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.
