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The paper presents a new efficient and robust method for rare event probability estimation for computational models of an engineering product or a process returning categorical information only, for example, either success or failure. For such models, most of the methods designed for the estimation of failure probability, which use the numerical value of the outcome to compute gradients or to estimate the proximity to the failure surface, cannot be applied. Even if the performance function provides more than just binary output, the state of the system may be a non-smooth or even a discontinuous function defined in the domain of continuous input variables. This often happens because the mathematical model features non-smooth components or discontinuities (e.g., in the constitutive laws), bifurcations, or even domains in which no reasonable model response is obtained. In these cases, the classical gradient-based methods usually fail. We propose a simple yet efficient algorithm, which performs a sequential adaptive selection of points from the input domain of random variables to extend and refine a simple distance-based surrogate model. Two different tasks can be accomplished at any stage of sequential sampling: (i) estimation of the failure probability, and (ii) selection of the best possible candidate for the subsequent model evaluation if further improvement is necessary. The proposed criterion for selecting the next point for model evaluation maximizes the expected probability classified by using the candidate. Therefore, the perfect balance between global exploration and local exploitation is maintained automatically. If there are more rare events such as failure modes, the method can be generalized to estimate the probabilities of all these event types. Moreover, when the numerical value of model evaluation can be used to build a smooth surrogate, the algorithm can accommodate this information to increase the accuracy of the estimated probabilities. Lastly, we define a new simple yet general geometrical measure of the global sensitivity of the rare-event probability to individual variables, which is obtained as a by-product of the proposed refinement algorithm. [Display omitted] • Accurate failure probability estimation for strongly nonlinear failure surfaces. • The method can work with just categorical limit state function for continuous inputs. • Adaptive sequential extension of small sample via the proposed ψ learning function. • Automatic balancing between global exploration and local exploitation in input space. • Efficient importance sampling in a ring excluding the safe ball in Gaussian space. [ABSTRACT FROM AUTHOR]

A thermodynamically consistent model proposed in this work introduces a generative symbolic framework for computational components, which can capture the inelastic behavior of interfaces with 3D kinematics in response to monotonic, cyclic, and fatigue loading histories. It contributes to a long list of existing cohesive zone models by introducing novel forms of potentials for free energy, threshold function, and dissipation to deliver the following model properties: (i) the evolution equations derived from the potentials are linked in such a way that damage develops along with the cumulative measure of plastic sliding, (ii) the convex, continuous, and smooth shape of the threshold function introduced in the effective stress domain enables a general and efficient time integration that automatically handles unloading and reloading, and (iii) the non-associative flow potential includes a scalable degree of coupling between normal and tangential damage evolution. The studies performed in the paper demonstrate that these model ingredients lead to a consistent coverage of arbitrary non-proportional loading scenarios in tangential and normal directions. For monotonic loading, the presented examples illustrate the ability of the model to reproduce the shear dilatancy, pressure sensitivity including the vertex effect, stiffness recovery in compression, and abrasion due to sliding. For cyclic fatigue loading, the studies show that the model reflects the link between the hysteretic behavior and the fatigue damage evolution. This link constitutes the basis for a physically sound description of fatigue degradation along material interfaces. It manifests itself in the presented energy breakdown with distinguished fractions of energy release due to damage and plasticity ascribed to normal and tangential directions. Two calibration and validation examples using pull-out tests exposed to monotonic and cyclic loading are provided to show the applicability of the model for the characterization of the bond between steel bars and concrete. A publicly available implementation using a computer algebra system (CAS) is provided in the form of an interactive Jupyter notebook to document the reproducibility of the results. [ABSTRACT FROM AUTHOR]

This paper presents a novel adaptive sequential sampling method for building Polynomial Chaos Expansion surrogate models. The technique enables one-by-one extension of an experimental design while trying to obtain an optimal sample at each stage of the adaptive sequential surrogate model construction process. The proposed sequential sampling strategy selects from a pool of candidate points by trying to cover the design domain proportionally to their local variance contribution. The proposed criterion for the sample selection balances both exploitation of the surrogate model and exploration of the design domain. The adaptive sequential sampling technique can be used in tandem with any user-defined sampling method, and here was coupled with commonly used Latin Hypercube Sampling and advanced Coherence D-optimal sampling in order to present its general performance. The obtained numerical results confirm its superiority over standard non-sequential approaches in terms of surrogate model accuracy and estimation of the output variance. • The sequential sampling reflecting the exploration and exploitation is proposed. • The accuracy of results is higher in comparison to non-sequential approach. • The proposed criterion for sequential sampling can be used with any sampling scheme. [ABSTRACT FROM AUTHOR]