Discussions on non-probabilistic convex modelling for uncertain problems

TL;DR

This paper introduces a unified framework for non-probabilistic convex models to better quantify uncertainty in structural analysis, providing theoretical evaluation criteria and practical assessment indexes validated through numerical examples.

Contribution

It proposes a unified formulation approach for convex models using correlation analysis and introduces validity and adaptability assessment criteria.

Findings

The framework simplifies convex model construction.

Evaluation criteria effectively verify model validity.

Assessment indexes estimate model adaptability to data.

Abstract

Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To overcome the complexity and diversity of the formulations of current convex models, in this paper, a unified framework for construction of the non-probabilistic convex models is proposed. By introducing the correlation analysis technique, the mathematical expression of a convex model can be conveniently formulated once the correlation matrix of the uncertain parameters is created. More importantly, from the theoretic analysis level, an evaluation criterion for convex modelling methods is proposed, which can be regarded as a test standard for validity verification of subsequent newly proposed convex modelling methods. And from the practical application level, two model assessment indexes are proposed, by which the adaptabilities of different convex models to a specific uncertain problem with given experimental samples can be estimated. Four numerical examples are investigated to demonstrate the effectiveness of the present study.