(475a) Multi-Objective Optimization Experimental Design Using a Exploration-Exploitation Trade-Off

Kinetic modelling has become an indispensable tool in the industry for a quantitative understanding of reaction systems. A reliable kinetic model can potentially be used to predict the system's behaviour outside of the experimental conditions used in the model validation and then be used for design, optimization and control in systems engineering applications [1]. The model capability of representing reliably and accurately the underlying phenomena depends on the model structure (i.e., the correlations and laws being used) and on the values of any parameters which may be calibrated to match the model to a specific real system data. Experimental data are typically required to assess the model validity and estimate the model parameters in the range of expected utilization. The approach of perturbing a process for system identification is a widespread and mature technique for parameter identification, particularly for systems represented by linear models [2]. However, in particular, for nonlinear systems, the experiments' choice to be carried out is critical to establish the most appropriate model structure and the best values of the parameters and save time and effort in experimental trials. In this regard, experimental conditions have a strong influence on parameter identifiability. They should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness [3]. When the model is highly nonlinear, the FIM-based MBDoE criteria may result in suboptimal solutions because 1) The FIM criteria rely on the first-order sensitivities of the model and 2) the design of the experiment is highly exploitative as it highly depends on the initial parameter estimates. Methods to address (1) have been proposed where curvature and parameter correlations have been incorporated [4]. Nevertheless, the exploitativeness of MBDoE has not been adequately addressed in the literature.

In data-driven optimization and specifically Bayesian optimization, it is common to design the next experiment given both the prediction of a data-driven model and the uncertainty of the prediction, i.e. the optimization maximizes the trade-off between prediction and prediction’s uncertainty [5]. This exploratory nature cannot trivially be accounted for the design space in the case of MBDoE, and for this reason, to perturb the optimal experimental design. A multi-objective optimization technique is proposed in this work, which maximizes the selected information criterion and maximizes the optimization variables' dispersion jointly. By using this approach the designed experiment accounts for the exploration of the design space and does not solely rely on the FIM that is based on the initial estimate of the parameters . The proposed methodology has been applied to optimize the online (re)-design of flow reactor experiments to demonstrate this new algorithm's effectiveness. The proposed technique has been tested on a case study adapted from [6] related to a nucleophilic aromatic substitution (SNAr) of 2, 4- difluoronitrobenzene with pyrrolidine in ethanol (EtOH) giving a mixture of the desired product ortho-substituted para-substituted and bis-adduct as side products.

[1] Marin G B, Yablonsky G S, Constales D, Kinetics of Chemical Reactions: Decoding Complexity, Second completely revised and enlarged Edition, 2019, Wiley

[2] Ljung, L., Söderström, T., & Willsky, A. S. (1985). Theory and Practice of Recursive Identification. Retrieved from https://books.google.co.uk/books?id=VPlQAAAAMAAJ

[3] Franceschini G, Macchietto S, Model-based design of experiments for parameter precision: State of the art. Chem Eng Sci. 2008, 63(19), 4846 -72.

[4] Manesso, E.; Sridharan, S.; Gunawan, R. Multi-Objective Optimization of Experiments Using Curvature and Fisher Information Matrix. Processes 2017, 5, 63.

[5] Jones D R, Schonlau M, Welch W J, Efficient Global Optimization of Expensive Black-Box Functions, 1998, Journal of Global Optimization, 13, 455–492

[6] Hone C A, Holmes N, Akien G R, Bourne R A, Muller F L, 2017. Rapid multistep kinetic model generation from transient flow data, Reaction Chemistry and Engineering, 2, 103–108.