## Global sensitivity and uncertainty analysis (GSUA)

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Global sensitivity and uncertainty analysis (GSUA) of dynamical and static systems using variance-based and OAT methods

Updated 02 May 2022

The GSUA Toolbox implements uncertainty, and global and local (OAT) sensitivity analysis of dynamical and static models. The toolbox only needs the following information (see examples):
• A mathematical model in a Simulink or m-file with some simple special structure. The models defined the factors into the vector x. The toolbox includes several models in several formats.
• A m-file with these data: 1) a cell with Np factor names (they are necessary to a good analysis), 2) a (2xNp) matrix with nominal values in the first row and uncertainty percent in the second row, 3) a description of the model (optional).
In the dynamical case the toolbox compute uncertainty and sensitivity plots for two functions:
• Vectorial output or time response y(t). Plots: 1) uncertainty plot as a time response (the nominal or experimental time output is highlighted), 2) plot of vectorial first-order sensitivity indices which depend on time, 3) plot of vectorial total sensitivity indices which depend on time.
• Scalar characteristic ys obtained from time response. Examples: squared error (adjust to a nominal or experimental time response), peak time, rise time, settling time, settling or final value, overshoot, etc. (it is possible to include manually other scalar characteristics). So, with the sensitivity analysis is possible to analyze the effect of every factor in some time output characteristic. Plots: 4) scalar first-order sensitivity indices for the scalar output using pie or bar plots, 5) scalar total sensitivity indices for the scalar output using pie or bar plots, 6) scatter plots (show the posible dependence between output and each factor).
For static models (simple mathematical functions) the toolbox compute uncertainty and sensitivity plots for two functions
• Scalar output y = f(x1,x2,...). Plots: 1) uncertainty plot as a histogram plot which shows how the output varies with changes on factors, 2) scalar first-order sensitivity indices for the scalar output using pie or bar plots, 3) scalar total sensitivity indices for the scalar output using pie or bar plots.
• Scalar characteristic ys obtained from y. Example: squared error (adjust to a nominal or experimental value). Plots: 4) scalar first-order sensitivity indices for the scalar output using pie or bar plots, 5) scalar total sensitivity indices for the scalar output using pie or bar plots, 6) scatter plots (show the posible dependence between output and each factor).

### Cite As

Carlos M. Velez S. (2022). Global sensitivity and uncertainty analysis (GSUA) (https://www.mathworks.com/matlabcentral/fileexchange/47758-global-sensitivity-and-uncertainty-analysis-gsua), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2021b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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