A Review of Interval Field Approaches for Uncertainty Quantification in Numerical Models

B-spline based interval field decomposition method

“…where f i (X) denotes the i-th output generated by f (X). The exact bounds for the output interval vector Y I are generally difficult to obtain and usually demand global optimisation methods [17]. However, the interval analysis often suffers from the over-conservatism that the interval radius of the output is usually larger than the true interval radius.…”

“…Numerous interval field modelling methods have been developed and can be broadly categorised into the following three groups: explicit formulation, Karhunen-Loéve (K-L) expansion based formulation and convex descriptors based formulation [17]. The explicit formulation, to which the original form of the interval field method belongs, can be expressed as the superposition of spatially dependent basis functions, scaled by independent interval scalars as indicators of the magnitude of uncertainty.…”

Uncertainty propagation with B-spline based interval field decomposition method in boundary value problems

“…These methods typically require the eigenpair of the knowledge-based correlation functions, often adopting a set of truncated terms to reduce the dimension of the problem at the cost of restricting the source of uncertainties to a few interval coordinates. For an extensive overview of interval field formulations, readers can refer to [24].…”