Sensitivity analysis with correlated inputs: comparison of indices for the linear case.

International audienceThe objective of a global sensitivity analysis is to provide indices to rank the importance of each and every system inputs when considering the impact on a given system output. This paper discusses few of the methods proposed throughout the literature when dealing with a linear model for which part or all the input variable can not be considered independent. The aim is here to review methods from the late eighties in order to compare them to more recent developments, by investigating their underlying hypothesis, cost (in term of resources usage) and results. This paper focuses on the case where no assumption on the knowledge of the probability density functions, assuming that the analysis can be done from a provided sample, without the use of refined techniques which would require a dedicated surrogate model generation. After an introduction of the general problem, as often discussed in the independent approach, a review of solutions not sorely relying on the variance decomposition is presented, along with their underlying hypothesis. A protocol is proposed, based on a statistical approach relying on random correlation matrix generation, to test and compare all methods with an increasing complexity, step-by-step procedure. Finally, dependencies with respect to parameters defining the problem, such as the input space size, the sample size, the nature of the input laws are tested before drawing conclusions on the methods and their usefulness