Optimal experiment design under parametric uncertainty: A comparison of a sensitivities based approach versus a polynomial chaos based stochastic approach

Abstract

This document contains the post-print pdf-version of the refereed paper: "Optimal experiment design under parametric uncertainty: a comparison of a sensitivities based approach versus a polynomial chaos based stochastic approach" by Philippe Nimmegeers, Satyajeet Bhonsale, Dries Telen, and Jan Van Impe which has been archived on the university repository Lirias (https://lirias.kuleuven.be/) of the KU Leuven.The content is identical to the content of the published paper, but without the final typesetting by the publisher.

Safe model-based design of experiments using Gaussian processes

“…This problem is often numerically intractable when candidate models are highly nonlinear. Various methods have been proposed to accommodate this limitation, including linearization of the inner optimization [30] and a sensitivity-based approximate robust approach assuming ellipsoidal joint confidence region model parameters [35]. The robust approaches are typically conservative as they require the optimality and satisfaction of constraints to hold for all the possible values within the predefined uncertainty region.…”

“…The stochastic (also called probabilistic) experimental design framework avoids the typical strong conservatism of the worst-case MBDoE techniques, as the probability of occurrence of different realizations is accounted for differently. Various approaches [61,35,19,58,33] have been proposed in this family of problems usually inspired by the techniques originated from optimal control problem.…”

“…Nevertheless, unscented transformation approaches may fail in the presence of strong nonlinear relationships between the parameters and the states of the model. In this context, polynomial chaos expansion (PCE) has been used to compute the required moments of the objective and constraints in [33] and recently in [35]. Polynomial chaos expansions have been used in stochastic model predictive control for the purposes of uncertainty propagation through a nonlinear model [67].…”

“…The methods of robust MBDoE, e.g. [4,35] use the confidence regions computed in the parameter estimation step. Such an assumption may be sufficient to accommodate the uncertainty for the objective of the information content.…”

Assessment of the parameter identifiability of population balance models for air jet mills

“…Apart from improving the sensor quality, designing input profiles which sufficiently excite the process provides with informative data. Such inputs are designed using optimal experiment design (OED) (Telen et al, 2012;Nimmegeers et al, 2020). OED calculates the inputs profiles by solving a dynamic optimization with a scalar metric based on the FIM as the objective.…”