Efficient Computation of the Sharpest Bounds on the Probability of Failure of a Sheet Metal Forming Process

Abstract

The determination of the sharpest bounds on the probability of failure (PoF) based on the Optimal Uncertainty Quantification (OUQ) framework relies on the solution of non‐convex global optimization problems. These problems are subjected to non‐linear constraints to reflect moment constraints from available data, which impedes the numerical efficiency of the method. A different parameterization approach of the optimization problem utilizing canonical moments allows the transformation to only bound constraints and hence, an improved numerical efficiency can be reached. The performance of this new approach is contrasted with the performance of the original approach on the basis of a numerical simulation of a sheet metal forming process.