Sequential model-based design of experiments for a heat-integrated biomass downdraft gasifier.

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.

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

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the scenario where we can sequentially update our beliefs about the model parameters through data gathered in the experiment. A class of models of particular interest for the natural and medical sciences are implicit models, where the data generating distribution is intractable, but sampling from it is possible. Even though there has been a lot of work on static BED for implicit models in the past few years, the notoriously difficult problem of sequential BED for implicit models has barely been touched upon. We address this gap in the literature by devising a novel sequential design framework for parameter estimation that uses the Mutual Information (MI) between model parameters and simulated data as a utility function to find optimal experimental designs, which has not been done before for implicit models. Our approach uses likelihood-free inference by ratio estimation to simultaneously estimate posterior distributions and the MI. During the sequential BED procedure we utilise Bayesian optimisation to help us optimise the MI utility. We find that our framework is efficient for the various implicit models tested, yielding accurate parameter estimates after only a few iterations.

Development of a framework for sequential Bayesian design of experiments: Application to a pilot-scale solvent-based CO2 capture process

In this paper, a methodology is developed for sequential design of experiments (SDoE) for process systems and applied to a solvent-based CO2 capture system. In this approach, the prior knowledge of the system is used to prioritize process data collection at specific operating conditions. These data are then incorporated into a Bayesian inference methodology for updating a stochastic model by refining estimations of its underlying parameters, and the updated model is then used to generate the next set of test runs. Thus, the new knowledge obtained from the data is used to guide subsequent iterations of the experimental runs, ensuring that the overall data collection is maximally informative given that most experimental campaigns, especially at pilot or higher-scale plants, are costly, time-consuming, and resource-limited. The test run objective for this work was to minimize the maximum model prediction uncertainty for key output variables, but the methodology is generic and can be readily applied to other test run objectives. This methodology is applied to an aqueous monoethanolamine (MEA) pilot plant campaign at the National Carbon Capture Center (NCCC) in Wilsonville, Alabama, USA. The SDoE framework was utilized for two iterations, while collecting 18 sets of data representing different process conditions, and this resulted in an overall average reduction in uncertainty of approximately 50% in the prediction of CO2 capture percentage. Moreover, 11 additional data sets were obtained with variation of absorber packing height for further model validation. This work shows the capability of the SDoE framework to maximize learning given limited resources, allowing for the reduction of model uncertainty, which is of great importance for many applications including reduction of technical risk associated with scale-up and economic analysis.

Surrogate-based sequential Bayesian experimental design using non-stationary Gaussian Processes

The need for first principles based models for chemical and biological processes has led to the development of techniques for model-based design of experiments (MBDOE). These techniques help in speeding up the parameter estimation efforts and typically lead to improved parameter precision with a relatively short experimental campaign. In the case of complex kinetic networks involving parallel and/or consecutive reactions, correlation among model parameters makes the inverse problem of parameter estimation very difficult. It is therefore important to develop experimental design techniques that not only increase information content about the system to facilitate precise parameter estimation but also reduce the correlation among parameters. This article presents a multiobjective optimization (MOO) based framework for experimental design, where, in addition to the traditional objective of eliciting maximally informative data for parameter estimation, an explicit objective to reduce correlation among parameters is included. The proposed MOO based framework is tested on two case studies, and results are compared with the traditional alphabetical designs. The approach provides a pictorial representation of trade-off between system information and correlation among parameters in the form of Pareto-optimal front, which offers the experimentalist the freedom to choose experimental design(s) that are most suitable to implement on the experimental system and realize the benefits of such experiments.

Sequential Design of Experiments to Maximize Learning from Carbon Capture Pilot Plant Testing

This work, under the optimal experimental design framework, investigates the sensor placement problem that aims to guide electromagnetic induction (EMI) sensing of multiple objects. We use the linearized model covariance matrix as a measure of estimation error to present a sequential experimental design (SED) technique. The technique recursively minimizes data misfit to update model parameters and maximizes an information gain function for a future survey relative to previous surveys. The fundamental process of the SED seeks to increase weighted sensitivities to targets when placing sensors. The synthetic and field experiments demonstrate that SED can be used to guide the sensing process for an effective interrogation. It also can serve as a theoretic basis to improve empirical survey operation. We further study the sensitivity of the SED to the number of objects within the sensing range. The tests suggest that an appropriately overrepresented model about expected anomalies might be a feasible choice.

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.

Model-based experimental design and parameter estimation, coupled with in situ infrared and laser backscattering instrumentation, was applied to the cooling crystallization of a drug compound to construct a model for use in the design of an optimal operating procedure. Because the model was constructed completely from in situ sensor data, with no sampling procedures, the amount of pharmaceutical compound required for batch process development was significantly reduced. Modeling issues involving the selection of the expressions for the supersaturation and nucleation rate, as well as the electronics mode in the laser backscattering instrument, were explored. All but one of the kinetic parameters from the gray-box model constructed using laser backscattering data were close to the kinetic parameters for a first-principles model constructed from data from off-line particle size measurements. The model was used to design batch operating procedures to minimize nucleation and maximize the sharpness of the crystal size distribution. This appears to be the first time that the procedure of model-based experimental design, parameter estimation, model selection, and optimization has been applied to the crystallization of a pharmaceutical, as well as the first time that this procedure has been applied to a crystallization process that forms loosely bound aggregates.

This study aims to optimize the variables involved in the wool dyeing process with cochineal (Dactylopius coccus Costa) to achieve the Mexican red hue, providing a scientific guide in the production of cochineal-dyed textiles. Sequential experimental designs and the steepest ascent method were employed to evaluate key factors, including insect quantity, mordant quantity, toner quantity, dyeing temperature, dyeing time, mordanting method, and dye pot material, by using color strength (K/S) maximum (at 530 nm) as a response variable. Colorimetric measurements were made in the CIELab color space for shade confirmation. The results highlighted the importance of pre-mordanting (using alum) and identified insect and toner quantities as the most significant variables. An optimal plateau was identified within the range of (45–55)% on weight of fabric (owf) for insect quantity and (20–25)% owf for toner (cream of tartar) quantity. Wash fastness tests demonstrated good to very good performance, with grayscale ratings of 3–4, and minimal to no staining on adjacent fabrics.

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.

This study describes the use of an analytical model, constructed using sequential design of experiments (DOEs), to optimize and quantify the uncertainty of a Diesel engine operating point. A genetic algorithm (GA) was also used to optimize the design. Three engine parameters were varied around a baseline design to minimize indicated specific fuel consumption (ISFC) without exceeding emissions (NOx and soot) or peak cylinder pressure constraints. An objective merit function was constructed to quantify the strength of designs. The engine parameters were start of injection (SOI), injection duration, and injector included angle. The engine simulation was completed with a sector mesh in the commercial computational fluid dynamics (CFD) software CONVERGE, which predicted the combustion and emissions using a detailed chemistry solver with a reduced mechanism for n-heptane. The analytical model was constructed using the SmartUQ software using DOE responses to construct kernel emulators of the system. Each emulator was used to direct the placement of the next set of DOE points such that they improve the accuracy of the subsequently generated emulator. This refinement was either across the entire design space or a reduced design space that was likely to contain the optimal design point. After sufficient emulator accuracy was achieved, the optimal design point was predicted. A total of 5 sequential DOEs were completed, for a total of 232 simulations. A reduced design region was predicted after the second DOE that reduced the volume of the design space by 96.8%. The final predicted optimum was found to exist in this reduced design region. The sequential DOE optimization was compared to an optimization performed using a GA. The GA was completed using a population of 9 and was run for 71 generations. This study highlighted the strengths of both methods for optimization. The GA (known to be an efficient and effective method) found a better optimum, while the DOE method found a good optimum with fewer total simulations. The DOE method also ran more simulations concurrently, which is an advantage when sufficient computing resources are available. In the second part of the study, the analytical model developed in the first part was used to assess the sensitivity and robustness of the design. A sensitivity analysis of the design space around the predicted optimum showed that injection duration had the strongest effect on predicted results, while the included angle had the weakest. The uncertainty propagation was studied over the reduced design region found with the sequential DoE in the first part. The uncertainty propagation results demonstrated that for the relatively large variations in the input parameters, the expected variation in the ISFC and NOx results were significant. Finally, the predictions from the analytical model were validated against CFD results for sweeps of the input parameters. The predictions of the analytical model were found to agree well with the results from the CFD simulation.

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