The Use of Copulas and MPP-Based Dimension Reduction Method (DRM) to Assess and Mitigate Engineering Risk in the Army Ground Vehicle Fleet

In reliability based design optimization RBDO problems with correlated input variables, a joint cumulative distribution function CDF needs to be obtained to transform, using the Rosenblatt transformation, the correlated input variables into independent standard Gaussian variables for the inverse reliability analysis. However, a true joint CDF requires infinite number of test data to be obtained, so in this paper, a copula is used, which models a joint CDF only using marginal CDFs and limited data. Then, the inverse reliability analysis can be carried out using the joint CDF modeled by the copula and the first order reliability method FORM, which has been commonly used in the inverse reliability analysis. However, because of the nonlinear Rosenblatt transformation, the FORM may yield inaccurate reliability analysis results. To resolve the problem, this paper proposes to use the most probable point MPP-based dimension reduction method DRM for more accurate inverse reliability analysis and RBDO. As an example of the proposed method, an RBDO study of an M1A1 Abrams tank roadarm is carried out.