An online reparametrisation approach for robust parameter estimation in automated model identification platforms

Abstract

Automated model identification platforms were recently employed to identify parametric models online in the course of unmanned experimental campaigns. The algorithms controlling these platforms include two computational elements: i) a tool for parameter estimation; ii) a tool for model-based experimental design. Both tools require the solution of complex optimisation problems and their effective outcome relies on their respective objective functions being wellconditioned. Ill-conditioned objective functions may arise when the model is characterised by a weak parametrisation, i.e. the model parameters are practically non-identifiable and/or extremely correlated. In this work, a robust reparametrisation technique is proposed and tested both in-silico and in an automated model identification platform. The benefit of reparametrisation is demonstrated on a case study for the identification of a kinetic model of catalytic esterification of benzoic acid with ethanol in a flow microreactor.

Safe model-based design of experiments using Gaussian processes

“…Particularly, (5) has extensively been utilized in the design of experiments [35,4] as the closed-form expression is available compare to the likelihood-subset ratio (4), where there is no closed-form expression available [54]. Nevertheless, the Wald confidence regions depend on the model reparameterization because of the (approximate) covariance term V θ , which may significantly affect the resulted confidence regions [50]. Additionally, in the same rationale, a Laplace approximation can be used for the posterior distribution of the parameter estimates given the available data:…”

Sequential model-based A- and V-optimal design of experiments for building fundamental models of pharmaceutical production processes

“…Structural identifiability issues can be addressed by obtaining new types of observations and by updating the model structure to include these observed responses. Also, the model can be reformulated or reparameterized to remove the non-identifiable parameters (Asprey and Naka, 1999;Espie and Macchietto, 1988;McLean and McAuley, 2012;Quaglio et al, 2019). Several different approaches have been developed to investigate structural identifiability problems including: a Taylor-series-expansion approach (Pohjanpalo, 1978), a generating-series approach (Walter and Lecourtier, 1982), a similarity transformation approach (Sandor Vajda et al, 1989) and a differential algebra approach (Ben-Zvi et al, 2010;Ljung and Glad, 1994).…”

Model-based design of transient flow experiments for the identification of kinetic parameters

“…20 MBDoE is a method of designing experiments which uses the information already known about a system from its model structure and initial parameter estimates to design an experiment in an optimal way, most commonly with the objective of either distinguishing between two or more candidate models, 22 or for precisely estimating the parameter values in a single chosen model. 2,[23][24][25] While MBDoE has previously been applied to transient flow experiments, this was for the purposes of model discrimination 26 and to the best of the authors' knowledge MBDoE has not been applied to transient microreactors for the purpose of precise estimation of the kinetic parameters.…”