Random Balance Design method

The Random Balance Design (RBD) method [25] allows the estimation or main effects (first order sensitivity indices). This means that such method can be used only for Factors Priorityzation (FP). The method adopts Satterthwaite’s application of random balance designs in regression problems, extending it to sensitivity analysis of model output for non-linear, non-additive models. The model input factors can have finite as well as infinite ranges. Since the method is easier to implement with respect to others available for global sensitivity analysis the computational cost of the analysis is significantly reduced. The RBD procedure combines Satterthwaite’s random balance designs with the Fourier Amplitude Sensitivity Test (FAST).
In the classic FAST method N design points are selected over a particular space-filling curve in the k-th dimensional input space, built as to explore each dimension (factor) with a different frequency {ω1,ω2,...,ωk}. A quite complex algorithm is used to set the frequencies such that they are free of interferences up to a given order M (usually M=6). The computational model is executed at each design point and the Fourier spectrum is calculated on the model output at specific frequencies {ωi,2ωi,...,i} to estimate the sensitivity index of factor Xi. The RBD method first selects N design points over a curve in the input space. Contrarily to FAST, the input space is explored using the same frequency ω, to avoid the use of the algorithm cited above. However, due to that, the curve is not space-filling but covers only a sub-set of the whole input space. Therefore, random permutations of the coordinates of such points are taken, to generate a set of scrambled points that cover the input space. The model is then evaluated at each design point. Subsequently, the model outputs are re-ordered such that the design points are in increasing order with respect to factor Xi. The Fourier spectrum is calculated on the model output at the frequency
ω and at its higher harmonics {ω,2ω,...,} and yields the estimate of the sensitivity index of factor Xi. The model outputs are re-ordered with respect to the other factors (and the Fourier spectra are calculated accordingly) to obtain all the other sensitivity indices.

IMPORTANT: the RBD method can be used only in tandem with the RBD sampling strategy i.e. with setMethodRandomBalanceDesign