Review of Uncertainty Quantification of Measurement and Computational Modeling in EMC Part II: Computational Uncertainty

Assessing Vircators’ Reliability Through Uncertainty and Sensitivity Analyses Using a Surrogate Model

“…As pointed out in [29], the PCE and SCT have demonstrated their high precision and efficiency, comparatively to MC methods. However, due to the tensor product in the relations ((5)-(7)), the techniques are facing the curse of dimensionality that avoids an optimum use of them when increasing N for a given truncation order n. Indeed, for the sake of simplicity, the equation 5is obtained for 1-RV case; obviously, increasing the number of RVs introduces tensor product (with respect to summation product) as evoked in [30].…”

“…Although, random variables are most likely associate with the resulting of random function and/or processes (so uncertain by definition), the terms random variables (RVs) in this work is referring only to, somewhat imprecisely, uncertain inputs. Assessing the influence of uncertain variables is of utmost importance for a large diversity of complex physical scenarios [29]. In this framework, Vircator modelling and experiments require a particular care since their performance (here mainly considering the output power level P and the radiating frequency f vc ) are subject to uncertain behaviour.…”

“…Thus, m and n will be defined following various statistical assumptions; for the sake of consistency regarding available information given by standards, in this example only Normal distributions will be considered, but the principles of the proposed methodology remain applicable to a variety of statistical laws (e.g. see details in [29]). Xiu [30] properly introduced the flexibility of spectral expansions for uncertainty quantification.…”

“…The precise assessment of such quantities (i.e. mean trends: average and variance) may be obtained at different computing costs including a large diversity of techniques [29], [35]). In the following, we will provide alternative measures (importance factors) for S i .…”

“…sions exists when dealing with stochastic surrogate modelling. In this framework, polynomial chaos expansion (PCE) and stochastic collocation techniques mainly differ by the choice of their polynomial expansion [29] (for instance Hermite polynomials). Here, Lagrange polynomials L i were chosen (non-orthogonal polynomials but useful to simplify weight computations w i as expressed in the following equation).…”