In order to advance the reliability analysis of practical engineering problems, a simplified iterative algorithm for forward and/or inverse first-order reliability method (FORM) is presented in this paper. The approach extends the well-known HLRF algorithms that are conventionally formulated in the uncorrelated standard normal space (u-space) into the correlated nonnormal space (x-space). Because the simplified algorithms are self-contained in x-space, the tedious mathematical transformations of random variables between statistical spaces as well as the inversion of Jacobian matrix for gradient vectors are not required, which are desirable for practitioners to implement FORM within standalone numerical codes. The convergence of the simplified iterative algorithms can be improved by properly adjusting the step length during the iterative computations. Verifications of the proposed algorithm are illustrated through a highly nonlinear problem for both forward and/or inverse reliability analysis. Based on the proposed inverse FORM algorithm, the geotechnical reliability-based designs (RBD) of a strip footing and an earth slope are performed and some insights gained.
- Correlated nonnormals
- Implicit limit state function
- Inverse reliability analysis
- Reliability index
- Simplified HLRF algorithm