Constrained observability method in static structural system identification

This is the peer reviewed version of the following article: [Lei J, Nogal M, Lozano-Galant JA, Xu D, Turmo J. Constrained observability method in static structural system identification. Struct Control Health Monit. 2018;25:e2040. https://doi.org/10.1002/stc.2040], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/stc.2040/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Identifiability of parameters in structural system identification (SSI) is of primary importance in any SSI method. It depends on the number and the location of the measurements, which is linked with sensor configuration. In this paper, under the framework of SSI by observability method (OM), the number of necessary measurements to identify all parameters of structural system was clarified first. Then, an example was solved step by step to show the lacking constraints among unknowns in SSI by OM. In a frame example, it was found that no measurement set having as many measurements as the number of unknowns was able to identify all parameters. To further understand this phenomenon, the observability of a simply supported beam was analyzed in an exhaustive way using 252 possible measurement sets. Three quarters of these sets were not able to identify all the parameters. In order to solve this issue, for the very first time, SSI by constrained observability method (COM), which appends the nonlinear constraints to SSI by OM, was proposed. With SSI by COM applied, the observability of the structural parameters with respect to the 252 sets was greatly improved. Finally, the efficacy of SSI by COM was verified by a 13-story frame building.