Novel second-order reliability method (SORM) using noncentral or generalized chi-squared distributions
By: Lee, Ikjin
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Contributor(s): Noh, Yoojeong.
Publisher: New York ASME 2012Edition: Vol.134(10), Oct.Description: 1-10p.Subject(s): Mechanical EngineeringOnline resources: Click here
In:
Journal of mechanical designSummary: This paper proposes a novel second-order reliability method (SORM) using noncentral or general chi-squared distribution to improve the accuracy of reliability analysis in existing SORM. Conventional SORM contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at most probable point in standard normal U-space, (2) error due to approximating the quadratic function in U-space by a parabolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. The proposed method contains the first type of error only, which is essential to SORM and thus cannot be improved. However, the proposed method avoids the other two types of errors by describing the quadratic failure surface with the linear combination of noncentral chi-square variables and using the linear combination for the probability of failure estimation. Two approaches for the proposed SORM are suggested in the paper.
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This paper proposes a novel second-order reliability method (SORM) using noncentral or general chi-squared distribution to improve the accuracy of reliability analysis in existing SORM. Conventional SORM contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at most probable point in standard normal U-space, (2) error due to approximating the quadratic function in U-space by a parabolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. The proposed method contains the first type of error only, which is essential to SORM and thus cannot be improved. However, the proposed method avoids the other two types of errors by describing the quadratic failure surface with the linear combination of noncentral chi-square variables and using the linear combination for the probability of failure estimation. Two approaches for the proposed SORM are suggested in the paper.
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