A sampling-based stochastic optimal experiment design formulation with application to the Williams-Otto reactor

Abstract

Governmental pressure and an industrially competitive climate force chemical companies to strive for a sustainable design and operation. Model-based optimization has been proven to be an indispensable tool to achieve these goals. For the development and maintenance of process models, experimental data with a high information content are required. Model-based optimal experiment design techniques have been developed to obtain experiments that yield a high information content for estimating the model parameters. Since the true parameter values are unknown, these experiment designs start from the current best guesses. In practice, this can result in a lower information content than originally expected. In addition, the experiment design can become practically infeasible (e.g., in terms of safety), due to the violation of operational constraints. In this work a sampling-based stochastic optimal experiment design formulation is employed to address these problems. If the uncertainty on the model parameters can be considered to be a priori known, the parametric uncertainty can be propagated towards the states, which makes the experiment design more robust with respect to information content. As a practical case study of this formulation, the optimal experiment design of a Williams-Otto fed-batch reactor is made robust with respect to information content and reactor temperature state constraint violations. The novelty in this contribution is twofold: (i) polynomial chaos expansion and sigma points approach are compared for stochastic experiment design and (ii) the presented approach based on polynomial chaos expansion is analyzed for robustness with respect to state constraint violations considering different parametric uncertainty distributions.