A Globally Optimal Robust Design Method for Complex Systems

Abstract

The uncertainty of the engineering system increases with the growing complexity of the engineering system; therefore, the tolerance to the uncertainty is essential. In the design phase, the output performance should reach the design criterion, even under large variations of design parameters. The tolerance to design parameter variations may be measured by the size of a solution space in which the output performance is guaranteed to deliver the required performance. In order to decouple dimensions, a maximum solution hyperbox, expressed by intervals with respect to each design parameter, is sought. The proposed approach combines the metaheuristic algorithm with the DIRECT algorithm where the former is used to seek the maximum size of hyperbox, and the latter is used as a checking technique that guarantees the obtained hyperbox is indeed a solution hyperbox. There are three advantages of the proposed approach. First, it is a global search and has a considerable high possibility to produce the globally maximum solution hyperbox. Second, it can be used for both analytically known and black-box performance functions. Third, it guarantees that any point selected within the obtained hyperbox satisfies the performance criterion as long as the performance function is continuous. Furthermore, the proposed approach is illustrated by numerical examples and real examples of complex systems. Results show that the proposed approach outperforms the GHZ and CES-IA methods in the literature.

Design Improvement for Complex Systems with Uncertainty

“…. , 1.0000), R low ck = 0.9995, R up ck = 0.9997, K = {2, 3,4,5,10,11,12,13,15,16,17,18,22,23,26,28,30,31,32,35,36,37,38,39,42,43,45,51,55,56,57,59,63,65,66,68,69,71,72,73, 82, 83}, f c = 0.9900 is the reliability threshold, and f (R) is the system reliability function which is evaluated by the GO method in [45]. Note that the volume here is replaced by the log-volume (logarithmic transformation of the volume) in order to calculate conveniently.…”

“…Because the locations of good and bad designs are estimated by Monte Carlo sampling, the obtained solution hyper-box may not have the maximum size. The second category is based on an analytical technique [24][25][26]. The algorithm presented in [24] applies interval arithmetic within an iterative optimization scheme to check whether the candidate hyper-box is a solution hyper-box.…”

“…Besides, the interval arithmetic cannot handle the black-box performance function. The algorithm proposed in [26] combines the DIRECT algorithm [27] with evolutionary algorithms, where the former is a checking technique to guarantee that the obtained hyper-box is indeed a solution hyper-box and the latter is to seek the maximum size of hyper-box. Unfortunately, the DIRECT algorithm requires very high computational effort for its work.…”