Sensitivity analysis

Generality

Sensitivity analysis is a methodology used to characterize the variability part due to the different variability sources on the outputs' variability (Fig 1). This characterization can be in qualitative or in quantitative form depending on the sensitivity method chosen. Sometimes sensitivity analysis and uncertainty analysis applied the same approach like monte-carlo with the difference that SA focused more on the inputs rather on the outputs Fig 1.

  Fig 1 : Synopsis of the sensitivity analysis

Review on sensitivity analysis can be found in   Christopher,  Hamby, Iooss, Andrianandraina,…

Sensitivity analysis methods

SA methods can be classified in general according to two criteria. The first criterion is the way of how the method takes into account each input parameters.  Methods can be classified in two: local if it considers only few characteristics of the input parameters and global if it considers all characteristics (range of variation, probability distribution).  The second criterion is the type and characteristics of the results that the method provides.  There are two classes of methods: qualitative if the results cannot be used or interpreted in a measured way and quantitative if the results is related to the measure of the input parameters influence (Fig 2).

Fig 2 : Classification of the different sensitivity analysis methods

In general local methods need lower times than global methods and are used usually for screening. To obtain quantitative information on the influence of each parameter, global methods are more efficient. However global methods are in general time consuming. We propose in this conference paper a sensitivity method based on the local sensitivity analysis of Morris in order to approach the global sensitivity indices of Sobol.

Applications

Here are programs in python of the Sobol and Morris sensitivity analysis. For the Sobol method the script permits the computation of the first and total indices. For the Morris methods the script permits the computation of the three indices the Mean, the absolute value of the mean and the standard deviation of the elementary effects. Other approaches used for the calculation are included in these scripts like the bootstrap approach for the confidence interval calculation, the sampling approach.