First excursion probability sensitivity in stochastic linear dynamics by means of Domain Decomposition Method

• Published in: Mechanical systems and signal processing Vol. 235; p. 112865
• Main Authors: Misraji, Mauricio A., Valdebenito, Marcos A., Faes, Matthias G.R.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.07.2025
• Subjects: Domain Decomposition Method; First excursion probability; Gaussian loading; Linear structure; Sensitivity analysis; Domain Decomposition Method; Gaussian loading; Sensitivity analysis; First excursion probability; Linear structure
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2025.112865

This contribution introduces a novel framework for the first excursion probability sensitivity estimation, applicable to linear dynamic systems subject to Gaussian excitation. The sensitivity estimator considered here is a local one and is calculated as the partial derivative of the first excursion probability with respect to a design parameter, such as the geometrical dimensions of the system. In the context of stochastic dynamical systems with low failure probability, obtaining both reliability and sensitivity estimates can be computationally expensive. In that sense, the linearity of the system plays a key role in order to build an efficient estimator. Domain Decomposition Method exploits this feature by exploring the failure domain in a very convenient way due to its special structure, characterized by the union of a large number of elementary linear failure domains. The proposed approach is based on the Domain Decomposition Method, enabling the derivation of the sensitivity estimator as a byproduct of the first excursion probability estimator. The effectiveness of the presented technique is illustrated through numerical examples involving both small- and large-scale models. •Sensitivity of failure probability estimated using Domain Decomposition Method.•Sensitivity is a byproduct of the first excursion probability.•Sensitivities of eigenvalues and eigenvectors required.•Nonproportional damping considered in the formulation.