A graphical method for measurement set selection in structural system identification with observability techniques

Abstract

The unknown properties of a structure can be identified from different measurement sets. The selection of an adequate set is a key pretest decision in any Structural System Identification (SSI) method. Among the different SSI methods, the authors recently proposed the novel application of observability techniques to SSI. This technique can be applied regardless of the types of load as it shares the same system of equations as the stiffness matrix method. A hitch that does not allow the practical application of the observability method is the fact that the measurement set selection needs to be carried out by a trial and error analysis, that is to say, without a systematic procedure. To fill this gap, this paper proposes an innovative tool, the observability trees, to address the selection of an adequate measurement set for adequate structural identification by observability techniques. This tool also illustrates graphically how the unknown estimates are successively calculated throughout the recursive process of the observability analysis. The trees are defined by two different elements: tree nodes (unknown variables that correspond with unknown estimates, as stiffness, areas or inertias) and tree branches (information measured in the nodes of the structure, such as rotations or deflections). The aim of the method is to define an observability flow that enables the connection of the pursued tree nodes. To illustrate the application of the observability trees, a set of beam bridges of growing complexity are analyzed in detail.