HLRF-BFGS-Based Algorithm for Inverse Reliability Analysis

Algorithm 1

Intermediate algorithm.

Select target reliability index .

Select the starting point values for and as and .

; i is the iteration counter.

is fixed as the identity matrix for the first iteration ().

REPEAT (while the stopping criterion is not satisfied)

   Compute and using Eqs. (18) and (7), respectively.

   Compute and using Eqs. (10) and (11), respectively.

   Compute and using Eqs. (12) and (13), respectively.

   Compute the search direction vector () using Eq. (9).

   Compute the step size based on Eq. (4) by trying several values for .

   Find and using Eq. (3).

   Update using the BFGS update formula as shown in Eq. (20).

    .

END