Computation‐with‐confidence for static elasticity: Data‐driven approach with order statistics

Abstract

This paper presents a data‐driven method to identify a bound for the structural response of interest when a data set of elastic material responses is available. The obtained bound is probable in the sense that, at least with a certain confidence level, the probability that the structural response is within the bound is no smaller than a certain target value of reliability. The confidence level is ensured by considering the order statistics of the given data points. In this manner, this paper introduces the concept of reliability to the framework of data‐driven computational elasticity to address uncertainty in the data set. The method does not require any statistical information of the data points. Two numerical examples demonstrate the use of the proposed method to analyze static responses of structures by using only given material data sets.