Global sensitivity and uncertainty analysis (GSUA)

Global sensitivity and uncertainty analysis (GSUA) of dynamical and static systems using variance-based and OAT methods
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Updated 11 Oct 2022

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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. In the case of a Simulink Model, it is neccesarry some simple special structure: use a "To Workspace" connected to the output with sample time, Variable name "yout" and "Structure with time" format. The parameters of models are defined with variable x. In the case of a m-file (ss model or ode model), see examples for information about the configuration of file.
  • A m-file with these data: 1) a description of the model, 2) a cell with Np factor names (they are necessary to a good analysis), 3) a (2xNp) matrix with nominal values in the first row and uncertainty percent in the second row, 4) name of file with the model (Simulink model or m-file model).
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. (2024). 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 R2022b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
4.5

It is easier to give the Simulink model in the right form: use a "To Workspace" connected to the output with sample time, Variable name "yout" and "Structure with time" format.

4.1

- Minor changes
- More examples

4.0

- Simplified environment
- OAT local method implemented
- Mathematical model using Simulink file, ODE file or state-space format (for linear systems)
- Live script as the main program
- More examples

3.0

(1) A main script is included to better application of toolbox. (2) A user manual is included.

2.8.0.0

All functions were optimized in three functions. Bar plots were included. All plots were improved. Sensitivity indices are shown for temporal responses and for scalar minimum square error (MSE) function. The estimated processing time is displayed.

2.1.0.0

The remaining time is displayed.

2.0.0.0

Other sensitivity methods are included (Sobol, Jansen, Saltelli).
The examples are better organized.

1.4.0.0

Integration as a toolbox.

1.3.0.0

New functions and examples are included.

1.2.0.0

Correction of pendulum example.

1.1.0.0

Correction of function description.

1.0.0.0