(324d) Gaussian Process-Based Optimal Design of Experiments Under Structural Model Uncertainty

Gaussian Process-Based Optimal Design of Experiments Under Structural Model Uncertainty

Panagiotis Petsagkourakis, Michail Stamatakis and Federico Galvanin


CPSE, Department of Chemical Engineering, University College London (UCL), Gower St., WC1E 6BT London, United Kingdom

Kinetic modeling has become an indispensable tool in industry for a quantitative understanding of reaction systems. A reliable kinetic model can potentially be used to predict the behavior of the system outside of the experimental conditions used in the model validation and then be used for design, optimization and control in systems engineering applications. Model based design of experiments (MBDoE) has been widely used for the purposes of improving parameter precision in highly nonlinear dynamic systems (1). Several methods have been proposed in the literature for maximizing the collection of information for a limited amount of resources available for conducting the experiments. However, the model that describes the physical system may suffer from both parametric and structural uncertainties. As a result, the nominal model may lead to a substantial miscalculation of the information in the experimental design stage. The predicted information content can significantly differ from that of the real experiment that may lead to a non-informative experiment as well as to the violation of potential constraints acting on the system resulting in unsafe experimental conditions. The problem of parametric uncertainty has been extensively studied in the literature including the use unscented transformations (2) and polynomial chaos expansions (3) for efficient uncertainty propagation. However, it is still challenging to perform optimal experimental design that accounts for structural mismatches; some progress on this front has been made in (4,5).

In this work, a novel experimental design technique is proposed, which accounts for structural model uncertainty. We propose the use a Gaussian processes to capture the model mismatch and propagate the uncertainty to the next time instances. The Gaussian process has been proven to accurately approximate the probability density function of an underlying system and propagate the uncertainties effectively (6). The use of uncertainty propagation is not trivially computed since the structural mismatch will produce a non-Gaussian distribution that needs to be approximated. Analytical expressions for the covariance of the iterated predictions for multi-step predictions are utilized allowing us to integrate the techniques in an efficient framework for MBDoE. In the same rationale, the dynamic sensitivity is affected by the model mismatch and the uncertainty propagation through the sensitivities and the respective expected information is also considered. Therefore, in an iterative approach, the model parameters are updated requiring the training of the Gaussian process to capture the new mismatch. The aforementioned algorithm is depicted in Figure 1. After a preliminary parameter estimation is carried out from available experimental data in the first and second step, a Gaussian process training algorithm is employed to estimate the model mismatch in step three. Subsequently, the MBDoE algorithm is applied using the extended system that incorporates the Gaussian process. The control variables are applied to the physical system and then, the model parameters are re-estimated in step 6. If the fitting is not satisfactory the Gaussian process is retrained in step three. In order to demonstrate the effectiveness of this new MBDoE algorithm, the proposed methodology has been applied to the identification of a kinetic model for the esterification of benzoic acidin a microreactor (7,8). The underlying algorithms are implemented in python and CasADi, a dedicated framework for efficient algorithmic differentiation and numerical optimization (9),enabling the fast computations of the proposed optimizations.

Figure 1. Flow chart for Gaussian process based MBDoE.

References

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