Parameter Identification of a Nonlinear Vertical Axis Rotating Machine through Reduced Order Modeling and Data Assimilation

One challenge in modeling nonlinear dynamic systems involves the uncertainty associated with certain parameters that cannot be directly measured or estimated, along with the complexity of incorporating all relevant physical phenomena into a mathematical model without increasing computational cost. A hybrid twin represents an advanced modeling approach that combines the system's physics-based mathematical model with the empirical data collected from the real-world system, using data assimilation. This strategy enhances the accuracy and reliability of both estimating the system's unknown parameters and predicting its overall behavior. Further improvements are achieved by using a reduced-order model, which significantly lowers the computational burden of the entire procedure. In this study, we construct a surrogate model for a Vertical Axis Rotating Machine (VARM) by deploying sparse Proper Generalized Decomposition (sPGD). The model is parametrized in terms of the machine's unidentified parameters, and we apply the Harmonic-Modal Hybrid (HMH) Frequency Approach to solve for sparse scenarios creating the library of solutions. This is then combined with the Levenberg-Marquardt optimization technique to identify the unknown parameters using the measured shaft displacements of an experimental rig of the machine. The results demonstrate that this method is effective for parameter estimation in complex nonlinear systems and allows for fast computations, whether the unknown force function is specified explicitly or presumed. Precisely estimating a system's parameters can serve as a crucial indicator for scheduling maintenance or predicting failures.