updated by two high fidelity reliability analysis. The total computational cost is three low
fidelity design response surface construction and three high fidelity reliability evaluation.
Converting RBDO to sequential deterministic optimization is computationally
more efficient than multi-fidelity technique for problem with low probability of failures.
However, it is seen in Table 7-4 and Table 7-5 that the design obtained by the latter
approach is more reliable and lighter than the previous one.
Table 7-5. RBDO using variable fidelity technique with probabilistic sufficiency factor
under strength constraint
Probabilistic Minimize obj ective function F while P > 4. 1974 or 0.000013 5 > pof
Sufficiency .Obj ective Pof/Safety factor from MCS of
factor Optima function F=wt 10 samples (Pf rj)
Initial design w=2.4526,
3' 9.5367 0.0012350/0.891938
(fi=1.0) t-3.8884
w=2.2522,
f2=0.891938' 10.3600 0.0000160/0.996375
t-4.6000
f3 2*"0.996375 w=2.4071,
'10.3510 0.0000108/1.003632
=0.88704 t-4.3000
Table 7-6. Range of design variables for design response surface
System variables w t
Range for f2 DRS 2.0" to 3.0" 3.6" to 4.6"
Range for f3 DRS 1.7" to 2.7" 4.3" to 5.3"
Summary
Since the probabilistic sufficiency factor represents a factor of safety relative to a
target probability of failure. It provides a measure of safety that can be used more readily
than probability of failure or safety index by optimizers or designers to estimate the
required weight increase to reach a target safety level. The RBDO is converted to
equivalent deterministic optimization using probabilistic sufficiency factor.
The probabilistic sufficiency factor also provides more information in the region of
such low probability that probability of failure or safety index cannot be estimated by