Sequential model‐based design of experiments (MDBOE) accounts for information from previous experiments when selecting conditions for new experiments. In the current study, sequential MBDOE is used ...to select operating conditions for experiments in a batch‐reactor that produces bio‐based polytrimethylene ether glycol (PO3G). These Bayesian A‐optimal experiments are designed to obtain improved estimates of 70 fundamental‐model parameters, while accounting for industrial data from eight previous runs. Settings are selected for three decision variables: reactor temperature, initial catalyst level, and initial water concentration. If only one new experiment is conducted, it should be run at high temperature, with relatively high concentrations of catalyst and initial water. When two new runs are conducted, one should use an intermediate catalyst concentration. The effectiveness of the proposed MBDOE approach is tested using Monte‐Carlo simulations, revealing that the selected experiments are superior compared to experiments selected randomly from corners of the permissible design space.
•To represent nutrient dynamics in microalgae growth, Droop model is typically used.•The estimation of Droop model parameters requires high experimental effort.•Model-based design of experiments is ...used to design information-rich experiments.•MBDoE allows estimating Droop parameters using two optimal dynamic experiments.•The calibrated model is able to capture complex dynamics in nutrient uptake.
The comprehension of nutrients uptake and exploitation dynamics is a key aspect to increase the efficiency and the environmental sustainability of microalgal production at industrial scale. The Droop model is suitable for the description of the effect of nutrients on microalgal growth, but presents challenges in parameter identification due to the high correlation between parameters and the significant experimental effort required.
Model-based design of experiments is employed to plan information-rich experiments for precise parameters estimation, based on dynamic variations of dilution rate and nitrogen concentration in a continuous photobioreactor growing microalga Tetradesmus obliquus. It is shown that only two optimal experiments of 8 days each are sufficient to attain a statistically satisfactory estimation of all model parameters, thus minimising time and resources. Validation experiments show that the model can capture nitrogen uptake dynamics effectively, and demonstrate that the design of optimal dynamic experiments allows calibrating the Droop model rapidly, making it a valuable tool for the study of nutrients dynamics in continuous microalgal cultivation systems.
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.
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•Model-based design of experiments (MBDoE) is incorporated into a computer-aided molecular design framework.•Two formulations of the MBDoE problem are compared.•MBDoE is shown to improve the accuracy of surrogate models.•The DoE-QM-CAMD method is demonstrated in three case studies of industrial interest.
The sustainable phaseout of high global warming potential hydrofluorocarbon (HFC) refrigerant mixtures requires novel solvents, such as ionic liquids (ILs), for new HFC reuse and recycle ...technologies. Accurate, predictive, and interpretable thermodynamic models for HFC/IL mixtures are essential for multiscale design schemes aiding this phaseout. Still, there is limited guidance regarding the best thermodynamic model for an HFC/IL system. We propose a rigorous thermodynamic model selection and analysis workflow for HFC/IL mixtures which harnesses data science tools – visualization, nonlinear regression, Akaike information criteria, Fischer information matrix (FIM)-based identifiability and uncertainty analyses, and model-based design of experiments methods – to evaluate the accuracy, predictive capability, and interpretability of a thermodynamic model. The open-source IDAES™ platform facilitates training and comparison of sixteen candidate HFC/IL thermodynamic models, including two cubic equations of state, Peng–Robinson and Soave–Redlich–Kwong, and eight variations on temperature dependence within a classical van der Waals mixing rule. We apply this analysis to models for three HFC/IL systems: HFC-32/emimTF2N, HFC-125/emimTF2N, and HFC-32/bmimPF6. For these mixtures, we observe that models with a temperature dependent mixing rule are consistently ranked higher by Akaike information criteria for model selection. However, these models may still have high parameter uncertainty and correlation, indicating that data at multiple temperatures should be obtained. This result differs from the current practice of generating single isotherm dataset for most new HFC/IL mixtures. Additionally, we find that the most valuable experiments are taken at the bounds of composition, temperature (e.g., 273 and 348 K), and pressure (e.g., 1 MPa) measurements. This analysis guides data generation efforts, showing that optimally selected measurements across multiple temperatures are adequate for regressing thermodynamic models for multiscale process design.
Determination of the optimal design of experiments that enables efficient parametrisation of fuel cell (FC) model with a minimum parametrisation data-set is one of the key prerequisites for ...minimizing costs and effort of the parametrisation procedure. To efficiently tackle this challenge, the paper present an innovative methodology based on the electrochemical FC model, parameter sensitivity analysis and application of D-optimal design plan. Relying on this consistent methodological basis the paper answers fundamental questions: a) on a minimum required data-set to optimally parametrise the FC model and b) on the impact of reduced space of operational points on identifiability of individual calibration parameters. Results reveal that application of D-optimal DoE enables enhancement of calibration parameters information resulting in up to order of magnitude lower relative standard errors on smaller data-sets. In addition, it was shown that increased information and thus identifiability, inherently leads to improved robustness of the FC electrochemical model.
•Analysis is based on a thermodynamically consistent electrochemical fuel cell model.•Optimal set of fuel cell model parameters is determined by sensitivity analysis.•D-optimal criterion is used to determine the optimal design of experiments.•Enhanced parameter information results in up to few orders of magnitude lower RSE.•It is shown that variation of inlet pressure significantly increases information.
•Model-based design of experiments is considered with subset selection.•Mean-squared-error-based criterion is proposed to address ill-conditioning problem.•Subset selection methods by ranking and ...transformation are compared.•The proposed criterion is shown to be well-suited for ill-conditioned cases.•It can also outperform the conventional ones for well-conditioned cases.
Model-based design of experiments (MBDoE) has been widely used for efficient development of mathematical models, which can then be used for various applications for real world systems. The conventional optimality criteria for MBDoE can suffer from ill-conditioning of design matrix, which can be easily encountered in practical systems. To alleviate this problem, in this work, an alternative optimality criterion is proposed, whose formulation depends on mean squared error of biased estimators obtained by parameter subset selection. Such formulation is applied to subset selection methods by ranking and by transformation. Then, using an illustrative linear example, the performance of the proposed criterion is compared with three conventional criteria: A-, D-, and E-optimality criteria. Through the case study, it is shown that the proposed criterion can outperform the conventional ones in all the cases, generating linear models with smaller prediction errors, and it can provide better results with subset selection by transformation.
•A new method for exploratory model-based design of experiments (G-map eMBDoE) is presented.•The method leverages G-optimality to minimize prediction uncertainty across the design space.•Fast ...reduction of uncertainty on model predictions and parameters is achieved.•G-map eMBDoE outperforms both space filling designs and standard MBDoE methods.•Method tested on two case studies characterised by models of increasing complexity.
The management of trade-off between experimental design space exploration and information maximization is still an open question in the field of optimal experimental design. In classical optimal experimental design methods, the uncertainty of model prediction throughout the design space is not always assessed after parameter identification and parameters precision maximization do not guarantee that the model prediction variance is minimized in the whole domain of model utilization. To tackle these issues, we propose a novel model-based design of experiments (MBDoE) method that enhances space exploration and reduces model prediction uncertainty by using a mapping of model prediction variance (G-optimality mapping). This explorative MBDoE (eMBDoE) named G-map eMBDoE is tested on two models of increasing complexity and compared against conventional factorial design of experiments, Latin Hypercube (LH) sampling and MBDoE methods. The results show that G-map eMBDoE is more efficient in exploring the experimental design space when compared to a standard MBDoE and outperforms classical design of experiments methods in terms of model prediction uncertainty reduction and parameters precision maximization.
Systematic model-based design of experiment is essential to maximise the information from an experimental campaign. This technique is even more important to design experiments in systems described by ...stochastic models where the information quantity is characterised by intrinsic uncertainty, which has a significant impact on the experimental design for yielding informative data for precisely estimating model parameters. In this work, a new method for stochastic model-based design of experiments (SMBDoE) is presented to simultaneously identify the optimal operating conditions and the allocation of sampling points in time. The optimal experiment is identified by two sampling strategies selecting sampling intervals based on the average and the uncertainty of Fisher information. Seed coating is used as a case study to illustrate the feasibility of the method in identifying optimal coating conditions and sampling strategy in an industrial application.
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•A new method for stochastic model-based design of experiments (SMBDoE) is presented.•SMBDoE allows to identify optimal experimental conditions and sampling intervals.•Stochastic Fisher information affects the selection of sampling intervals.•The proposed method is applied to an industrial seed coating process.
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In oral solid dosage production through direct compression powder lubrication must be carefully selected to facilitate the manufacturing of tablets without degrading product ...manufacturability and quality (e.g. dissolution). To do so, several semi-empirical models relating compression performance to process operating conditions have been developed. Among them, we consider an extension of the Kushner and Moore model (Kushner and Moore, 2010, International Journal Pharmaceutics, 399:19) that is useful for the purpose, but requires an extensive experimental campaign for parameters identification. This implies the preparation and compression of multiple powder blends, each one with a different lubrication extent. In turn, this translates into a considerable consumption of Active Pharmaceutical Ingredient (API), and into time-consuming experiments. We tackled this issue by proposing a novel model-based design of experiments (MBDoE) approach, which minimizes the number of optimal blends for model calibration, while obtaining statistically sound parameters estimates and model predictions. Both sequential and parallel MBDoE configurations were compared. Experimental results involving two placebo blends with different lubrication sensitivity showed that this methodology is able to reduce the experimental effort by 60–70% with respect to the standard industrial practice independently of the formulation considered and configuration (i.e. parallel vs. sequential) adopted.
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