Optimal experiment design for dynamic processes

Bhonsale, Satyajeet; Nimmegeers, Philippe; Akkermans, Simen; Telen, Dries; Stamati, Ioanna; Logist, Filip; Impe, Jan Van

doi:10.1016/b978-0-323-85043-8.00010-6

Cited by 3 publications

(6 citation statements)

References 41 publications

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“…However, this claim has been dismissed by different studies, 7,8 where none of the proposed criteria meet the intended condition (efficient parameter estimation and what with call hereafter decorrelation ). As a matter of fact, minimizing the determinant of a

2 \times 2

covariance matrix means minimizing the product of the variances while maximizing the covariance:

(||, Σ) = σ_{1}^{2} σ_{2}^{2} - σ_{12}^{2} .

…”

Section: Optimal Estimators For Two‐parameter Modelsmentioning

confidence: 99%

“…What can be deduced from the previously mentioned works is that the strategy of obtaining an indicator that achieves a simultaneous optimization of both the estimation of the parameters and their correlations has not been found successfully. Therefore, the attempt to create multi‐criteria indicators to solve the problem has generated wide interest 7,8 . Under this approach, two types of optimality can be distinguished: (1) compound optimality criteria, which combine properties of more than one criterion, for example, a weighted sum of two criteria such as

ϕ_{D}

and

ϕ_{E M}

, 7

ϕ_{A}

and

ϕ_{E M}

, 12 or

ϕ_{c}

with restrictions on eigenvalues, 4,12 and (2) select from a set of optimal solutions using Pareto fronts 7,8,19 .…”

Section: Optimal Estimators For Two‐parameter Modelsmentioning

confidence: 99%

“…Therefore, the attempt to create multi‐criteria indicators to solve the problem has generated wide interest 7,8 . Under this approach, two types of optimality can be distinguished: (1) compound optimality criteria, which combine properties of more than one criterion, for example, a weighted sum of two criteria such as

ϕ_{D}

and

ϕ_{E M}

, 7

ϕ_{A}

and

ϕ_{E M}

, 12 or

ϕ_{c}

with restrictions on eigenvalues, 4,12 and (2) select from a set of optimal solutions using Pareto fronts 7,8,19 . Some authors have highlighted that taking into account A‐optimality only contains the information of the parameters per se, then this criterion seems very convenient to be combined with another criterion that gives weight to the correlation of parameters 4 …”

Section: Optimal Estimators For Two‐parameter Modelsmentioning

confidence: 99%

“…In such situations, one could proceed by calculating the variance and covariance terms which are of special interest in addition to using the overall criterion. 3 However, this claim has been dismissed by different studies, 7,8 where none of the proposed criteria meet the intended condition (efficient parameter estimation and what with call hereafter decorrelation). As a matter of fact, minimizing the determinant of a 2 Â 2 covariance matrix means minimizing the product of the variances while maximizing the covariance:…”

mentioning

confidence: 99%

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Experimental designs for controlling the correlation of estimators in two‐parameter models

Benitez,

López‐Fidalgo

2023

Journal of Chemometrics

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The state of the art related to parameter correlation in two‐parameter models has been reviewed in this paper. The apparent contradictions between the different authors regarding the ability of D‐optimality to simultaneously reduce the correlation and the area of the confidence ellipse in two‐parameter models were analyzed. Two main approaches were found: (1) those who consider that the optimality criteria simultaneously control the precision and correlation of the parameter estimators and (2) those that consider a combination of criteria to achieve the same objective. An analytical criterion combining in its structure both the optimality of the precision of the estimators of the parameters and the reduction of the correlation between their estimators is provided. The criterion was tested both in a simple linear regression model, considering all possible design spaces, and in a nonlinear model with strong correlation of the estimators of the parameters (Michaelis–Menten) to show its performance. This criterion showed a superior behavior to all the strategies and criteria to control at the same time the precision and the correlation.

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2 \times 2

covariance matrix means minimizing the product of the variances while maximizing the covariance:

(||, Σ) = σ_{1}^{2} σ_{2}^{2} - σ_{12}^{2} .

…”

Section: Optimal Estimators For Two‐parameter Modelsmentioning

confidence: 99%

ϕ_{D}

and

ϕ_{E M}

, 7

ϕ_{A}

and

ϕ_{E M}

, 12 or

ϕ_{c}

with restrictions on eigenvalues, 4,12 and (2) select from a set of optimal solutions using Pareto fronts 7,8,19 .…”

Section: Optimal Estimators For Two‐parameter Modelsmentioning

confidence: 99%

ϕ_{D}

and

ϕ_{E M}

, 7

ϕ_{A}

and

ϕ_{E M}

, 12 or

ϕ_{c}

Section: Optimal Estimators For Two‐parameter Modelsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Experimental designs for controlling the correlation of estimators in two‐parameter models

Benitez,

López‐Fidalgo

2023

Journal of Chemometrics

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“…The aim of optimal experimental design is to maximize the information collected in an experimental data set [19]. To enhance the estimation of the parameter set, θ, we solve an optimization problem to find an experimental design vector, ϕ, that best excites the system,…”

Section: B Optimal Experimental Designmentioning

confidence: 99%

Optimal Experimental Design to Estimate Insulin Response in Type 2 Diabetes

Engell,

Bengtsson,

Benam

et al. 2023

2023 IEEE Conference on Control Technology and Applications (CCTA)

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In late-stage type 2 diabetes, automated titration algorithms provide a promising alternative to the current standard-of-care. Many published methods rely on personalized dose-response models to predict a safe and effective insulin dose. In this case study, we address the challenge of how to collect an informative data set to ensure practical identifiability of such models. We apply optimal experimental design to enhance the performance of a published titration algorithm. For a 24-hour experiment, we solve an optimization problem to select the size of three meals and the hourly fast-acting insulin infusion rate. In simulation, we demonstrate how the optimized protocol improves the safety of the algorithm's dose-predictions. The results indicate that optimal experimental design has the potential to improve model-based algorithms and may be used as a qualitative tool when planning clinical experiments.

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