Experimental Data Have to Decide Which of the Nonprobabilistic Uncertainty Descriptions—Convex Modeling or Interval Analysis—to Utilize

Abstract

This study shows that the type of the analytical treatment that should be adopted for nonprobabilistic analysis of uncertainty depends on the available experimental data. The main idea is based on the consideration that the maximum structural response predicted by the preferred theory ought to be minimal, and the minimum structural response predicted by the preferred theory ought to be maximal, to constitute a lower overestimation. Prior to the analysis, the existing data ought to be enclosed by the minimum-volume hyper-rectangle V1 that contains all experimental data. The experimental data also have to be enclosed by the minimum-volume ellipsoid V2. If V1 is smaller than V2 and the response calculated based on it R(V1) is smaller than R(V2), then one has to prefer interval analysis. However, if V1 is in excess of V2 and R(V1) is greater than R(V2), then the analyst ought to utilize convex modeling. If V1 equals V2 or these two quantities are in close vicinity, then two approaches can be utilized with nearly equal validity. Some numerical examples are given to illustrate the efficacy of the proposed methodology.