Failure probability estimation and detection of failure surfaces via adaptive sequential decomposition of the design domain

We propose an algorithm for selection of points from the design domain small to moderate dimension and failure probability estimation. The proposed active learning detects events progressively refines boundary between safe domains thereby improving method is particularly useful when each evaluation performance function g(x) very expensive can be characterized as either highly nonlinear, noisy, or even discrete-state (e.g., binary). In such cases, only a limited number calls feasible, gradients cannot used. input segmented by expanding adaptively refining mesh-like lock-free geometrical structure. triangulation-based approach effectively combines features simulation approximation methods. performs two independent tasks: (i) estimation probabilities through ingenious combination deterministic cubature rules application divergence theorem (ii) sequential extension experimental with new points. future carried out decision approach, which maximizes instantaneous information gain in terms classification that corresponds local region. may halted at any time, e.g., sufficiently accurate estimations are obtained. Due use exact geometric representation domain, most effective problems low dimension, not exceeding eight. handle random vectors correlated non-Gaussian marginals. When values valid credible, accuracy improved employing smooth surrogate model based on evaluated set Finally, we define factors global sensitivity entire surface weighted density vector.