A Sequential Iterative Scheme for Design of Experiments in Complex Polymerizations

Abstract

The Bayesian design approach is an experimental design technique which has many advantages over standard experimental designs. It incorporates prior knowledge about the process into the design to suggest a set of future experiments in an optimal, sequential, and iterative fashion. Since for many complex polymerizations prior information is available, either in the form of experimental data or mathematical models, the use of Bayesian design methodology could be beneficial. Exploiting this technique in complex polymerizations could hopefully lead to optimal performance in fewer trials, thus saving time and money. Advantages of the Bayesian design approach are illustrated via case studies drawn from the nitroxide-mediated radical polymerization as an example. However, since this technique is perfectly general, it can be potentially applied to other polymerization variants. IntroductionFor many complex polymerizations some sort of experimental information might be available (even in preliminary form) either from industrial or exploratory laboratory work. In addition, mathematical models (of different level of detail, empirical, or semi-mechanistic) usually do exist, albeit with unreliable and/or highly correlated parameters and sometimes even unverified mechanistic bases. Hence, ideas from the modelbased design of experiments applied as early as possible (in the design/brainstorming stage) can be very beneficial for the clarification of polymerization kinetics.Standard experimental design methods, e.g., (fractional) factorial designs, have been employed extensively and are useful in optimizing a wide variety of systems. However, these designs usually suffer from several limitations and cannot handle certain situations, as listed in Tab. 1. In addition, these approaches do not take direct advantage of the considerable prior knowledge that is available about the reaction system to design experiments. As prior information is already available within existing data, it is logical that it should be used in order to contribute to the optimality of the designed experiments, and hence to improved models and performance of the process in question.Although some of the issues with standard designs cited in Tab. 1 have solutions, these are usually known only to experts in the design of experiments. Hence, it often happens that the practicing scientist or engineer is not aware of the solutions, cannot easily handle the issues faced, and gives up on the use of statistical designs altogether. Using more efficient experimental designs which can accommodate these restrictions could lead to optimal performance in fewer trials, thus saving time and money.Such efficient designs can be found in the family of Bayesian approaches. The Bayesian design is a powerful and in the poly- [9]. The common characteristic of all these Bayesian framework applications (including the ones mentioned above as well as others from the scientific literature not cited herein for the sake of brevity), to a split of about 7 or 8 to 2, is that they are concern...

Diagnostic Checks and Measures of Information in the Bayesian Design of Experiments with Complex Polymerizations

“…Even more recently, Nabifar et al, [2] in a companion paper, expanded on and reinforced the advantages of the Bayesian technique by looking at additional polymerization case studies and demonstrating the attractiveness of the technique, which can suggest a set of future process experiments in an optimal, sequential and iterative fashion. Exploiting the Bayesian design in complex polymerizations (and in other processes, since the technique is perfectly general), could hopefully lead to optimal performance in fewer trials, thus saving time and money.…”

“…Two typical questions that often arise in Bayesian design implementations have to do with how effectively one can make statements about the quality of prior knowledge and the significance of the estimated effects (from the designed experiments), and about the gain in information content. These two important questions were not addressed in detail in earlier Bayesian design implementations, [1][2][3][4] and hence they are the topic of the present contribution. In other words, the following questions, intimately related to the Bayesian experimental design technique, will be addressed in what follows: (1) What statistical diagnostic criteria can one use in order to shed light on the quality of prior knowledge (see step 3, and implicitly step 2, of Table 3) and the significance of estimated effects (see step 7 of (1) and (2) above not only clarifies the design steps further but also could only make one more confident in the effectiveness and practicality of the Bayesian design of experiments procedure.…”

“…Since details about the Bayesian analysis steps have been discussed in Nabifar et al, [1,2] they are not repeated herein for the sake of brevity. Instead, a summary of the different steps for implementing the Bayesian design of experiments is given in a point form in Table 3, along with the pertinent equations used.…”

Model Discrimination between RAFT Polymerization Models Using Sequential Bayesian Methodology

“…This is the goal of sequential Bayesian design of experiments. These techniques have been used in polymerization and in many general Chemical Engineering modeling studies before, for the purpose of both modeling/parameter estimation and model discrimination …”

Deterministic Approaches for Simulation of Nitroxide-Mediated Radical Polymerization

“…This technique uses process models to design experiments in an optimal way in order to maximize the information that can be extracted from them and minimize the experimental effort required to estimate model parameters. Nabifar et al [129] demonstrated the benefits of the Bayesian design methodology in complex polymerization processes using an NMP system as a case study. Scott et al [130] carried out a model-based D-optimal design of experiments in the NMP of styrene.…”