# Sensitivity

Sensitivity analysis (SA) is the study of how the variation (uncertainty) in the output of a mathematical model can be apportioned, qualitatively or quantitatively, to different sources of variation in the input of a model [1].

 This article may require cleanup to meet quality standards. Please improve this article if you can.. It should be more general. It seems to be applicable only to the FE

## Introduction

Finite Element models usually involve a large set of input variables whose values are often imprecisely known. When dealing with problems of this type, it is important to understand the relationship between the input variables and the output. The input parameters can be uncertain quantities modelled by probability distributions, design parameters or parameters describing the distributions. The output quantity is the response of interest, like e.g. the response quantities obtained by deterministic structural analysis (displacement, stress, acceleration, etc.), the variance of these quantities or also the reliability in terms of failure probabilities or reliability index.

Sensitivity analysis studies these relationships and identifies the most significant factors or variables affecting the results of the model. It analyses which parameters contribute most to the output variability and which parameters are insignificant and can be removed from the final model. In addition, it provides a means for analysis if and which groups of parameters interact with each other. Sensitivity analysis becomes therefore an indispensable tools for the design process, such as for uncertainty assessment, design exploration, design optimization, model calibration and model validation.

Sensitivity analysis can be classified into local and global methods. Local methods explore the change of the quantity of interest around a certain reference point, e.g. around the nominal settings. Global methods, on the other hand, study the effect of changes of the input parameters in the entire range of the input space. A comprehensive overview on sensitivity analysis can be found in e.g. [2][3][4][5][6][7][8][9][10][11].

## References

1. Saltelli, Andrea. 2008, Sensitivity Analysis, Wiley (December 31, 2008) ISBN 978-0470743829
2. I.M. Sobol. Sensitivity estimates for nonlinear mathematical models . Mathematical modelling and computational experiments. 1:407-414, 1993.
3. T. Homma and A. Saltelli. Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering and System Safety . 52:1-17, 1996.
4. M.D. McKay. Evaluating Prediction Uncertainty, NUREG/CR-6311, LA-12915-MS, Los Alamos National Laboratory, Prepared for U.S. Nuclear Regulatory Commission, 1995.
5. M.D. Morris. Factorial Sampling Plans for Preliminary Computational Experiments, Technometrics , 33(2):161-177, 1991.
6. C.B. Storlie, L.P. Swiler, J.C. Helton, C.J. Sallaberry. Implementation and Evaluation of Nonparametric Regression Procedures for Sensitivity Analysis of Computationally Demanding Models, Sandia Report SAND2008-6570 , 2008.
7. I.M. Sobol and S. Kucherenko,. Derivative based global sensitivity measures and their link with global sensitivity indices, Mathematics and Computers in Simulation . 79(10): 3009-3017, 2009.
8. A. Saltelli, S. Tarantola, K. P.-S. Chan. A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output. Technometrics . 41(1): 39-56, 1999.
9. A. Saltelli. Making best use of model evaluations to compute sensitivity indices.Computer Physics Communications . 145: 280-297, 2002
10. M. Ratto, S. Tarantola and A. Saltelli. Sensitivity analysis in model calibration: GSA-GLUE approach. Computer Physics Communications . 136: 212-224. 2001.
11. A. Saltelli, Sensitivity Analysis for Importance Assessment. Risk Analysis . 22(3): 579-590, 2002.