Global sensitivity analysis in high dimensions with PLS-PCE

Global sensitivity analysis is a central part of uncertainty quantification with engineering models. Variance-based sensitivity measures such as Sobol’ and total-effect indices are amongst the most popular and commonly used tools for global sensitivity analysis. Multiple sampling-based estimators of these measures are available, but they often come at considerable computational cost due to the large number of required model evaluations. If the computational model is expensive to evaluate, these approaches are quickly rendered infeasible. An alternative is the use of surrogate models, which reduce the computational cost per sample significantly. This contribution focuses on a recently introduced latent-variable-based polynomial chaos expansion (PCE) based on partial least squares (PLS) analysis, which is particularly suitable for high-dimensional problems. We develop an efficient way of computing variance-based sensitivities with the PLS-PCE surrogate. By back-transforming the surrogate model from its latent variable space-basis to the original input variable space-basis, we derive analytical expressions for the sought sensitivities. These expressions depend on the surrogate model coefficients exclusively. Thus, once the surrogate model is built, the variance-based sensitivities can be computed at negligible computational cost and no additional sampling is required. The accuracy of the method is demonstrated with two numerical experiments of an elastic truss and a thin steel plate.