Uncertainty Propagation — Monte Carlo Analysis
Studying the uncertainty propagation of a model is equivalent to approximating the PDF of the QoI. To construct the PDF of the QoI accurately, a large number of samples is required. Such an operation is very expensive and the analysis therefore uses the surrogate model. Both PCE and the GP model are used for uncertainty propagation. To approximate the PDF, the KDE method is used, in which density is formulated in terms of known kernel functions, which have the form
where Kh is a specified symmetric PDF. Here, the standard normal distribution is used, and h is a smoothing parameter termed the bandwidth.
By default, the Uncertainty Quantification Module uses Silverman’s rule for the smoothing parameter h. More details related to the KDE can be found in Ref. 12. In addition to the approximation of the probabilistic distribution, the confidence interval table of each QoI is computed. In this table, it gives the mean, maximum, minimum, and standard deviation of each QoI. It also computes the value of the QoI corresponding to different CDF levels. Such information can also serve as a lookup table to a rough estimate of finding the probability that a QoI is larger than a certain threshold.