Estimating uncertainty of model parameters obtained using numerical optimisation

Obtaining accurate models that can predict the behaviour of dynamic systems is important for a variety of applications. Often, models contain parameters that are difficult to calculate from system descriptions. Hence, parameter estimation methods are important tools for creating dynamic system models. Almost all dynamic system models contain uncertainty, either epistemic, due to simplifications in the model, or aleatoric, due to inherent randomness in physical effects such as measurement noise. Hence, obtaining an estimate for the uncertainty of the estimated parameters, typically in the form of confidence limits, is an important part of any statistically solid estimation procedure. Some uncertainty estimation methods can also be used to analyse the practical and structural identifiability of the parameters, as well as parameter inter-dependency and the presence of local minima in the objective function. In this paper, selected methods for estimation and analysis of parameters are reviewed. The methods are compared and demonstrated on the basis of both simulated and real world calibration data for two different case models. Recommendations are given for what applications each of the methods are suitable for. Further, differences in requirements for system excitation are discussed for each of the methods. Finally, a novel adaption of the Profile Likelihood method applied to a moving window is used to test the consistency of dynamic information in the calibration data for a particular model structure