The optimum design for the case with strength failure mode obtained in Chapter 6
using probabilistic sufficiency factor and Wu's exact optimum are shown in Table 7-2.
The probability of failure is calculated by direct MCS with 100,000 samples based on the
exact stress in Equation (7-1). It is seen that the design from probabilistic sufficiency
factor DRS is very close to the exact optimum.
Table 7-2. Optimum designs for strength failure mode obtained from double loop RBDO
Minimize obj ective function F while 0.0013 5 > pof
DRS of .Obj ective Pof/Safety factor from MCS of
Optima
function F=wt Exact stress
Probabilistic w=2.4526,
'9.5365 0.00128/1.0021
sufficiency factor t-3.8884
Exact optimum w=2.4484,
'9.5204 0.00135/1.00
(Wu et al., 2001) t-3.8884
Reliability-Based Design Optimization Using Sequential Deterministic Optimization
with Probabilistic Sufficiency Factor
To verify the validity of the proposed method, converting RBDO to sequential
deterministic optimization using probabilistic sufficiency factor for target probability of
failure of 0.00135 is performed (Table 7-3).
Table 7-3. Design history of RBDO based on sequential deterministic optimization with
probabilistic sufficiency factor under strength constraint for target probability
of failure of 0.0013 5
Probabilistic Minimize obj ective function F while P 2 3 or 0.0013 5 > pof
sufficiency .Objective Pof/Safety index/Safety factor
facrtor Optima functio F= wt fro MC S of 10 sample
Initial design w=1.9574,
3' 7.6630 0.49883/0.00293/0.7178
(s =1.0) t- 3.9149
s2=S1/0.7177 w=2.1862,
'9.5589 0.00140/2.98889/0.9986
=1.3932 t-4.3724
s3=S2/0.9986 w=2.1872,
'9.5676 0.00130/3.01145/1.0006
=1.3951 t-4.3744
It is seen that the final design has a slightly higher weight than the optimum in
Table 7-2. The reason is that this method employs a safety factor based on the mean