Statistical topology optimization for structural damage detection

Abstract

This study proposes a new scheme named statistical topology optimization (TO) which collects and analyzes local optimal solutions to improve accuracy of structural damage detection. As degradation, damage or crack of structures modifies, alters, and changes mechanical properties such as stiffness, mass, at least theoretically, it is possible to compare structural responses of healthy and suspicious systems for the sake of the fault identification. For accurate prediction, it is especially possible to rely on structural TO to identify damage. However, due to the local optima issue in TO, slight modifications in responses by relatively small damage, or the inadequate comparison of insufficient vibration information, it is rare and difficult to apply TO in a damage detection problem. This research presents a new approach that collects local optima (layouts) and adopts statistical process (clustering with averaging of layouts). Through several numerical examples, it is revealed that local optima of the existing TO scheme can be classified as a cluster and outliers. Several local optima around a global optimum can be clustered to find out a damaged structure, which is one of the main contributions of the present study. To illustrate the concept of the proposed scheme, several examples are solved.