Model-based Optimal Experimental Design Research Articles

Optimal experimental design for the identification of a reaction kinetic model for the hydroaminomethylation of 1-decene in a thermomorphic multiphase system

The transition toward green chemicals production requires new processes which are able to handle sustainable feedstock comprising unsaturated, long-chain hydrocarbons. The homogeneously rhodium-catalyzed tandem hydroaminomethylation (HAM) is able to convert long-chain olefins to amines and, therefore, represents an example reaction of high interest for the next generation of chemical processes. This work improves upon an existing mechanistic reaction kinetic model for 1-decene in a methanol/dodecane thermomorphic multiphase system (TMS) by structural adjustment of the catalyst pre-equilibrium, the investigation of the water influence on the reaction equilibria as well as the re-estimation of kinetic and inhibition parameters to provide accurate predictions under a wide range of operating conditions. This is achieved by pairing model-based optimal experimental design (mbOED) with perturbed-chain statistical associating fluid theory (PC-SAFT)-based phase equilibrium calculations to account for experiment setup-specific limitations while ensuring monophasic operation throughout all experiments. The subsequent model identification is able to substantially improve the prediction quality of the hydroaminomethylation model in edge cases over the previous model while maintaining a quantitative agreement of experimental and simulated concentration profiles under nominal conditions.

From Optimal Design of Experiment to Safe System Identification in Type 2 Diabetes

Model-based design of experiment (MBDoE) provides a framework to collect informative data for system identification. However, a parametric and structural mismatch between the design model and the underlying physical system can lead to hazardous experiments in safety critical systems. In this work, we present a method to safely improve system identification based on insights from a model-based optimal experimental design. From a visual inspection of a MBDoE, we select an approximated output curve fulfilling system constraints as a reference for the physical system. To avoid open-loop implementation of the MBDoE, we use our approximated reference together with a reference-tracking controller to collect experimental data in closed-loop. In this type 2 diabetes (T2D) case study, the proposed design method is safe and provides informative experimental data for system identification.

Iterative model-based optimal experimental design for mixture-process variable models to predict solubility

Crystallization process design relies heavily on predictive solubility models. However, their calibration is resource- and labour-intensive, especially for multicomponent solvent mixtures at different process temperatures. Additionally, solubility data collection often occurs in a constrained design space due to e.g., polymorphism and solvent miscibility limitations. Optimal experimental design techniques enable the efficient use of resources by specifying a (minimum) number of maximally informative experiments focused on improving a statistical criterion for a given model structure in a constrained design space. This work generates D-, A- and I-optimal experimental designs for the commonly applied Van’t-Hoff Jouyban-Acree (VH-JA) solubility regression model, in which it is demonstrated that I-optimal designs reduce the experimental burden for model calibration by approximately 25 % as compared to a typical screening dataset. Alternatively, existing datasets can be augmented to significantly improve model prediction power. The suggested workflow is applied to two case studies: itraconazole in tetrahydrofuran-water and mesalazine in ethanol-polyethylene glycol-water. The screening datasets of 72 and 212 runs were augmented with 16 additional experiments, resulting in a 33 % and 67 % reduction in the corresponding model prediction variance, respectively, which translates to improved model reliability at unprobed conditions.

Optimal experiment design under parametric uncertainty: A comparison of a sensitivities based approach versus a polynomial chaos based stochastic approach

In order to estimate parameters accurately in nonlinear dynamic systems, experiments that yield a maximum of information are invaluable. Such experiments can be obtained by exploiting model-based optimal experiment design techniques, which use the current guess for the parameters. This guess can differ from the actual system. Consequently, the experiment can result in a lower information content than expected and constraints are potentially violated. In this paper an efficient approach for stochastic optimal experiment design is exploited based on polynomial chaos expansion. This stochastic approach is compared with a sensitivities based approximate robust approach which aims to exploit (higher order) derivative information. Both approaches aim at a more conservative experiment design with respect to the information content and constraint violation. Based on two simulation case studies, practical guidelines are provided on which approach is best suited for robustness with respect to information content and robustness with respect to state constraints.

Robust Sampling Time Designs for Parametric Uncertain Systems

Robust experimental design (RED) of sampling time scheduling has been discussed for parametric uncertain systems. Four RED methods, i.e., the pseudo-Bayesian design, the maximin design, the expectation-variance design, and the online experimental redesign, are investigated under the framework of model-based optimal experimental design (OED). Both the D-optimal and the E-optimal criteria are used as performance metrics. Two numerical procedures, the Powell’s method and the semi-definite programming (SDP), are employed to obtain the optimum solution for REDs. The robustness performance of the four REDs are compared using a benchmark enzyme reaction system. In comparison to a typical uniform sampling strategy, the sampling time profiles from REDs are more focused on regions where the dynamic system has higher parametric sensitivities, indicating choice of informative data for parameter identification. The designed sampling strategies are also assessed by bootstrap parameter estimation with randomly generated initial points, where the difference between the REDs can be observed.

Monte Carlo Simulations for the Analysis of Non-linear Parameter Confidence Intervals in Optimal Experimental Design.

Especially in biomanufacturing, methods to design optimal experiments are a valuable technique to fully exploit the potential of the emerging technical possibilities that are driving experimental miniaturization and parallelization. The general objective is to reduce the experimental effort while maximizing the information content of an experiment, speeding up knowledge gain in R&D. The approach of model-based design of experiments (known as MBDoE) utilizes the information of an underlying mathematical model describing the system of interest. A common method to predict the accuracy of the parameter estimates uses the Fisher information matrix to approximate the 90% confidence intervals of the estimates. However, for highly non-linear models, this method might lead to wrong conclusions. In such cases, Monte Carlo sampling gives a more accurate insight into the parameter's estimate probability distribution and should be exploited to assess the reliability of the approximations made through the Fisher information matrix. We first introduce the model-based optimal experimental design for parameter estimation including parameter identification and validation by means of a simple non-linear Michaelis-Menten kinetic and show why Monte Carlo simulations give a more accurate depiction of the parameter uncertainty. Secondly, we propose a very robust and simple method to find optimal experimental designs using Monte Carlo simulations. Although computational expensive, the method is easy to implement and parallelize. This article focuses on practical examples of bioprocess engineering but is generally applicable in other fields.

Optimal experimental design for calibration of a new sewer water quality model

Water quality data in the sewer system are indispensable for modelling, but rarely available, as measurements in sewers are challenging to conduct. Optimal experimental design (OED) is a powerful tool to identify and maximize the information content of measurement data. This paper adopts a model-based OED methodology to efficiently plan a measurement campaign for final model calibration and validation of a new sewer water quality model. To do so, a preliminary calibrated model of the case study is used to evaluate the information content of different potential measurement locations and scenarios for suspended solids as measured variable. The case study first demonstrates how OED can identify the best measurement location within a complex sewer network. It secondly demonstrates that measuring the beginning of a big rain event results in the most information-rich data among all scenarios evaluated. Thirdly, it analyses in detail the information content of dry weather flow (DWF) data. In comparison to previous studies the methodology is improved by considering the actual measurement error characteristics when calculating the information content of measurement data.

Optimal experiment design in nonlinear parameter estimation with exact confidence regions

A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the least-squares parameter estimates. The optimal design is achieved by using the available (experimental) degrees of freedom such that more informative measurements are obtained. Unlike the commonly used approaches, which base the OED procedure upon the linearized CRs, we explore a path where we explicitly consider the exact CRs in the OED framework. We use a methodology for a finite parametrization of the exact CRs within the OED problem and we introduce a novel approximation technique of the exact CRs using inner- and outer-approximating ellipsoids as a computationally less demanding alternative. The employed techniques give the OED problem as a finite-dimensional mathematical program of bilevel nature. We use two small-scale illustrative case studies to study various OED criteria and compare the resulting optimal designs with the commonly used linearization-based approach. We also assess the performance of two simple heuristic numerical schemes for bilevel optimization within the studied problems.

On-Line Optimal Input Design Increases the Efficiency and Accuracy of the Modelling of an Inducible Synthetic Promoter

Synthetic biology seeks to design biological parts and circuits that implement new functions in cells. Major accomplishments have been reported in this field, yet predicting a priori the in vivo behaviour of synthetic gene circuits is major a challenge. Mathematical models offer a means to address this bottleneck. However, in biology, modelling is perceived as an expensive, time-consuming task. Indeed, the quality of predictions depends on the accuracy of parameters, which are traditionally inferred from poorly informative data. How much can parameter accuracy be improved by using model-based optimal experimental design (MBOED)? To tackle this question, we considered an inducible promoter in the yeast S. cerevisiae. Using in vivo data, we re-fit a dynamic model for this component and then compared the performance of standard (e.g., step inputs) and optimally designed experiments for parameter inference. We found that MBOED improves the quality of model calibration by ∼60%. Results further improve up to 84 % when considering on-line optimal experimental design (OED). Our in silico results suggest that MBOED provides a significant advantage in the identification of models of biological parts and should thus be integrated into their characterisation.

The Impact of Global Sensitivities and Design Measures in Model-Based Optimal Experimental Design

In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients. Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.

Using Sigma-Points to Identify Optimal Experimental Design for Dike Monitoring

In geotechnical engineering, using monitored data for model validation is common practice. However, a model-based optimal experimental design for parameter identification is unusual when planning a monitoring set-up. As soils are subjected to large parameter uncertainties, model validation is of high interest to enable a precise prediction of the system behaviour. Due to the complexity of considered cases and employed FE-models, time-efficient solutions are of interest. For the case of a dike subjected to a rapid drawdown of the current water level, a Monte-Carlo based approach was previously employed. In the present study, it is intended to improve the efficiency by applying the so-called sigma-Points method that substitutes random sampling by defined characteristics of model response distribution to set-up a monitoring design that allows to identify the relevant system parameters.

Application of iterative robust model-based optimal experimental design for the calibration of biocatalytic models.

The aim of model calibration is to estimate unique parameter values from available experimental data, here applied to a biocatalytic process. The traditional approach of first gathering data followed by performing a model calibration is inefficient, since the information gathered during experimentation is not actively used to optimize the experimental design. By applying an iterative robust model-based optimal experimental design, the limited amount of data collected is used to design additional informative experiments. The algorithm is used here to calibrate the initial reaction rate of an ω-transaminase catalyzed reaction in a more accurate way. The parameter confidence region estimated from the Fisher Information Matrix is compared with the likelihood confidence region, which is not only more accurate but also a computationally more expensive method. As a result, an important deviation between both approaches is found, confirming that linearization methods should be applied with care for nonlinear models. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1278-1293, 2017.

A sampling-based stochastic optimal experiment design formulation with application to the Williams-Otto reactor

Governmental pressure and an industrially competitive climate force chemical companies to strive for a sustainable design and operation. Model-based optimization has been proven to be an indispensable tool to achieve these goals. For the development and maintenance of process models, experimental data with a high information content are required. Model-based optimal experiment design techniques have been developed to obtain experiments that yield a high information content for estimating the model parameters. Since the true parameter values are unknown, these experiment designs start from the current best guesses. In practice, this can result in a lower information content than originally expected. In addition, the experiment design can become practically infeasible (e.g., in terms of safety), due to the violation of operational constraints. In this work a sampling-based stochastic optimal experiment design formulation is employed to address these problems. If the uncertainty on the model parameters can be considered to be a priori known, the parametric uncertainty can be propagated towards the states, which makes the experiment design more robust with respect to information content. As a practical case study of this formulation, the optimal experiment design of a Williams-Otto fed-batch reactor is made robust with respect to information content and reactor temperature state constraint violations. The novelty in this contribution is twofold: (i) polynomial chaos expansion and sigma points approach are compared for stochastic experiment design and (ii) the presented approach based on polynomial chaos expansion is analyzed for robustness with respect to state constraint violations considering different parametric uncertainty distributions.

A Probabilistic Approach to Robust Optimal Experiment Design with Chance Constraints

Accurate estimation of parameters is paramount in developing high-fidelity models for complex dynamical systems. Model-based optimal experiment design (OED) approaches enable systematic design of experiments to generate input-output data sets with high information content for parameter estimation. Standard OED approaches however face two challenges: (i) experiment design under incomplete system information due to unknown true parameters, which usually requires many iterations of OED; and (ii) incapability of systematically accounting for the inherent uncertainties of complex systems, which can lead to diminished effectiveness of the designed optimal excitation signal as well as violation of system constraints. This paper presents a robust OED approach for nonlinear systems with arbitrarily-shaped time-invariant probabilistic uncertainties. Polynomial chaos is used for efficient uncertainty propagation. The distinct feature of the robust OED approach is the inclusion of chance constraints to ensure constraint satisfaction in a stochastic setting. The presented approach is demonstrated by optimal experimental design for the JAK-STAT5 signaling pathway, which regulates various cellular processes in a biological cell.

Robustifying optimal experiment design for nonlinear, dynamic (bio)chemical systems

Dynamic experiments that yield as much information as possible are highly valuable for estimating parameters in nonlinear dynamic processes. Techniques for model-based optimal experiment design enable to systematically design such experiments. However, these experiments depend on the current best estimate of the parameters, which are not necessarily the true values. Consequently, in real experiments (i) the information content can be lower than predicted and (ii) state constraints can be violated. This paper presents a novel, computationally tractable formulation that enables the robustification of optimally designed experiments with respect to (i) information content and (ii) constraint satisfaction. To this end, the objective function is the expected value of a scalar function of the Fisher information matrix, which is efficiently computed using the sigma point method. This approach already has a robustifying effect. The sigma point method also enables the efficient computation of constraints’ variance–covariance matrix, this can be exploited for further robustification.

Microfluidic diffusion measurements: The optimal H-cell

This article reports the optimal design and measurement conditions for microfluidic diffusion experiments. For this purpose, we conducted and experimentally validated the model-based Optimal Experimental Design (OED) of a pressure-driven H-cell microchannel for diffusion measurements in liquids. While earlier work employed low Fourier numbers (i.e., low contact times), our results show the existence of an optimal finite Fourier number for which the measurement sensitivity increases drastically. For the optimal contact times (Fo=0.30…0.39), the accuracy of diffusion measurements is improved by orders of magnitude compared to the previously used sub-optimal low Fourier region (Fo<0.01). A general design rule for optimal H-cell diffusion experiments is derived. To demonstrate the utility of the optimized microfluidic method, diffusion coefficients are measured for a variety of binary mixtures. We show that H-cell measurements designed and operated according to the identified principles lead to a fast, efficient and cheap method for high-throughput diffusion analysis.

A Novel Multi-Objective Optimization based Experimental Design and its Application for Physiological Model of Type 1 Diabetes

The design of optimal model based experiments is finding increasing use in various fields including chemical, pharmaceutical, biological engineering, and biomedicine. The traditional Model Based Optimal Experimental Design (MBOED) techniques focus on improving the parameter precision but do not consider the undesired possibility of increasing the correlation among the estimated parameters. In this paper, we propose a multi-objective optimization based experimental design technique, which provides the trade-off curve between information measure and correlation measure in the form of a Pareto-optimal front. This Pareto-optimal front gives the experimenter the freedom to choose appropriate experimental designs for real world system under investigation. The proposed methodology is illustrated using an example involving the identification of physiological models for characterizing Type 1 diabetic patients.

Local Optima in Model-Based Optimal Experimental Design

Model-based nonlinear optimal experimental design (OED) has advanced to a relevant systematic tool in model development. However, the high nonlinearity of OED problems and their required high computational effort makes the optimization a challenging task. The objective of this work is to point out a crucial aspect of OED problems, namely, the existence of local minima. For this purpose, general characteristics of OED problems are presented and discussed, using different OED criteria and approaches (sequential/parallel). Furthermore, five different approaches are compared to overcome the local minima problem. Tuning options to improve the computation time of hybrid approaches are derived and discussed. The approaches are compared, based on the results of two case studies. To solve high-dimensional complex OED problems, a proposed hybrid framework is found to be a promising approach.

Handling Uncertainty in Model-Based Optimal Experimental Design

In contrast to the majority of published works in the field of model-based optimal experimental design which focused on numerical studies so as to demonstrate the validity of the OED approach or th...

Optimal Experimental Design for Discriminating Numerous Model Candidates: The AWDC Criterion

While model-based optimal experimental design (OED) strategies aiming at maximizing the parameter precision are regularly applied in industry and academia, only a little attention has been payed to OED techniques for model discrimination in practical applications. A broader use of these techniques is mainly hindered by two drawbacks: (i) The use of such techniques is desirable in an early model identification phase, where only a little knowledge on the process is available. The known methods, however, rely on good estimates of the parameters of all candidate model structures. (ii) The available methods are tailored to few (ideally two) model candidates and do not work well if numerous candidate structures are taken into account. In this work we propose a novel design criterion for model-based OED for model discrimination in the case of multiple model candidates. The resulting OED method is thus well-suited for designing experiments in an early stage of the model identification process to efficiently reduce the number of model candidates, thereby reducing the overall cost for model identification.