Detection and quantification of non-linear structural behavior using principal component analysis

The detection of non-linear behavior in structural dynamics is a very important step to the extent that the presence of non-linearities, even local, can affect the global dynamic behavior of a structure. A large number of techniques that enable engineers to detect non-linear behavior can be found in the literature but most of these methods exploit frequency domain data and give better results with a stepped-sine excitation. The goal of this paper is to propose an alternative methodology that is based on the principal component analysis and uses time responses obtained with a random excitation. Two criteria will be used to quantify the difference between two response subspaces, based on the angle between them and the residual error resulting from the projection of one on the other. The concept of limit of linearity and design decision margins is also addressed in this paper. The methodology is demonstrated using an academic simulated system and then using measured data of a simplified solar array system.

► A technique for detecting non-linear structural behavior is described. ► Two criteria are proposed based on a singular value decomposition of time signals. ► The two criteria quantify the level of non-linearity in structural responses. ► A limit of linearity threshold is introduced to avoid subjective conclusions. ► The proposed methodologies are illustrated on real experimental measurements.