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Global sensitivity analysis is now established as a powerful approach fordetermining the key random input parameters that drive the uncertainty of modeloutput predictions. Yet the classical computation of the so-called Sobol'indices is based on Monte Carlo simulation, which is not affordable whencomputationally expensive models are used, as it is the case in mostapplications in engineering and applied sciences. In this respect metamodelssuch as polynomial chaos expansions (PCE) and Gaussian processes (GP) havereceived tremendous attention in the last few years, as they allow one toreplace the original, taxing model by a surrogate which is built from anexperimental design of limited size. Then the surrogate can be used to computethe sensitivity indices in negligible time. In this chapter an introduction toeach technique is given, with an emphasis on their strengths and limitations inthe context of global sensitivity analysis. In particular, Sobol' (resp. totalSobol') indices can be computed analytically from the PCE coefficients. Incontrast, confidence intervals on sensitivity indices can be derivedstraightforwardly from the properties of GPs. The performance of the twotechniques is finally compared on three well-known analytical benchmarks(Ishigami, G-Sobol and Morris functions) as well as on a realistic engineeringapplication (deflection of a truss structure).

Metamodel-based sensitivity analysis: Polynomial chaos expansions and Gaussian processes