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Ni, P. H., Jerez, D. J., Fragkoulis, V. C., Faes, M. G. R., Valdebenito, M. A., & Beer, M. (2022). Operator Norm-Based Statistical Linearization to Bound the First Excursion Probability of Nonlinear Structures Subjected to Imprecise Stochastic Loading. ASCE-ASME J. Risk Uncertain. Eng. Syst. A-Civ. Eng., 8(1), 04021086.
Abstract: This paper presents a highly efficient approach for bounding the responses and probability of failure of nonlinear models subjected to imprecisely defined stochastic Gaussian loads. Typically, such computations involve solving a nested double-loop problem, where the propagation of the aleatory uncertainty has to be performed for each realization of the epistemic parameters. Apart from near-trivial cases, such computation is generally intractable without resorting to surrogate modeling schemes, especially in the context of performing nonlinear dynamical simulations. The recently introduced operator norm framework allows for breaking this double loop by determining those values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. However, the method in its current form is only applicable to linear models due to the adopted assumptions in the derivation of the involved operator norms. In this paper, the operator norm framework is extended and generalized by resorting to the statistical linearization methodology to
Keywords: Uncertainty quantification; Imprecise probabilities; Operator norm theorem; Statistical linearization
Yuan, X. K., Liu, S. L., Faes, M., Valdebenito, M. A., & Beer, M. (2021). An efficient importance sampling approach for reliability analysis of time-variant structures subject to time-dependent stochastic load. Mech. Syst. Sig. Process., 159, 107699.
Abstract: Structural performance is affected by deterioration processes and external loads. Both effects may change over time, posing a challenge for conducting reliability analysis. In such context, this contribution aims at assessing the reliability of structures where some of its parameters are modeled as random variables, possibly including deterioration processes, and which are subjected to stochastic load processes. The approach is developed within the framework of importance sampling and it is based on the concept of composite limit states, where the time-dependent reliability problem is transformed into a series system with multiple performance functions. Then, an efficient two-step importance sampling density function is proposed, which splits time-invariant parameters (random variables) from the time-variant ones (stochastic processes). This importance sampling scheme is geared towards a particular class of problems, where the performance of the structural system exhibits a linear dependency with respect to the stochastic load for fixed time. This allows calculating the reliability associated with the series system most efficiently. Practical examples illustrate the performance of the proposed approach.
Keywords: RESPONSE-SURFACE APPROACH; LINEAR-SYSTEMS; DISCRETIZATION; PROBABILITIES; DESIGN