Uncertainty Quantification

We developed a comprehensive Uncertainty Quantification (UQ) framework capable of modeling both aleatory and epistemic uncertainties. Additionally, the application propagates mixed uncertainties through the implementation of Non-Intrusive Polynomial Chaos (NIPC) methods. NIPC has been shown to be both an efficient and accurate technique for quantifying uncertainties.

The following NIPC methodologies have been implemented:

  • Point-collocation NIPC
  • Sampling-based NIPC
  • Quadrature-based NIPC

In an effort to address the “curse of dimensionality,” as the number of independent random variables of a given system increases, sensitivity analysis coupled with a dimensional reduction capability have been integrated within the framework. Quantifying your system’s uncertainty.Sensitivity techniques include the computation of the L2-norms and L∞ -norms based on finite differencing at local sample points. The UQ framework also implements a sensitivity technique which approximates the global sensitivities by computing the contribution of variance for each independent random variable using local sensitivity information. Non-linear global sensitivity analysis is achieved by performing a variance-based decomposition to compute the Sobol indices.