its target value. Another major difference between the design potential approach and
double loop approach is that the reliability constraints are approximated at the design
potential point dk (DPP), which defined as the design that renders the probabilistic
constraint active, instead of the current design point. Since the DPP is located on the
limit-state surface of the probabilistic constraint, the constraint approximation of DPM
becomes exact at (DPP). Thus DPM provides a better constraint approximation without
additional costly limit state function evaluation. Therefore, a faster rate of convergence
can be achieved.
Partial safety factor approach (Partial SF)
Wu et al. (1998 and 2001) developed a partial safety factor similar to Birger's
safety factor in order to replace the RBDO with a series of deterministic optimizations by
converting reliability constraints to equivalent deterministic constraints.
After performing reliability analysis, the random variables x are replaced by safety-
factor based values x*e, which is the MPP of the previous reliability analysis. The shift of
limit state function G needed to satisfy the reliability constraints is s, which satisfies
P(G(x)+s)<0)=Pt. Both x*k and s can be obtained as the byproducts of reliability analysis.
Since in design optimization, the random variables x are replaced by x* (just as in the
case of traditional deterministic design, where random variables are replaced by
deterministic values after applying some safety factor), the method is called partial safety
factor approach (Figure 2-3). The target reliability is achieved by adjusting the limit state
function via design optimization. It is seen that the required shift s is similar to the target
probabilistic performance measure g*.
The significant difference between Partial SF and DPM or nest MPP is that
reliability analysis (FORM in the paper, can be any MPP-based method) is decoupled