Estimating uncertainty of model parameters obtained using numerical optimisation

Abstract

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.

Design of a short perturbation method for on-site estimation of a building envelope thermal performance

“…Brastein et al [8] assessed the identifiability and physical interpretation of a second order RC model. The model was calibrated using a 10-day dataset shown in Figure 2d.…”

“…(a) Heating power induced perturbation in Madsen and Schultz (see Fig.3in[6]. Note from the authors : "the sampling index corresponds to 5 minutes at the two periods of 42 hours, and to L hour at the long period of 300 hours") (b) ROLBS heating sequence perturbation in Baker and van Dijk (see Fig.10in[7]) Heating power induced perturbation in Brastein et al (see Fig.18in[8]) (e) Heating power induced perturbation in the QUB method (see Fig.1in[12])…”

Towards automated stochastic Grey-Box Model Calibration for Heat Transfer Coefficient Inference

“…Brastein et al [7] show indeed how a randomised initial guess of the model parameters is a way of assessing the identifiability of a model with respect to a certain dataset. Each initial guess is followed by a parameter estimation.…”

“…As any minimisation algorithm, each parameter and state can be initialised as to favour convergence. In literature, parameter initialisation is based either on default values or on expert knowledge [7,8], hereafter respectively called strategy (0) and strategy (1), such as in Figure 1.…”