Model-Form and Parameter Uncertainty Quantification in Structural Vibration Simulation Using Fractional Derivatives

Abstract

Extensive research has been devoted to engineering analysis in the presence of only parameter uncertainty. However, in modeling process, model-form uncertainty arises inevitably due to the lack of information and knowledge, as well as assumptions and simplifications made in the models. It is undoubted that model-form uncertainty cannot be ignored. To better quantify model-form uncertainty in vibration systems with multiple degrees-of-freedom, in this paper, fractional derivatives as model-form hyperparameters are introduced. A new general model calibration approach is proposed to separate and reduce model-form and parameter uncertainty based on multiple fractional frequency response functions (FFRFs). The new calibration method is verified through a simulated system with two degrees-of-freedom. The studies demonstrate that the new model-form and parameter uncertainty quantification method is robust.