Data-driven structural identification of nonlinear assemblies: Structures with bolted joints

Abstract

The identification of nonlinearities that have a significant impact on dynamic behaviour of complex mechanical structures is necessary for ensuring structural efficiency and safety. A new methodology for structural identification of nonlinear assemblies is proposed in this paper that enables the discovery of stiffness and damping nonlinear models especially when it is not possible to directly measure the degrees of freedom where non-trivial nonlinearities are located. Input-output time-domain data collected at accessible locations on the structure are used to learn nonlinear models in the unmeasured locations. This is accomplished by making use of virtual sensing and model reduction schemes along with a physics-informed identification method recently developed by the authors (Safari and Londoño 2021). The methodology is suited for weakly nonlinear systems with localised nonlinearities for which their location is assumed to be known. It also takes into account dominant modal couplings within the identification process. The proposed methodology is demonstrated on a case study of a nonlinear structure with a frictional bolted joint, in numerical and experimental settings. It is shown that the model selection and parameter estimation for weakly nonlinear elements can be carried out successfully based on a reduced-order model which includes only a modal equation along with relevant modal contributions. Using the identified localised nonlinear models, both the reduced and full-order models can be updated to simulate the dynamical responses of the structure. Results suggests that the identified nonlinear model, albeit simple, generalises well in terms of being able to estimate the structural responses around modes which were not used during the identification process. The identified model is also interpretable in the sense that it is physically meaningful since the model is discovered from a predefined library featuring different nonlinear characteristics.