from and driven by the design optimization to improve the efficiency of RBDO. If n

iterations are needed for convergence, the approach needs n deterministic optimizations

and n probabilistic analyses. However, the convergence rate of subsequent probabilistic

analyses is expected to increase after obtaining a reasonable MPP. Wu et al. (2001)

demonstrated the efficiency of this approach by optimizing a beam subject to multiple

reliability constraints.


 Deterministic Design
 Optimization

 Probabilistic Analyses:
 FORM/SORM Probabilistic analyses to
 replace random variable
 with deterministic values
 Safety factor based x* x*


 Deterministic Design
 Otimization with x* j Deterministic design
 optimization with x*
 New design d


 No ign and Reii

 Yes

 Stop

Figure 2-3. Partial safety factor approach: decouple reliability analysis and design
 optimization

 Summary

 Since the reliability analyses involved in our study are for system probability of

failure, MCS was used to perform reliability analysis. We developed an analysis RS

approach to reduce the high computational cost of MCS and design response surface

approach to filter noise in RBDO (Chapter 3).