On the use of Directional Importance Sampling for reliability-based design and optimum design sensitivity of linear stochastic structures

• Published in: Probabilistic engineering mechanics Vol. 70; p. 103368
• Main Authors: Jerez, Danko J., Jensen, Héctor A., Valdebenito, Marcos A., Misraji, Mauricio A., Mayorga, Franco, Beer, Michael
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.10.2022; Elsevier Science Ltd
• Subjects: Algorithms; Design; Design optimization; Directional Importance Sampling; First excursion probability; Gaussian loading; Importance sampling; Interior point algorithm; Linear structures; Optimization; Optimum design sensitivity; Reliability; Reliability analysis; Sensitivity analysis; Structural design; Structural design; Linear structures; First excursion probability; Directional Importance Sampling; Gaussian loading; Interior point algorithm; Optimum design sensitivity
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2022.103368

This contribution focuses on reliability-based 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 first-order derivatives of the failure probabilities as a byproduct of the sampling process. Thus, gradient-based solution schemes can be adopted by virtue of this feature. In particular, a class of feasible-direction interior point algorithms are implemented to obtain optimum designs, while a direction-finding 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. •Reliability-based design of linear structures under Gaussian excitation is addressed.•Directional Importance Sampling is used for reliability and sensitivity assessment.•A first-order scheme for optimization is implemented.•Optimum design sensitivities are obtained as a byproduct of the optimization results.