TY - JOUR

T1 - Sensitivity estimation of first excursion probabilities of linear structures subject to stochastic Gaussian loading

AU - Valdebenito, Marcos A.

AU - Misraji, Mauricio A.

AU - Jensen, Héctor A.

AU - Franco Mayorga, C.

N1 - Funding Information:
This research is partially supported by ANID — (National Agency for Research and Development, Chile) under its program FONDECYT, Grant Nos. 1180271 and 1200087 , and Universidad Tecnica Federico Santa Maria – Dirección de Postgrado y Programas under its programs PAC (Programa Asistente Científico 2017) and PIIC (Programa de Incentivo a la Iniciación Científica). This support is gratefully acknowledged by the authors.
Publisher Copyright:
© 2021 Elsevier Ltd

PY - 2021/5

Y1 - 2021/5

N2 - 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 post-processing 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 large-scale structural models illustrate the procedure for probability sensitivity estimation.

AB - 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 post-processing 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 large-scale structural models illustrate the procedure for probability sensitivity estimation.

KW - Directional Importance Sampling

KW - First excursion probability

KW - Linear structure

KW - Sensitivity analysis

KW - Stochastic Gaussian loading

UR - http://www.scopus.com/inward/record.url?scp=85101410370&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2021.106482

DO - 10.1016/j.compstruc.2021.106482

M3 - Article

AN - SCOPUS:85101410370

SN - 0045-7949

VL - 248

JO - Computers and Structures

JF - Computers and Structures

M1 - 106482

ER -