designs in Table 8-19 and 8-20, it is seen that the correction with actual safety margins is
more accurate than that using the safety factor, because PANDA2 Superopt employs
approximation in the optimization process, which might results in slightly positive safety
margin in its optimum design. In the second design, the actual safety margin of PANDA2
superopt design (S2= 1.437514) is 0.0532, which should be zero if PANDA2 Superopt
did not employ approximation in optimization and results in the difference in the third
designs in Table 8-19 and 8-20. Therefore, the second correction formula, Equation (8-3)
is more accurate than the first one, Equation (8-4).
Reliability-Based Design Optimization using DIRECT Optimization
The discrepancy of safety factor and actual safety margin can also be eliminated by
using an optimizer such as DIRECT (Jones et al. 1993) that doesn't use approximation
and use only PANDA2 analysis. However, DIRECT is a sampling-based global
optimization algorithm that is computationally more expensive than the multiple starting
points global optimization in PANDA2, DIRECT is chosen to be performed after
several PANDA2 design iterations.
DIRECT Global Optimization Algorithm
DIRECT is a modified Lipschitzian optimization algorithm (Jones et al. 1993).
The name is an acronym for "DIvide RECTangles," which is a simple description of how
the algorithm works. It works in a space normalized to 0 < xi < 1 for i = [1, 2, ... N],
where N is the dimensionality of the design space. DIRECT begins by evaluating the
function to be minimized, J at the center of the design space, cl = 0.5ei for i = [1, 2, ... N]
(the Oth iteration). It then evaluates the function at the points cl & 1/3 81 (the 1st iteration).
Each dimension then has 2 function evaluations, and DIRECT defines