A Robust Modeling Method for Uncertainty Convex Polyhedron Models Based on Outlier Detection

Accurate quantification of uncertainty is a prerequisite for achieving reliable structural design. The convex polyhedron model, which considers correlations between variables, is a non-probabilistic method for quantifying uncertainty. However, when significant outliers are present, the convex hull constructed by the convex polyhedron method can become distorted and stretched, affecting the model's predictive capability for future samples. This paper proposes a robust convex polyhedron modeling method based on outlier detection, which is insensitive to outliers in the sample set. First, outlier detection algorithms are used to exclude outliers from the sample points. Then, a convex polyhedron model is constructed based on the remaining sample points, and an expansion factor is defined to ensure that the volume of the new convex hull is the same as that of the original convex hull, thereby maintaining the new model's predictive capability. An engineering example demonstrates the superiority of this modeling method in the presence of outliers.