Faes, M. G. R., & Valdebenito, M. A. (2021). Fully decoupled reliabilitybased optimization of linear structures subject to Gaussian dynamic loading considering discrete design variables. Mech. Syst. Sig. Process., 156, 107616.
Abstract: Reliabilitybased optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. However, due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure, the corresponding computational cost is usually high, impeding the applicability of the methods. This computational cost is even further enlarged when one or several design variables must belong to a discrete set, due to the requirement of resorting to integer programming optimization algorithms. To alleviate this issue, this contribution proposes a fully decoupled approach for a specific class of problems, namely minimization of the failure probability of a linear system subjected to an uncertain dynamic load of the Gaussian type, under the additional constraint that the design variables are integervalued. Specifically, by using the operator norm framework, as developed by the authors in previous work, this paper shows that by reducing the RBO problem with discrete design variables to the solution of a single deterministic optimization problem followed by a single reliability analysis, a large gain in numerical efficiency can be obtained without compromising the accuracy of the resulting optimal design. The application and capabilities of the proposed approach are illustrated by means of three examples.

Fina, M., Lauff, C., Faes, M. G. R., Valdebenito, M. A., Wagner, W., & Freitag, S. (2023). Bounding imprecise failure probabilities in structural mechanics based on maximum standard deviation. Struct. Saf., 101, 102293.
Abstract: This paper proposes a framework to calculate the bounds on failure probability of linear structural systems whose performance is affected by both random variables and interval variables. This kind of problems is known to be very challenging, as it demands coping with aleatoric and epistemic uncertainty explicitly. Inspired by the framework of the operator norm theorem, it is proposed to consider the maximum standard deviation of the structural response as a proxy for detecting the crisp values of the interval parameters, which yield the bounds of the failure probability. The scope of application of the proposed approach comprises linear structural systems, whose properties may be affected by both aleatoric and epistemic uncertainty and that are subjected to (possibly imprecise) Gaussian loading. Numerical examples indicate that the application of such proxy leads to substantial numerical advantages when compared to a traditional doubleloop approach for coping with imprecise failure probabilities. In fact, the proposed framework allows to decouple the propagation of aleatoric and epistemic uncertainty.

Jerez, D. J., Jensen, H. A., Valdebenito, M. A., Misraji, M. A., Mayorga, F., & Beer, M. (2022). On the use of Directional Importance Sampling for reliabilitybased design and optimum design sensitivity of linear stochastic structures. Probabilistic Eng. Mech., 70, 103368.
Abstract: This contribution focuses on reliabilitybased design and optimum design sensitivity of linear dynamical structural systems subject to Gaussian excitation. Directional Importance Sampling (DIS) is implemented for reliability assessment, which allows to obtain firstorder derivatives of the failure probabilities as a byproduct of the sampling process. Thus, gradientbased solution schemes can be adopted by virtue of this feature. In particular, a class of feasibledirection interior point algorithms are implemented to obtain optimum designs, while a directionfinding approach is considered to obtain optimum design sensitivity measures as a post processing step of the optimization results. To show the usefulness of the approach, an example involving a building structure is studied. Overall, the reliability sensitivity analysis framework enabled by DIS provides a potentially useful tool to address a practical class of design optimization problems.

Valdebenito, M. A., Misraji, M. A., Jensen, H. A., & Mayorga, C. F. (2021). Sensitivity estimation of first excursion probabilities of linear structures subject to stochastic Gaussian loading. Comput. Struct., 248, 106482.
Abstract: This contribution focuses on evaluating the sensitivity associated with first excursion probabilities of linear structural systems subject to stochastic Gaussian loading. The sensitivity measure considered is the partial derivative of the probability with respect to parameters that affect the structural response, such as dimensions of structural elements. The actual calculation of the sensitivity demands solving high dimensional integrals over hypersurfaces, which can be challenging from a numerical viewpoint. Hence, sensitivity evaluation is cast within the context of a reliability analysis that is conducted with Directional Importance Sampling. In this way, the sought sensitivity is obtained as a byproduct of the calculation of the failure probability, where the postprocessing step demands performing a sensitivity analysis of the unit impulse response functions of the structure. Thus, the sensitivity is calculated using sampling by means of an estimator, whose precision can be quantified in terms of its standard deviation. Numerical examples involving both small and largescale structural models illustrate the procedure for probability sensitivity estimation. (C) 2021 Elsevier Ltd. All rights reserved.
