An Adaptive Non-Probabilistic Convex Modeling Method Based on Cluster Analysis

Abstract

Non-probabilistic convex models have significant advantages in dealing with limited sample data with unimodal distributions but often struggle to capture complex features when facing multimodal distribution data effectively. To address this limitation, this paper proposes an adaptive non-probabilistic convex modeling method based on cluster analysis, constructing a new convex polyhedron clustering (CPC) model. The proposed method begins by partitioning sample data into multiple sub-class clusters using a combination of posterior evaluation and K-means clustering techniques. A preprocessing step is incorporated to adaptively adjust the number of sub-class clusters according to the variability within the sample data. Sub-convex polyhedrons are then constructed within each sub-class cluster to quantify small uncertainty domains precisely. These sub-convex polyhedrons are integrated to form the CPC model, with mathematical expressions derived from the characteristics of convex polyhedrons to model the uncertainty domain of the entire dataset. Additionally, the model introduces volume ratio and minimum distance as reliability indices and establishes corresponding criteria to evaluate the performance of the proposed convex modeling method. The effectiveness of the method is further validated through three numerical examples, demonstrating its advantages over existing advanced convex modeling approaches.

Keywords: Non-probabilistic convex model, Uncertainty quantification, Convex modeling, Convex polyhedron, Cluster analysis