Model updating of model parameters and model form error in a uniform framework

The typical model updating techniques mainly focus on calibrating the model parameters, e.g. Young's modulus and density, while being inefficient for the model form error due to the inevitable approximation and simplification during numerical modeling. In this paper, an integrated model updating approach for both uncertain material parameters and model form error is proposed. This objective is achieved by a combined optimisation procedure, where both material parameters and shape basis vectors serve as design variables in order to capture uncertainties related to the geometry of the structure and variability of Young's modulus and density. This approach is validated via an updating process of a solid finite element model with regard to the practical experiment, where a nearly-periodic beam is considered. The approximately periodic property, i.e. unequal length and unsteady thickness of different sections, clearly introduce severe model form error in the finite element model of the beam. The updating results show that the predicted natural frequencies are calibrated with a high precision, implying that both the parameter uncertainty and the modelling uncertainty are reduced in the uniform updating framework.