New Analytical Solution of the First-Passage Reliability Problem for Linear Oscillators

by Sara Ghazizadeh, Graduate Research Assistant; Dept. of Civil and Environmental Engineering, Louisiana State Univ. and A&M College, 2400 Patrick F. Taylor Hall, Nicholson Extension, Baton Rouge, LA 70803, sghazi1@lsu.edu,
Michele Barbato, (corresponding author), Ph.D., (A.M.ASCE), Assistant Professor; Dept. of Civil and Environmental Engineering, Louisiana State Univ. and A&M College, 3418H Patrick F. Taylor Hall, Nicholson Extension, Baton Rouge, LA 70803, mbarbato@lsu.edu,
Enrico Tubaldi, Postdoctoral Researcher; Dipt. di Architettura Costruzione e Strutture, Univ. Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy, etubaldi@libero.it,


Serial Information: Issue 6, Pg. 695-706


Document Type: Journal Paper

Abstract: The classical first-passage reliability problem for linear elastic single-degree-of-freedom (SDOF) oscillators subjected to stationary and nonstationary Gaussian excitations is explored. Several analytical approximations are available in the literature for this problem: the Poisson, classical Vanmarcke, and modified Vanmarcke approximations. These analytical approximations are widely used because of their simplicity and their lower computational cost compared with simulation techniques. However, little is known about their accuracy in estimating the time-variant first-passage failure probability (FPFP) for varying oscillator properties, failure thresholds, and types of loading. In this paper, a new analytical approximation of the FPFP for linear SDOF systems is proposed by modifying the classical Vanmarcke hazard function. This new approximation is verified by comparing its failure probability estimates with the results obtained using existing analytical approximations and the importance sampling using elementary events method for a wide range of oscillator properties, threshold levels, and types of input excitations. It is shown that the newly proposed analytical approximation of the hazard function yields a significantly more accurate estimate of the FPFP compared with the Poisson, classical Vanmarcke, and modified Vanmarcke approximations.

Subject Headings: Linear analysis | Approximation methods | Oscillations | Structural reliability | Failure loads | Failure analysis | Stochastic processes | Dynamic structural analysis | Excitation (physics) |

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