Toward a Comprehensive and Efficient Robust Optimization Framework for (Bio)chemical Processes

Abstract

Model-based design principles have received considerable attention in biotechnology and the chemical industry over the last two decades. However, parameter uncertainties of first-principle models are critical in model-based design and have led to the development of robustification concepts. Various strategies have been introduced to solve the robust optimization problem. Most approaches suffer from either unreasonable computational expense or low approximation accuracy. Moreover, they are not rigorous and do not consider robust optimization problems where parameter correlation and equality constraints exist. In this work, we propose a highly efficient framework for solving robust optimization problems with the so-called point estimation method (PEM). The PEM has a fair trade-off between computational expense and approximation accuracy and can be easily extended to problems of parameter correlations. From a statistical point of view, moment-based methods are used to approximate robust inequality and equality constraints for a robust process design. We also apply a global sensitivity analysis to further simplify robust optimization problems with a large number of uncertain parameters. We demonstrate the performance of the proposed framework with two case studies: (1) designing a heating/cooling profile for the essential part of a continuous production process; and (2) optimizing the feeding profile for a fed-batch reactor of the penicillin fermentation process. According to the derived results, the proposed framework of robust process design addresses uncertainties adequately and scales well with the number of uncertain parameters. Thus, the described robustification concept should be an ideal candidate for more complex (bio)chemical problems in model-based design.

Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

“…For instance, recent studies use p-box design concepts for linear optimization problems in process design [30] and algebraic structural reliability analysis [28]. For dynamical systems, however, uncertainty analysis and propagation are challenging, because the computational costs when standard Monte Carlo simulation techniques are used [34].In the case of robust process design for nonlinear dynamic systems, highly efficient methods for uncertainty propagation are mandatory [35]. In addition to (quasi-) Monte Carlo simulations and improved sampling techniques [36], surrogate models (e.g., neural networks, Gaussian processes, and polynomial chaos expansion) are used to accelerate uncertainty propagation problems in robust process design, but typically suffer the curse of dimensionality [37][38][39][40]; that is, the cost increases exponentially with the number of uncertain model parameters.…”

“…In addition to (quasi-) Monte Carlo simulations and improved sampling techniques [36], surrogate models (e.g., neural networks, Gaussian processes, and polynomial chaos expansion) are used to accelerate uncertainty propagation problems in robust process design, but typically suffer the curse of dimensionality [37][38][39][40]; that is, the cost increases exponentially with the number of uncertain model parameters. Alternatively, in our previous work, we demonstrated the usefulness of the point estimate method (PEM) [41] for the robust design of pharmaceutical manufacturing processes [35]. The PEM ensures superior efficiency and workable accuracy for many problems in engineering [41,42].…”

“…In the case of robust process design for nonlinear dynamic systems, highly efficient methods for uncertainty propagation are mandatory [35]. In addition to (quasi-) Monte Carlo simulations and improved sampling techniques [36], surrogate models (e.g., neural networks, Gaussian processes, and polynomial chaos expansion) are used to accelerate uncertainty propagation problems in robust process design, but typically suffer the curse of dimensionality [37][38][39][40]; that is, the cost increases exponentially with the number of uncertain model parameters.…”

Special Issue on “Process Modelling and Simulation”

“…Our objective was to provide interested readers with an overview of the current state of research, tools and applications on the use of models for simulation and decision support in the process industry. The special issue brings together fourteen contributions on topics ranging from the process systems [1-3] and (bio)chemical engineering [4,5] fields, to software development [6] and applications in heat and power systems [7,8]. Moreover, the hot topic of data mining and machine learning is also discussed from a process engineering perspective in [9,10].…”

“…Nevertheless, the use of models is not limited to offline or real-time predictive simulation, but is likely to extend to process (dynamic and real time) optimization in the near future. Although model-based optimization was not directly within the scope of this special issue, the authors of [5,6] proposed steps in this direction from the application and software viewpoints, respectively.…”