Numerical Approach to Identifiability Test of Parametric Models in Nonlinear Mechanical Systems

Abstract

Model parameters of a nonlinear mechanical system are identifiable if a unique relationship exists between its input–output behavior and the parameter values. The identifiability analysis of the parameters is one of the most important steps in the parametric model identification of nonlinear mechanical systems. The concept and two numerical approaches of analyzing the identifiability are presented in this paper. We propose that, via case studies, one had better check of the local identifiability of a parametric model at the identified parameter point using the numerical approach, when the parameter identification procedure has been finished.

Calibration of multi-physics computational models using Bayesian networks

“…Another possible case occurs when we add a discrepancy function to the numerical solutions of some governing equations, which in fact forms a new model without any analytical expression to consider [24]. Various analytical and numerical methods have been developed to detect the structural non-identifiability of dynamic models [25][26][27], whereas the second possible case does not appear to have been studied in the literature. This section addresses this case.…”

Selection of model discrepancy priors in Bayesian calibration

“…Another possible case occurs when we add a discrepancy function to the numerical solutions of some governing equations, which in fact forms a new model without any closed-form analytical expression [7]. Various analytical and numerical methods have been developed to detect the structural non-identifiability of dynamic models [21][22][23], whereas the second possible case does not appear to have been studied in the literature. This section addresses this case.…”

Single-shooting homotopy method for parameter identification in dynamical systems

“…In such cases, an optimization approach [13,14] is required, of which there are two varieties: single-shooting and multiple-shooting, the latter of which can be implemented with [3,4] or without [14] penalty terms. Provided the conditions of parameter identifiability [15] are met, it is possible to recover the system parameters using only partial state measurements; however, it might not be possible to recover the unknown initial conditions of unmeasured states. Single-shooting algorithms involve repeatedly simulating a mathematical model of the physical system for the same duration as the experiment, comparing the simulated response to the measured response and updating the parameter estimates after each simulation.…”