GSA Report

Global Sensitivity Analysis Report

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. This experiments shows the first, second and total order sensitivities of the provided features (input) and visualises them in an interactive way. The different sensitivity algorithms can provide additional insight and information in the underlying process.

Experiment: SA
Started: 2023-10-04 15:03:33

Number of parameters: 5
Showing the top 5 parameters
Random Forest mean R² score over 3 folds: 0.5227423370867968

Print report

Function Landscape

Interactive surface plot of a slice (using a Random Forest model) with sheet_thickness on the X axis and r on the Y axis. All other parameters are set to the center of their range.

Morris analysis results

The elementary effects calculated by the Morris [1] algorithm. On the left the covariance plot with mu_star, the absolute of the mean elementary effect, against sigma, the standard deviation of the elementary effect. Points highlighted are the parameters with the highest mu_star and these are also shown below with the confidence of the algorithm.

SHAP

A summary plot of the SHAP values across the whole dataset. * Note that the shap values are calculated using the trained Random Forest model and not using the real data set, as this is computationally more efficient.

Sobol analysis results

Sobol [2] total and first order sensitivity indexes on the left for the top parameters. The second order sensitivity indexes are shown on the right for each pair of parameters. Both total and second order sensitivities are visualized in the network plot on the right.

Sobol Network Plot

A visualisation of both first and second order sensitivities using Sobol analysis. The size of each node is the total sensitivity, the blue halo is the confidence and the edges between the nodes display the second order sensitivities.

View full resolution

Delta

The Delta Moment-Independent Measure [3] uses a Latin Hypercube sampling to calculate the delta and S1 (first order sensitivity) for each parameter.

RBD Fast

The S1 results of the RBD-FAST - Random Balance Designs Fourier Amplitude Sensitivity Test [4].

Pawn

The minimum, median and maximum results from the PAWN method [5]. The PAWN method is a moment-independent approach to GSA. It is described as producing robust results at relatively low sample sizes.

References

[1] Morris, M.D., 1991. Factorial Sampling Plans for Preliminary Computational Experiments. Technometrics 33, 161–174. https://doi.org/10.1080/00401706.1991.10484804

[2] Campolongo, F., Saltelli, A., Cariboni, J., 2011. From screening to quantitative sensitivity analysis. A unified approach. Computer Physics Communications 182, 978–988. https://doi.org/10.1016/j.cpc.2010.12.039

[3] Borgonovo, E. (2007). “A new uncertainty importance measure.” Reliability Engineering & System Safety, 92(6):771-784, doi:10.1016/j.ress.2006.04.015.

[4] S. Tarantola, D. Gatelli and T. Mara (2006) “Random Balance Designs for the Estimation of First Order Global Sensitivity Indices”, Reliability Engineering and System Safety, 91:6, 717-727 https://doi.org/10.1016/j.ress.2005.06.003

[5] Pianosi, F., Wagener, T., 2015. A simple and efficient method for global sensitivity analysis based on cumulative distribution functions. Environmental Modelling & Software 67, 1–11. https://doi.org/10.1016/j.envsoft.2015.01.004

Cite our paper

Checkout our Github page for more information.