Model-based design of experiments in the presence of structural model uncertainty: an extended information matrix approach

Abstract

The identification of a parametric model, once a suitable model structure is proposed, requires the estimation of its non-measurable parameters. Model-based design of experiment (MBDoE) methods have been proposed in the literature for maximising the collection of information whenever there is a limited amount of resources available for conducting the experiments. Conventional MBDoE methods do not take into account the structural uncertainty on the model equations and this may lead to a substantial miscalculation of the information in the experimental design stage. In this work, an extended formulation of the Fisher information matrix is proposed as a metric of information accounting for model misspecification. The properties of the extended Fisher information matrix are presented and discussed with the support of two simulated case studies.

Probabilistic framework for optimal experimental campaigns in the presence of operational constraints

“…In particular, the definition of R α in (6) assumes that any structural mismatch present in the model η is captured through the probability distribution π of the model parameters θ . Note that other methods directly account for the presence of structural model mismatch, for instance by further restricting the experimental space to subdomains where the model is deemed reliable, 46,47 but these are outside the scope of this work.…”

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

“…A N U S C R I P T 6 uncertainties when selecting new experiments (John and Draper, 1975;Welch, 1984). Using MBDoE, it is straightforward to select any number of experiments that match available resources for experimentation (Quaglio et al, 2018).…”

Implementation and Application of Model-Based Design of Experiments in a Flowsheet Simulator

“…Walz et al 12 describe the use of global optimizer for a bilevel formulation for the guaranteed parameter estimation problem, which seems at the time being out of scope for an implementation in flowsheeting software. Newer developments also take structural uncertainties in the model into account 13 T h i s c o n t e n t i s or the online reparameterization using automated experimental setups. 14 To increase the efficiency in terms of computation time the previously described DoE method based on global sensitivities 6 was complemented by classical methods of model-based design of experiments with local sensitivities based on derivatives.…”

“…14 To increase the efficiency in terms of computation time the previously described DoE method based on global sensitivities 6 was complemented by classical methods of model-based design of experiments with local sensitivities based on derivatives. In this first implementation, the newer advanced methods of DoE 10,11,13,14 have not been addressed, since emphasis was on workflow integration and user support.…”

“…Walz et al describe the use of global optimizer for a bilevel formulation for the guaranteed parameter estimation problem, which seems at the time being out of scope for an implementation in flowsheeting software. Newer developments also take structural uncertainties in the model into account or the online reparameterization using automated experimental setups …”