An Advanced First-Order Method for System Reliability

by Sankaran Mahadevan, Vanderbilt Univ, Nashville, United States,
Thomas A. Cruse, Vanderbilt Univ, Nashville, United States,

Document Type: Proceeding Paper

Part of: Probabilistic Mechanics and Structural and Geotechnical Reliability


This paper proposes an iterative first-order method for accurate estimation of the joint failure region of two nonlinear limit states. Current methods use either a first-order approach which is very approximate, or a second-order approach which is more accurate but computationally cumbersome. The proposed method starts with linear approximations to the limit states to find an initial guess for the intersection. However, since the limit states are nonlinear, their values are not zero at the intersection. Therefore, an iterative search procedure for the actual intersection is formulated based on the values and slopes of the linear approximations to the two limit states in the previous iteration. The procedure is repeated till convergence to the actual intersection, resulting in a close approximation to the joint failure region.

Subject Headings: System reliability | Intersections | Approximation methods | Construction methods | Linear functions | Failure analysis | System analysis | Structural failures

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