Interval uncertainty propagation by a parallel Bayesian global optimization method

Application of interval field method to the stability analysis of slopes in presence of uncertainties

“…The algorithm predicts the probability distribution of the function values at any point based on the function values at a set of sampled points, which is achieved by Gaussian process regression. In this subsection, a Bayesian global optimization method that can simultaneously find the minimum and maximum values of the objective function is introduced (Dang et al, 2022). The formula for calculating the minimum value is exhibited in this section.…”

“…To reduce the computational efforts required by heuristic global optimization algorithms (e.g., genetic algorithm), Kriging-assisted global optimization techniques have been investigated in the context of interval uncertainty propagation (Catallo, 2004). In this direction, a Bayesian global optimization is also presented to obtain the lower and upper response bounds of a computationally expansive model subject to multiple interval variables (Dang et al, 2022).…”

Structural reliability analysis: A Bayesian perspective

“…To illustrate the practical applicability of the proposed method, a transmission tower structure subject to horizontal loads (Fig. 8) is considered as the last example, which is modified from [39]. The structure is modelled as a three-dimensional (3-D) truss using the finite element software OpenSees.…”

Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds

“…The existing approaches for propagating precise probabilistic uncertainty can be roughly divided into five categories: stochastic simulation methods [11][12][13], approximate analytical methods [14,15], surrogate-assisted methods [16][17][18], numerical integration methods [19][20][21][22][23] and probability conservation-based methods [24,25]. Differently, the propagation of non-probabilistic uncertainty follows another district philosophy, more relaying on, e.g., interval arithmetic [26], optimization methods [27,28], perturbation methods [29,30] and etc. Also advanced sampling approaches for interval analysis have been introduced [31,32].…”