Comparison Study Between Probabilistic and Possibilistic Approach for Problems With Correlated Input and Lack of Input Statistical Information

Abstract

Due to expensive experimental testing costs, in most industrial engineering applications, only limited statistical information is available to describe the input uncertainty model. It would be unreliable to use an estimated input uncertainty model, such as distribution types and parameters including the standard deviations for the distributions, that is obtained from insufficient data for the design optimization. Furthermore, when input variables are correlated, we would obtain non-optimum design if we use the assumption of independency for the design optimization. In this paper, two methods for problems with 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 a mathematical example and Abrams roadarm of an M1A1 tank. The comparison study shows that the PBDO could provide an unreliable optimum design when the number of samples is very small and that it provides an optimum design that is too conservative when the number of samples is relatively large. Furthermore, the optimum design does not converge to the optimum design obtained using the true input distribution as the number of samples increases. On the other hand, the RBDO with confidence level on the input model provides a conservative and reliable optimum design in a stable manner, and the optimum design converges to the optimum design obtained using the true input distribution as the number of samples increases.