Step Direction Computation of the First-Order Reliability Analysis Based on Two-Step Root-Finding Methods

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Ghorbanzadeh Mehrshad; Homami Peyman; Shahruzi Mohsen

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Journal Paper

Paper Information

Journal: International Journal of Reliability, Risk and Safety: Theory and Application Year:2023 | Volume:6 | Issue:1 Page(s): 71-76

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Information Journal Paper

Title

Step Direction Computation of the First-Order Reliability Analysis Based on Two-Step Root-Finding Methods

Author(s)

Ghorbanzadeh Mehrshad | Homami Peyman | Shahruzi Mohsen | Issue Writer Certificate

Keywords

Reliability analysis method

Two-step root-finding

Step direction

Convergence rate

Nonlinear limit state function

Abstract

The iHLRF algorithm is a popular iterative algorithm for determining the failure probability in structural reliability problems. It belongs to the family of first-order reliability methods (FORM) and is known for its fast convergence and remarkable simplicity. However, in cases where the limit state function oscillates significantly near the design point, which often occurs in high Nonlinear limit state functions, the iHLRF algorithm may suffer from convergence issues. To address these convergence issues, this paper proposes three two-Step direction determination techniques for first-order analysis. These techniques are based on Two-step root-finding methods with a higher Convergence rate than existing methods. The proposed techniques aim to improve the accuracy and robustness of the iHLRF algorithm, especially in cases where the limit state function shows highly nonlinear behavior. A numerical example with high Nonlinear limit state functions in standard normal space is presented to demonstrate the proposed techniques' efficiency and capability. The performance of each proposed technique is compared with other existing methods, highlighting the advantages and limitations of each approach. Overall, this paper aims to contribute to developing more accurate and reliable methods for determining the reliability index in structural reliability problems, with the potential to be applied in various engineering fields.

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