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

Marcos A. Valdebenito, Mauricio A. Misraji, Héctor A. Jensen, C. Franco Mayorga

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4 Scopus citations


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.

Original languageEnglish
Article number106482
JournalComputers and Structures
StatePublished - May 2021
Externally publishedYes


  • Directional Importance Sampling
  • First excursion probability
  • Linear structure
  • Sensitivity analysis
  • Stochastic Gaussian loading


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