Applying dimensional and similarity analyses to the propagation of uncertainties of a laser simulator

Trivial reductions of dimensionality in the propagation of uncertainties: a physical example

“…m , b, K d m is transformed through very simple transformations into a reduced set of just two random variables , x. This is what we call trivial reductions in dimensionality versus the reductions obtained through much more sophisticated techniques like dimensional analysis; see Mira et al (2001) and Langhaar (1951).…”

“…; Fðt u ÞÞ is smaller. This idea is equally essential when we have obtained the reduced set by more sophisticated techniques as in Mira et al (2001).…”

“…In O' Hagan et al (1998), the propagation of uncertainties is carried out through a simplified, less expensive version of the original code. Mira et al (2001) have shown how reducing the dimensionality of the set of input variables through the dimensional and similarity analyses of the physics literature (Langhaar, 1951) improves the efficiency of variance reduction techniques. In this article, we apply the same idea to a reduction of dimensionality of the input space obtained in a much more inmediate, less sophisticated way, which we call here 'trivial reductions of dimensionality': it frequently occurs that in the differential equations which describe the behaviour of the system, some coefficients appear as elementary functions of a number of, let us say, original coefficients, such that, for physical reasons related to expert judgement, the uncertainty of the problem has been expressed in terms of probability distributions for these original coefficients.…”