Influence of the objective function in the dynamic model updating of girder bridge structures

In the context of model updating of bridge structures, dynamic approaches are currently dominant. This is mainly due to the opportunity of performing dynamic tests under environmental and traffic loadings, without putting the bridges out of service. Several techniques have been proposed in the literature to control and address the relevant model updating workflow. These methods typically consider the structural frequencies, or a combination of frequencies with vibration modes. Dissipative properties are, on the contrary, more rarely considered in updating procedures, given their strong dependence on the amplitude of the vibrations and on the type of forcing load. In this work, six ruling objective functions are considered for the dynamic model updating of girder bridge structures. The first one, taken from the literature, is a widely used function based on discrepancies among numerical and experimental frequencies. Two additional functions, also derived from the existing literature, are subsequently considered: one focuses on vibration modes, utilizing the Modal Assurance Criterion (MAC), and the other incorporates both structural frequencies and mode shapes, deploying the Modal Flexibility Matrix (MFM). Three novel objective functions are introduced, which are adaptations of the previously mentioned ones, with alternative applications of MAC and MFM. These six functions are analyzed and discussed through two comprehensive experimental case studies, in which the relative weights of the specific function terms are also investigated. A quantitative selection criterion is proposed and examined in order to choose the most suitable objective function based on identifiability. The method implementation, leveraging second-order derivatives, is executed via a finite difference scheme.