Model-based Experimental Design Research Articles

Model-Based Design of Experiments in the Presence of Continuous Measurement Systems

Model-based design of experiments (MBDoE) techniques are a useful tool to maximize the information content of experimental trials when the purpose is identifying the set of parameters of a deterministic model in a statistically sound way. Traditionally, the problem of MBDoE has been addressed for discrete measurement systems. In this case, formulation of the optimal design problem is based on maximization of the expected information, usually calculated from discrete forms of the Fisher information matrix. However, current measurement technology allows measurements to be taken at a much higher frequency than in the past, to a point that measurements may be assumed to be obtained in a continuous way. A novel design criterion allowing for the continuous model-based design of the experiments (CMBDoE) is formulated in this paper by optimizing a continuous measurement function of the Fisher information matrix, with the purpose of reaching a statistically satisfactory estimation of model parameters in a computationally efficient way. The benefits of the proposed strategy are discussed by means of two simulated case studies, where the effectiveness of the design is assessed by comparison to a standard MBDoE approach.

Optimal design of clinical tests for the identification of physiological models of type 1 diabetes in the presence of model mismatch

How to design a clinical test aimed at identifying in the safest, most precise and quickest way the subject-specific parameters of a detailed model of glucose homeostasis in type 1 diabetes is the topic of this article. Recently, standard techniques of model-based design of experiments (MBDoE) for parameter identification have been proposed to design clinical tests for the identification of the model parameters for a single type 1 diabetic individual. However, standard MBDoE is affected by some limitations. In particular, the existence of a structural mismatch between the responses of the subject and that of the model to be identified, together with initial uncertainty in the model parameters may lead to design clinical tests that are sub-optimal (scarcely informative) or even unsafe (the actual response of the subject might be hypoglycaemic or strongly hyperglycaemic). The integrated use of two advanced MBDoE techniques (online model-based redesign of experiments and backoff-based MBDoE) is proposed in this article as a way to effectively tackle the above issue. Online model-based experiment redesign is utilised to exploit the information embedded in the experimental data as soon as the data become available, and to adjust the clinical test accordingly whilst the test is running. Backoff-based MBDoE explicitly accounts for model parameter uncertainty, and allows one to plan a test that is both optimally informative and safe by design. The effectiveness and features of the proposed approach are assessed and critically discussed via a simulated case study based on state-of-the-art detailed models of glucose homeostasis. It is shown that the proposed approach based on advanced MBDoE techniques allows defining safe, informative and subject-tailored clinical tests for model identification, with limited experimental effort.

A cubic equation of state based on saturated vapor modeling and the application of model-based design of experiments for its validation

For simulation of chemical processes, a sufficiently accurate mathematical description of phase equilibria is essential. In order to achieve this, high-quality measured data and model equations are indispensable. A new gamma-function as a replacement for the common alpha-function in cubic equations of state is proposed here for polar compounds with an existing vapor phase. The equation parameters of the gamma-function are fitted to state data on the dew line instead of, as usual, on the vaporization curve. The quality of the description is compared to the customary equations of state using statistical parameters. A further validation used for the description is the prediction of caloric parameters and the comparison thereof with measured data. By means of model-based experimental design, the gamma-function and the equation of state based thereon are validated. Multiple setpoint optimization allows a uniform experimental design for validation of a vapor pressure equation and of a vapor density equation to be calculated for polar compounds. The experiments calculated optimally in this way reduce large test series to a few experiments which are significant for the specific model equation.

Optimal determination of steric mass action model parameters for β-lactoglobulin using static batch experiments

In this work, parameters of the steric mass-formalism SMA are optimally ascertained for a reliable determination of the adsorption isotherms of β-lactoglobulin A and B under non-isocratic conditions. For this purpose, static batch experiments are used in contrast to the protocols based on different experimental steps, which use a chromatographic column. It is shown that parameters can already be determined for a small number of experiments by using a systematic procedure based on optimal model-based experimental design and an efficient NLP-solver. The in different works observed anti-Langmuir shape of the isotherm for small concentrations of β-lactoglobulin A was corroborated. Moreover, we also found indications for a porosity variation with changing protein concentrations.

A framework for model-based design of experiments in the presence of continuous measurement systems

Model-based design of experiments (MBDoE) techniques are a useful tool to maximise the information content of experimental trials when the purpose is identifying the set of parameters of a deterministic model in a statistically sound way. When samples are collected in a discrete way, the formulation of the optimal design problem is based on the maximisation of the expected information, usually calculated from discrete forms of the Fisher information matrix. However, if a continuous measurement system is available, information can be acquired gradually in a continuous way, and a new MBDoE approach is required to take into account the specificity of the measurement system. In this paper a novel design criterion is formulated by optimising a continuous measurement of the Fisher information matrix, with the purpose of reaching a statistically satisfactory estimation of model parameters in the easiest and quickest way. The benefits of the proposed strategy are discussed through a simulated case study, where the effectiveness of the design is assessed by comparison to a standard MBDoE approach.

Investigating Bayesian Robust Experimental Design with Principles of Global Sensitivity Analysis

The purpose of model-based experimental design is to maximise the information gathered for quantitative model identification. Instead of the commonly used optimal experimental design, robust experimental design aims to address parametric uncertainties in the design process. In this paper, the Bayesian robust experimental design is investigated, where both a Monte Carlo sampling strategy and local sensitivity evaluation at each sampling point are employed to achieve the robust solution. The link between global sensitivity analysis (GSA) and the Bayesian robust experimental design is established. It is revealed that a lattice sampling based GSA strategy, the Morris method, can be explicitly interpreted as the Bayesian A-optimal design for the uniform hypercube type uncertainties.

Model-based experimental design for assessing effects of mixtures of chemicals

We exposed flour beetles ( Tribolium castaneum) to a mixture of four poly aromatic hydrocarbons (PAHs). The experimental setup was chosen such that the emphasis was on assessing partial effects. We interpreted the effects of the mixture by a process-based model, with a threshold concentration for effects on survival. The behavior of the threshold concentration was one of the key features of this research. We showed that the threshold concentration is shared by toxicants with the same mode of action, which gives a mechanistic explanation for the observation that toxic effects in mixtures may occur in concentration ranges where the individual components do not show effects. Our approach gives reliable predictions of partial effects on survival and allows for a reduction of experimental effort in assessing effects of mixtures, extrapolations to other mixtures, other points in time, or in a wider perspective to other organisms.

Global Sensitivity Analysis Challenges in Biological Systems Modeling

Mammalian cell culture systems produce high-value biologics, such as monoclonal antibodies, which are increasingly being used clinically. A complete framework that interlinks model-based design of experiments (DOE) and model-based control and optimization to the actual industrial bioprocess could assist experimentation, hence reducing costs. However, high fidelity models have the inherent characteristic of containing a large number of parameters, which is further complicated by limitations in the current analytical techniques, thus resulting in the experimental validation of merely a small number of parameters. Sensitivity analysis techniques can provide valuable insight into model characteristics. Traditionally, the application of sensitivity analysis on models of biological systems has been treated more or less as a black box operation. In the present work, we elucidate the aspects of sensitivity analysis and identify, with reasoning, the most suitable group of sensitivity analysis methods for applicati...

Iterative Design of Dynamic Experiments in Modeling for Optimization of Innovative Bioprocesses

Finding optimal operating conditions fast with a scarce budget of experimental runs is a key problem to speed up the development and scaling up of innovative bioprocesses. In this paper, a novel iterative methodology for the model-based design of dynamic experiments in modeling for optimization is developed and successfully applied to the optimization of a fed-batch bioreactor related to the production of r-interleukin-11 (rIL-11) whose DNA sequence has been cloned in an Escherichia coli strain. At each iteration, the proposed methodology resorts to a library of tendency models to increasingly bias bioreactor operating conditions towards an optimum. By selecting the ‘most informative’ tendency model in the sequel, the next dynamic experiment is defined by re-optimizing the input policy and calculating optimal sampling times. Model selection is based on minimizing an error measure which distinguishes between parametric and structural uncertainty to selectively bias data gathering towards improved operating conditions. The parametric uncertainty of tendency models is iteratively reduced using Global Sensitivity Analysis (GSA) to pinpoint which parameters are keys for estimating the objective function. Results obtained after just a few iterations are very promising.

Online Model-Based Redesign of Experiments for Parameter Estimation in Dynamic Systems

The optimal model-based design of experiments aims at designing a set of dynamic experiments yielding the most informative process data to be used for the estimation of the parameters of a first-principles dynamic process model. According to the usual procedure for parameter estimation, the experiment is first designed offline; then, the experiment is carried out in the plant, and process measurements are collected; and finally, parameters are estimated after completion of the experiment. Therefore, the information gathered during the evolution of the experiment is analyzed only at the end of the experiment itself. Since the experiment is designed on the basis of the parameter estimates available before the experiment is started, the progressive increase of the information resulting from the progress of the experiment is not exploited by the designer until the end of that experiment. In this paper, a strategy for the online model-based redesign of experiments is proposed to exploit the information as soon...

Anti-Correlation Approach to Model-Based Experiment Design: Application to a Biodiesel Production Process

Advanced model-based experiment design techniques are a reliable tool for rapid development and refining of process models, in particular in the area of chemical kinetics. The high parameter correlations, which are typical of the most common reaction networks (parallel, consecutive reactions, etc.), often make the identification and proper estimation of the model parameters extremely difficult. For this reason, a novel approach to model-based experiment design able to yield optimally informative experiments while simultaneously reducing the correlations between the model parameters was proposed in a previous publication1 and was demonstrated to be highly effective. This article presents the application of this novel anti-correlation approach to the identification of a kinetic model for biodiesel transesterification from rapeseed oil, using isothermal experiments. The actual, as opposed to simulated, execution of laboratory experiments provides a further and much more significant demonstration of the effectiveness of our innovative design method. By following the suggested algorithm, three experiments were optimized for each of the two design iterations, providing statistically validated estimates for the six kinetic constants involved in the model with, on average, a medium correlation level.

Experimental design for the identification of hybrid reaction models from transient data

Model identification from dynamic experimental data may involve the conduction of multiple experiments to identify a suitable model with adequate accuracy. In contrast to the a priori specification of design sets, an iteratively conducted model-based experimental design exploiting previous data promises significantly better results with lower effort. Yet, in dynamic systems, the inputs of the model to be identified often cannot be designed directly, but depend on the experimental degrees of freedom. To allow for model-based design for the identification of dynamic hybrid or fully unstructured models, a new design criterion is developed in this work. It is based on an input-space coverage approach and allows to simultaneously design the experiment for multiple models to be identified. Incremental identification is applied to efficiently construct the unknown models from data. The resulting iterative design and identification methodology is illustrated on a reaction kinetic model identification for the acetoacetylation of pyrrole in a simulation study.

Model-based design of experiments for parameter precision: State of the art

Due to the wide use and key importance of mathematical models in process engineering, experiment design is becoming an essential tool for the rapid building and validation of these mechanistic models. Several experiment design techniques have been developed in the past and applied successfully to a wide range of systems. This paper is focused on the so-called model-based design of experiments (DOE) and aims at presenting an up-to-date state of the art in this important field. In order to provide an adequate and thorough background to this technique, a detailed description of the key elements of a model identification procedure (the model itself, the experiment, the statistical tools, etc.) and the major steps of a model-building strategy are introduced before focusing on the experiment design for parameter precision, which is the topic of this survey. An overview and critical analysis of the state of the art in this sector are proposed. The main contributions to model-based experiment design procedures in terms of novel criteria, mathematical formulations and numerical implementations are highlighted. A list of the most recent applications of these techniques in various fields (from chemical kinetics to biological modelling) is then presented highlighting the key role of model-based DOE in the process engineering area.

Model-Based Design of Parallel Experiments

Advanced model-based experiment design techniques are essential for the rapid development, refinement, and statistical assessment of deterministic process models. One objective of experiment design is to devise experiments yielding the most informative data for use in the estimation of the model parameters. Current techniques assume that multiple experiments are designed in a sequential manner. However, multiple equipment can sometimes be available, and simultaneous (parallel) experiments could be advantageous in terms of time and resources utilization. The concept of model-based design of parallel experiments is presented in this paper. Furthermore, a novel criterion for optimal experiment design is proposed: the criterion aims at maximizing complementary information by considering different eigenvalues in the information matrix. The benefits of adopting such an approach are discussed through an illustrative case.

Validation of a Model for Biodiesel Production through Model-Based Experiment Design

Advanced model-based experiment design techniques are a reliable tool for the rapid development and refining of process models. Through a practical case study of current interest (a biodiesel production process), we demonstrate the validity of this approach as applied to the planning of optimal experiments for complex kinetics elucidation. The need for an appropriate use of these tools, in particular a judicious problem formulation, is highlighted. A trade-off is found between the predicted precision of the estimates and important experimental aspects (for example, times and costs of the analytical work). The intelligent application of these techniques allows finding experiments which are suitable for the collection of data for complex kinetic networks. A methodology capable of dealing with experiment design problems which involve complex reaction mechanisms is also presented, and advantages and limitations of this procedure are discussed in the light of the results obtained from the parameter estimation.

Hierarchical multiscale model-based design of experiments, catalysts, and reactors for fuel processing

In this paper a hierarchical multiscale simulation framework is outlined and experimental data injection into this framework is discussed. Specifically, we discuss multiscale model-based design of experiments to optimize the chemical information content of a detailed reaction mechanism in order to improve the fidelity and accuracy of reaction models. Extension of this framework to product (catalyst) design is briefly touched upon. Furthermore, we illustrate the use of such detailed and reduced kinetic models in reactor optimization as an example toward more conventional process design. It is proposed that hierarchical multiscale modeling offers a systematic framework for identification of the important scale(s) and model(s) where one should focus research efforts on. The ammonia decomposition on ruthenium to produce hydrogen and the water–gas shift reactions on platinum for converting syngas to hydrogen serve as illustrative fuel processing examples of various topics. The former is used to illustrate hierarchical multiscale model development and model-based parameter estimation as well as product engineering. The latter is employed to demonstrate model reduction and process optimization. Finally, opportunities for process design and control in portable microchemical devices (lab-on-a chip) for power generation are discussed.

Perspectives on the design and control of multiscale systems

New applications in materials, medicine, and computers are being discovered where the control of events at the molecular and nanoscopic scales is critical to product quality, although the primary manipulation of these events during processing occurs at macroscopic length scales. This motivates the creation of tools for the design and control of multiscale systems that have length scales ranging from the atomistic to the macroscopic. This paper describes a systematic approach that consists of stochastic parameter sensitivity analysis, Bayesian parameter estimation applied to ab initio calculations and experimental data, model-based experimental design, hypothesis mechanism selection, and multistep optimization.

Distributed performance testing using statistical modeling

This article briefly presents some of our recent research in distributed continuous performance analysis. In general this work pushes substantial parts of performance analysis out of developer laboratories and onto remote, end-user machines.To do this effectively we have found it useful to recast performance analysis as a model-based experimental design and execution problem.Our experience suggests that this approach has merit, but that much future work remains to be done. We therefore discuss some of the limitations of our current efforts and describe some plans for future work.

Multiscale systems engineering with applications to chemical reaction processes

New applications in materials, medicine, and computers are being discovered where the control of events at the molecular and nanoscopic scales is critical to product quality, although the primary manipulation of these events during processing occurs at macroscopic length scales. This motivates the creation of tools for the engineering of multiscale reacting systems that have length scales ranging from the atomistic to the macroscopic. This paper describes a systematic approach that consists of stochastic parameter sensitivity analysis, Bayesian parameter estimation applied to ab initio calculations and experimental data, model-based experimental design, hypothesis mechanism selection, and multistep optimization.

Parameter Estimation and Optimization of a Loosely Bound Aggregating Pharmaceutical Crystallization Using in Situ Infrared and Laser Backscattering Measurements

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.