-Analysis-icon.png]] Sensitivity Analysis
+
:[[File:Sensitivity-Analysis-icon.png]] Sensitivity Analysis
 
;Provider
 
;Provider
 
:[[Institute of Systems Biology]]
 
:[[Institute of Systems Biology]]
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The method calculates sensitivities associated with the steady state of the purely temporal system
 
The method calculates sensitivities associated with the steady state of the purely temporal system
  
:: [[File:DAE-models-Sensitivity-Analysis-sa1.png]]
+
:: [[File:Sensitivity-Analysis-sa1.png]]
  
 
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.
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The local sensitivities ∂''c''/∂''α<sub>j</sub>'' are calculated via finite difference approximations
 
The local sensitivities ∂''c''/∂''α<sub>j</sub>'' are calculated via finite difference approximations
  
:: [[File:DAE-models-Sensitivity-Analysis-sa2.png]]
+
:: [[File: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.

Revision as of 12:32, 16 May 2013

Analysis title
File:Sensitivity-Analysis-icon.png Sensitivity Analysis
Provider
Institute of Systems Biology
Plugin
biouml.plugins.modelreduction (Model reduction plug-in)

Description

The method calculates sensitivities associated with the steady state of the purely temporal system

File:Sensitivity-Analysis-sa1.png

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 sensitivities ∂c/∂αj are calculated via finite difference approximations

File:Sensitivity-Analysis-sa2.png

where css(αj) and css(αjαj) correspond to the solutions of the algebraic systems f(c, αj) = 0 and f(c, αjαj) = 0 respectively.

References

  1. H Rabitz, M Kramer, D Dacol, "Sensitivity analysis in chemical kinetics". Annu. Rev. of Phys. Chem., 34:419-461.
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