Full-field sensitivity analysis through dimension reduction and probabilistic surrogate models

Computational mechanics models often are compromised by uncertainty in their governing parameters, especially when the operating environment is incompletely known. Computational sensitivity analysis of a spatially distributed process to its governing parameters therefore is an essential, but often costly, step in uncertainty quantification. A sensitivity analysis method is described which features probabilistic surrogate models developed through equitable sampling of the parameter space, proper orthogonal decomposition (POD) for compact representations of the process’ variability from an ensemble of realizations, and cluster-weighted models of the joint probability density function of each POD coefficient and the governing parameters. Full-field sensitivities, i.e. sensitivities at every point in the computational grid, are computed by analytically differentiating the conditional expected value function of each POD coefficient and projecting the sensitivities onto the POD basis. Statistics of the full-field sensitivities are estimated by sampling the surrogate model throughout the parameter space. Major benefits of this method are: (1) the sensitivities are computed analytically and efficiently from regularized surrogate models, and (2) the conditional variances of the surrogate models may be used to estimate the statistical uncertainty in the sensitivities, which provides a basis for pursuing more data to improve the model. Synthetic examples and a physical example involving near-ground sound propagation through a refracting atmosphere are presented to illustrate the properties of the surrogate models and how full-field sensitivities and their uncertainties are computed.