sufficiency factor. In the next design iteration, the safety factor of the next deterministic
optimization is chosen to be
s~x~d(k+1)S(x d(k)(71
which is used to reduce the yield strength of the material, R. The optimization problem is
formulated as
minimize A = wt
such that
R (7-2)
cr <- 0
s(x, d)(k+1)
The process is repeated until the optimum converges and the reliability constraint is
sati sfied.
Reliability-Based Design Optimization Using Multi-Fidelity Technique with
Probabilistic Sufficiency Factor
For problems with very low probability of failure, a good estimate of probability
requires a very large MCS sample. In addition, the DRS must be extremely accurate in
order to estimate well a very low probability of failure. Thus we may require an
expensive MCS at a large number of design points in order to construct the DRS. The
deterministic optimization may be used to reduce the computational cost associated with
RBDO for very low probability of failure. However, since it does not use any derivative
information for the probabilities, it is not likely to converge to an optimum design when
competing failure modes are disparate in terms of the cost of improving their safety.
A compromise between the deterministic optimization and the full probabilistic
optimization is afforded by the Pyfby using an intermediate target probability PI, which is
higher than the required probability P,- and can be estimated via a less expensive MCS