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This study presents an efficient algorithm for calculating sensitivity derivatives in reliability-based optimization. The method, based on the advanced first-order second-moment (AFOSM) approach, is implemented in VBA for practical application.

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Area of Science:

  • Engineering
  • Optimization
  • Reliability Analysis

Background:

  • Sensitivity derivatives are crucial for reliability-based optimization.
  • Calculating these derivatives is computationally expensive due to the complex nature of failure probability functions.

Purpose of the Study:

  • To develop a step-by-step algorithm for computing sensitivity derivatives of failure probability and safety index.
  • To implement the algorithm in a VBA-programmed spreadsheet for practical use.

Main Methods:

  • Utilized the advanced first-order second-moment (AFOSM) reliability method.
  • Developed a novel algorithm for derivative calculation.
  • Implemented the algorithm in Visual Basic for Application (VBA).

Main Results:

  • Successfully calculated sensitivity derivatives for geotechnical and structural examples.
  • Demonstrated the robustness of the method using Gaussian random perturbations.
  • Validated the proposed model against the forward finite difference (FFD) method.

Conclusions:

  • The proposed algorithm provides an efficient and practical approach for determining sensitivity derivatives in reliability-based optimization.
  • The VBA implementation facilitates ease of use in engineering applications.
  • The method accurately calculates derivatives, including those for model uncertainty.