Reliability-Based Design Optimization Using Sequential Deterministic Optimization
with Probabilistic Sufficiency Factor
Wu et al. (1998, 2001) proposed a decoupled approach using partial safety factor to
replace reliability constraints by equivalent deterministic constraints. After performing
reliability analysis, the random variables x are replaced by safety-factor based values x*,
which is the most probable point (MPP) of the previous reliability analysis. The required
shift of limit state function g in order to satisfy the reliability constraints is s, which
satisfy P(g(x)+s)<0)=Pt. Both x*k and s can be obtained as the byproducts of reliability
analysis. 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 probabilistic sufficiency
factor (Qu and Haftka 2003) presented in Chapter six. The significant difference between
Wu's partial safety factor and coupled RBDO is that reliability analysis is decoupled
from and driven by the design optimization to improve the efficiency of RBDO. Thus
RBDO is performed in a deterministic fashion and corrected by reliability analysis after
optimization. The PSF is employed in this chapter to convert RBDO to equivalent
deterministic optimization. Converting RBDO to equivalent deterministic optimization
enables further exploration of the design space for those problems where the design space
is characterized to have multiple local optima and only limited number of analyses are
available due to its high computational cost, such as design of stiffened panels addressed
in chapter eight.
By starting from a mean value based design, where the deterministic safety factor is
one, an initial design was found by deterministic optimization. Reliability analysis using
Monte Carlo simulation shows the deficiency in probability of failure and probabilistic