Comparison study between probabilistic and possibilistic methods for problems under a lack of correlated input statistical information

In most industrial applications, only limited statistical information is available to describe the input uncertainty model due to expensive experimental testing costs. It would be unreliable to use the estimated input uncertainty model obtained from insufficient data for the design optimization. Furthermore, when input variables are correlated, we would obtain non-optimum design if we assume that they are independent. In this paper, two methods for problems with a lack of input statistical information—possibility-based design optimization (PBDO) and reliability-based design optimization (RBDO) with confidence level on the input model—are compared using mathematical examples and an Abrams M1A1 tank roadarm example. The comparison study shows that PBDO could provide an unreliable optimum design when the number of samples is very small. In addition, PBDO provides an optimum design that is too conservative when the number of samples is relatively large. Furthermore, the obtained PBDO designs do not converge to the optimum design obtained using the true input distribution as the number of samples increases. On the other hand, RBDO with confidence level on the input model provides a conservative and reliable optimum design in a stable manner. The obtained RBDO designs converge to the optimum design obtained using the true input distribution as the number of samples increases.