Identifiability Classes: A Novel Framework for Evaluating Parameter Identifiability

Finite Element Model Updating (FEMU) methods are a class of inverse methods that allows calibrating model parameters based on sensitivity analyses of an FE model. They have the advantage of being non-intrusive to the simulation model, and being able to take into account measurement uncertainties of various measurement sources altogether. In these methods, parameter identifiability is crucial as it directly impacts the convergence of inverse problems as well as the reliability of inferred parameter values. The current methods for assessing identifiability are usually qualitative, lacking a quantitative criterion that considers couplings between parameters. Not being able to assess the identifiablity before running an inverse analysis leads to time-consuming back-and-forth analyses between problem setup and results, especially for large Finite Element simulations and complex constitutive laws. This work introduces ”Identifiability Classes,” a novel framework combining multiple data sources, sensitivity analyses, measurement uncertainties, and eigenspace analyses to provide a quantitative evaluation of (eigen)parameter identifiability. Each (eigen)parameter is associated with an (eigen)class, giving an information on its identifiability relative to uncertainty levels. This approach provides a more nuanced understanding of parameter estimation. It facilitates the development of new identification strategies with respect to the available experimental data and the design of optimal experiments. The application of Identifiability Classes is demonstrated through a case study including the identification of Finite Element model parameters (constitutive properties as well as boundary conditions).