3.6 Step V: Evaluation of Convergence, Accuracy and Efficiency of Approximation

Once the coefficients of the polynomial chaos expansion are obtained using one of the methods described above, the convergence of the approximation is determined through comparison with the results from a higher order approximation. The next order polynomial chaos expansion is used, and the process for the estimation of unknown coefficients is repeated. If the estimates of pdfs of output metrics agree closely, the expansion is assumed to have converged, and the higher order approximation is used to calculate the pdfs of output metrics. If the estimates differ significantly, yet another series approximation, of the next order, is used, and the entire process is repeated until convergence is reached.

In the present work, the accuracy of the approximation is evaluated by comparing the results from SRSM with the results obtained from Monte Carlo analyses. This verification is performed to ensure that the approximation converges to the true distribution. The efficiency of the SRSM is further evaluated by comparing the number of simulations required for the SRSM method, with the number required for a Latin Hypercube sampling method.