Model calibration using Identifiability Classes: improved accuracy, robustness and speed

Finite Element Model Updating (FEMU) methods enable for the calibration of model parameters by minimizing the discrepancy between computed and measured data. However, the accuracy and reliability of these methods depend on the identifiability of the parameters, which may be challenging to determine. The recently introduced "Identifiability Classes" offer a novel framework for quantitatively evaluating parameter identifiability by combining multiple data sources, sensitivity analyses, and measurement uncertainties. Each parameter is associated with an Identifiability Class, providing insight into its sensitivity and identifiability relative to uncertainty levels, and enabling for a clear distinction between identifiable and non-identifiable parameters. This information is utilized to inform various aspects of the model updating strategy, including data source selection, temporal data selection, and regularization techniques. By analyzing the Identifiability Classes, the most relevant data source or combination of data sources is determined, with the goal of maximizing the number of identifiable parameters. Additionally, the Identifiability Classes are used to optimize the temporal resolution of simulations and measurements, by selecting the most relevant time steps with respect to the Identifiability Classes, reducing the computational costs while maintaining accuracy. When dealing with non-identifiable parameters, regularization techniques such as Tikhonov regularization are necessary. The Identifiability Classes are then used to determine the optimal level of regularization required to prevent overfitting and avoid learning noise, while still achieving accurate parameter estimates. This strategy enables for rapid updating of models while maintaining their robustness and reliability. A subsequent relaxation strategy is then employed to further refine the updated model. The application of Identifiability Classes will be demonstrated through a case study, where the constitutive parameters are updated. By selecting the most informative data sources, time steps, and regularization levels based on Identifiability Classes, accuracy and reliability of parameter estimate is improved, while reducing the computational costs. While this study focuses on constitutive parameters updating, the Identifiability Classes approach can be applied to update other FE parameters, such as boundary conditions. Furthermore, the Identifiability Classes can be used in conjunction with virtual testing to optimize experimental design, including sample geometry and loading paths, potentially reducing the number of physical experiments required while improving the speed, accuracy, and reliability of model calibration.