Second‐Order Reliability Approximations

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Abstract
A simple method is presented for a second‐order structural reliability approximation. The method is based on an approximating paraboloid which is fitted to the limit‐state surface at discrete points around the point with minimal distance from the origin. An expression for the second‐order error in the approximation is derived, and the error is shown to be small, even for large dimensions and dispersed curvatures. In comparison to the existing approximation method, the proposed method is simpler and requires less computation. It is insensitive to noise in the limit‐state surface, approximately accounts for higher‐order effects, and facilitates the use of an existing formula for the probability content of parabolic sets.

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