Data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

TL;DR

This paper introduces a data-driven method using segmented least squares and mixed-integer programming to compute conservative bounds on structural response, accounting for material data uncertainty with guaranteed confidence levels.

Contribution

It develops a novel approach combining segmented least squares with mixed-integer programming to obtain global optimal bounds in structural response analysis.

Findings

The method guarantees conservative bounds with specified confidence levels.

Numerical examples demonstrate effectiveness on different skeletal structures.

The approach handles nonconvex uncertainty sets efficiently.

Abstract

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.