A comprehensive framework for model evaluation and refinement using MBDoE estimability and structural identifiability: application to a crystallization process

Flatness-Based Design of Experiments for Model Selection

A review on model-based design of experiments for parameter precision – Open challenges, trends and future perspectives

Conducting new experiments for biomass gasifiers is expensive and time consuming. Therefore, it is important to select conditions for new experiments so maximum information is obtained. In this study, sequential Bayesian model-based design of experiments (MBDoE) is used to design new experimental runs for a heat-integrated biomass downdraft gasifier. This MBDoE approach is valuable because it accounts for model structure, prior information about plausible parameter values, and previous experimental data in a relatively simple way. Operating conditions selected for each new run are biomass moisture content, water injection rate, and the desired energy demand from the downstream engine. Three types of MBDoE with different objective functions are considered: A-optimal, V-optimal, and a proposed new type of focused V-optimal design. A-optimal design is used to when the goal is to obtain improved parameter estimates, without specifying how the model will be used. Performing two new A-optimal runs reduced the standard deviations for model parameters by 18.4% on average compared to when only old data are available. The three most-improved parameter estimates are activation energies for char gasification reactions involving carbon dioxide, hydrogen, and steam, respectively. The focused V-optimal methodology results in greater improvements in prediction accuracy for tar concentration and outlet temperature, which are key model responses. Using two designed Vf-optimal runs reduces standard deviations for these variables by 59.4%, on average, compared to when only old data are available. New A-optimal and V-optimal runs lead to corresponding improvements of 30.7% and 50%, respectively.

Optimization of ethylene and propylene yields from n-hexane catalytic cracking over H-ZSM-5 catalyst using model based design of experiments (DOE)

Type 410 stainless steel is used in petro-chemical refineries for its high resistance to halide stress corrosion cracking, sulfide corrosion cracking, and sulfur attack at elevated temperatures. Along with its adequate corrosion resistance 410SS also exhibits low cost and hardenability making it an ideal material for hydro-processing applications. Problems related to meeting toughness and hardness code requirements within the weld metal and heat effected zone (HAZ) have been experienced during fabrication of 410SS welded components. The loss of toughness has been related to excessive amounts of delta ferrite in the weld metal and HAZ. The objective of this study was to quantify the effect of cooling rate and alloying compositions within ASTM and AWS specifications for 410SS on delta ferrite formation. C, Cr, Ni, and Mo, were used as factors in a model-based design of experiment (DOE) within CALPHAD based software DICTRA™ to simulate the effects of composition and cooling rate on delta ferrite formation. Based on the DOE results, a predictive model for quantification of retained delta ferrite in 410SS welds was developed along with evidence for cooling rate effect on retained delta ferrite. Optical metallography was also used to demonstrate possible ferrite content within the 410 composition range.

Model-integrated process development demonstrated on the optimization of a robotic cation exchange step

Stoichio-kinetic model discrimination and parameter identification in continuous microreactors

A recently described C(sp3)–H activation reaction to synthesise aziridines was used as a model reaction to demonstrate the methodology of developing a process model using model-based design of experiments (MBDoE) and self-optimisation approaches in flow. The two approaches are compared in terms of experimental efficiency. The self-optimisation approach required the least number of experiments to reach the specified objectives of cost and product yield, whereas the MBDoE approach enabled a rapid generation of a process model.

This model-based design of experiments (MBDOE) method determines the input magnitudes of an experimental stimuli to apply and the associated measurements that should be taken to optimally constrain the uncertain dynamics of a biological system under study. The ideal global solution for this experiment design problem is generally computationally intractable because of parametric uncertainties in the mathematical model of the biological system. Others have addressed this issue by limiting the solution to a local estimate of the model parameters. Here we present an approach that is independent of the local parameter constraint. This approach is made computationally efficient and tractable by the use of: (1) sparse grid interpolation that approximates the biological system dynamics, (2) representative parameters that uniformly represent the data-consistent dynamical space, and (3) probability weights of the represented experimentally distinguishable dynamics. Our approach identifies data-consistent representative parameters using sparse grid interpolants, constructs the optimal input sequence from a greedy search, and defines the associated optimal measurements using a scenario tree. We explore the optimality of this MBDOE algorithm using a 3-dimensional Hes1 model and a 19-dimensional T-cell receptor model. The 19-dimensional T-cell model also demonstrates the MBDOE algorithm’s scalability to higher dimensions. In both cases, the dynamical uncertainty region that bounds the trajectories of the target system states were reduced by as much as 86% and 99% respectively after completing the designed experiments in silico. Our results suggest that for resolving dynamical uncertainty, the ability to design an input sequence paired with its associated measurements is particularly important when limited by the number of measurements.

The pharmaceutical and specialty chemical industries are challenged with the requirement of faster time-to-process to meet market demands. Here, Modular Plants made up of predesigned process equipment assemblies (PEAs) are advantageous. Moreover, equipment-based Digital Twins of these modules can further reduce the time-to-process when combined with methods such as Quality by Design (QbD) and model-based design of experiments (MBDoE) to reduce uncertainty. This paper presents a lab scale-based workflow using an equipment-based Digital Twin, which applies QbD and MbDoE methods to identify the Design Space in the lab scale which can be transferred to production scale equipment as part of a Digital Twin based workflow for scale-up in Modular Plants.

Continuous flow laboratory reactors are typically used for the development of kinetic models for catalytic reactions. Sequential model-based design of experiments (MBDoE) procedures have been proposed in literature where experiments are optimally designed for discriminating amongst candidate models or for improving the estimation of kinetic parameters. However, the effectiveness of these procedures is strongly affected by the initial model uncertainty, leading to suboptimal design solutions and higher number of experiments to be executed. A joint model-based design of experiments (j-MBDoE) technique, based on multi-objective optimization, is proposed in this paper for the simultaneous solution of the dual problem of discriminating among competitive kinetic models and improving the estimation of the model parameters. The effectiveness of the proposed design methodology is tested and discussed through a simulated case study for the identification of kinetic models of methanol oxidation over silver catalyst.

Computer-aided molecular design (CAMD) methods can be used to generate promising solvents with enhanced reaction kinetics, given a reliable model of solvent effects on reaction rates. Herein, we use a surrogate model parameterised from computer experiments, more specifically, quantum-mechanical (QM) data on rate constants. The choice of solvents in which these computer experiments are performed is critical, considering the cost and difficulty of these QM calculations. We investigate the use of model-based design of experiments (MBDoE) to identify an information-rich solvent set and integrate this within a QM-CAMD framework. We find it beneficial to consider a wide range of solvents in designing the solvent set, using group contribution techniques to predict missing solvent properties. We demonstrate, via three case studies, that the use of MBDoE yields surrogate models with good statistics and leads to the identification of solvents with enhanced predicted performance with few iterations and at low computational cost.

Towards in silico Process Modeling for Vaccines

Quantitative systems models have been increasingly used to accelerate the development of pharmaceutical processes that traditionally require time and resource-intensive experimental campaigns. However, despite the potential benefits of modelling in pharmaceutical process development, there is often a lack of confidence from stakeholders to adopt these approaches in a systematic way. This is particularly important in a highly regulated sector such as the pharmaceutical industry, where model uncertainty evaluation may have to be quantified and filed if model results are to be included as part of a regulatory submission. In this study, a systematic procedure is proposed, combining both standard techniques (e.g., global sensitivity analysis, model-based design of experiments) and new methods based on data analytics to assess model fidelity and to support practitioners in model usage for pharmaceutical development. A direct compression systems model for manufacturing oral solid dosage products is used as a case study. The systems model is comprised of the following sub-models: (1) Tablet press unit operation, (2) Tablet disintegration test unit, (3) In vitro dissolution test unit. The implementation of the methodology is critically discussed, showing the effectiveness of the approach and the benefits of the proposed techniques in (i) evaluating model fidelity as a result of uncertainty in parameter estimation, (ii) assessing whether it is necessary to estimate all systems model parameters in a statistically satisfactory way, and (iii) analyzing whether model calibration should be carried out on a unit basis or considering the overall system.

Optimal design of infusion tests for the identification of physiological models of acquired von Willebrand syndrome