Test-Based Uncertainty Quantification and Propagation Using Hurty/Craig-Bampton Substructure Representations

Abstract

This work presents a method for uncertainty propagation that is consistent with the “building-block approach” in which components of a system are tested and validated individually instead of an integrated vehicle test and validation being performed. The approach gives a unified methodology for representing and quantifying uncertainty in a Hurty/Craig-Bampton component based on component test results and propagating the uncertainty in component models into system-level predictions. Uncertainty in the Hurty/Craig-Bampton representations is quantified using a new hybrid parametric variation approach based on Soize’s maximum entropy method. The proposed approach combines parametric and nonparametric uncertainty by treating the Hurty/Craig-Bampton fixed-interface eigenvalues as random variables and treating the corresponding mass and stiffness as random matrices. The proposed method offers several advantages over traditional approaches to uncertainty quantification in structural dynamics: the number of parametric random variables is relatively small compared to the usually large number of potential random finite element model parameters; therefore, time-consuming parametric sensitivity studies do not have to be performed. In addition, nonparametric model-form uncertainty is easily included using random matrix theory. The method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues and the corresponding mass and stiffness matrices. Test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, and test/analysis cross-orthogonality is used to identify the Hurty/Craig-Bampton stiffness matrix dispersion value. Currently, the mass matrix dispersion is based on engineering judgment, past experience, and historical results. The proposed uncertainty quantification methodology is applied to the Space Launch System liftoff configuration. Robustness of the attitude control system is studied by propagating derived component uncertainty models into gain uncertainty in specific transfer functions relating engine inputs to rate sensors on the core stage, and frequency uncertainty for the fundamental bending and roll modes.