scholarly journals Optimization of model parameters and experimental designs with the Optimal Experimental Design Toolbox (v1.0) exemplified by sedimentation in salt marshes

2015 ◽  
Vol 8 (3) ◽  
pp. 791-804 ◽  
Author(s):  
J. Reimer ◽  
M. Schuerch ◽  
T. Slawig
Keyword(s):  
Experimental Design ◽  
Salt Marshes ◽  
Weighted Least Squares ◽  
Experimental Designs ◽  
Optimal Experimental Design ◽  
Model Parameters ◽  
Optimization Approach ◽  
Discrete Optimization Problem ◽  
Advantages And Disadvantages ◽  
Optimizing Model

Abstract. The geosciences are a highly suitable field of application for optimizing model parameters and experimental designs especially because many data are collected. In this paper, the weighted least squares estimator for optimizing model parameters is presented together with its asymptotic properties. A popular approach to optimize experimental designs called local optimal experimental designs is described together with a lesser known approach which takes into account the potential nonlinearity of the model parameters. These two approaches have been combined with two methods to solve their underlying discrete optimization problem. All presented methods were implemented in an open-source MATLAB toolbox called the Optimal Experimental Design Toolbox whose structure and application is described. In numerical experiments, the model parameters and experimental design were optimized using this toolbox. Two existing models for sediment concentration in seawater and sediment accretion on salt marshes of different complexity served as an application example. The advantages and disadvantages of these approaches were compared based on these models. Thanks to optimized experimental designs, the parameters of these models could be determined very accurately with significantly fewer measurements compared to unoptimized experimental designs. The chosen optimization approach played a minor role for the accuracy; therefore, the approach with the least computational effort is recommended.

scholarly journals Optimization of experimental designs and model parameters exemplified by sedimentation in salt marshes

2014 ◽  
Vol 7 (5) ◽  
pp. 6439-6487
Author(s):  
J. Reimer ◽  
M. Schürch ◽  
T. Slawig
Keyword(s):  
Experimental Design ◽  
Salt Marshes ◽  
Weighted Least Squares ◽  
Asymptotic Properties ◽  
Sediment Concentration ◽  
Experimental Designs ◽  
Model Parameters ◽  
Discrete Optimization Problem ◽  
Advantages And Disadvantages ◽  
Weighted Least Squares Estimator

Abstract. The weighted least squares estimator for model parameters was presented together with its asymptotic properties. A popular approach to optimize experimental designs called local optimal experimental designs was described together with a lesser known approach which takes into account a potential nonlinearity of the model parameters. These two approaches were combined with two different methods to solve their underlying discrete optimization problem. All presented methods were implemented in an open source MATLAB toolbox called the Optimal Experimental Design Toolbox whose structure and handling was described. In numerical experiments, the model parameters and experimental design were optimized using this toolbox. Two models for sediment concentration in seawater of different complexity served as application example. The advantages and disadvantages of the different approaches were compared, and an evaluation of the approaches was performed.

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

Processes ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 27 ◽  
Author(s):  
René Schenkendorf ◽  
Xiangzhong Xie ◽  
Moritz Rehbein ◽  
Stephan Scholl ◽  
Ulrike Krewer
Keyword(s):  
Experimental Design ◽  
Mathematical Models ◽  
Chemical Engineering ◽  
Protein Kinase Inhibitors ◽  
Optimal Experimental Design ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Global Parameter ◽  
Model Based ◽  
The Impact

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.

Multiple-objective criteria for optimal experimental design: application to ferrokinetics

1985 ◽  
Vol 248 (3) ◽  
pp. R378-R386 ◽  
Author(s):  
M. H. Nathanson ◽  
G. M. Saidel
Keyword(s):  
Experimental Design ◽  
Optimal Design ◽  
Objective Function ◽  
Information Matrix ◽  
Optimal Experimental Design ◽  
Multiple Objective ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Experimental Conditions ◽  
New Criterion

Optimal experimental design is used to predict the experimental conditions that will allow the "best" estimates of model parameters. A variety of criteria must be considered before an optimal design is chosen. Maximizing the determinant of the information matrix (D optimality), which tends to produce the most precise simultaneous estimates of all parameters, is commonly considered as the primary criterion. To complement this criterion, we present another whose effect is to reduce the interaction among the parameter estimates so that changes in any one parameter can be more distinct. This new criterion consists of maximizing the determinant of an appropriately scaled information matrix (M optimality). These criteria are applied jointly in a multiple-objective function. To illustrate the use of these concepts, we develop an optimal experimental design of blood sampling schedules using a detailed ferrokinetic model.

Synthesis of optimal experiment designs under the conditions of Generalized Lambda-distribution of errors for models with errors in variables

2020 ◽  
pp. 130-141
Author(s):  
Владимир Семенович Тимофеев ◽  
Екатерина Алексеевна Хайленко
Keyword(s):  
Experimental Design ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Experimental Designs ◽  
Optimal Experimental Design ◽  
Efficiency Function ◽  
Explanatory Variables ◽  
Generalized Lambda Distribution ◽  
Optimal Experiment

Рассмотрена задача планирования эксперимента в условиях появления ошибок в объясняющих переменных. Сформулировано и доказано утверждение о способе вычисления элементов информационной матрицы Фишера с использованием обобщенного лямбда-распределения, доказано следствие о способе вычисления функции эффективности плана эксперимента. Сравнение результатов вычисления функции эффективности с использованием выведенного в следствии соотношения и с помощью известного соотношения для нормального распределения ошибок показало, что результаты совпадают. Построены оптимальные планы эксперимента для различных распределений случайных компонент. The problem of experimental design under conditions of errors in the explanatory variables is considered. The proposition of the method for calculating the Fisher information matrix elements using the Generalized Lambda-distribution is formulated and proved, the consequence of the method for calculating the efficiency function of the experimental design is proved. This method of calculating the Fisher information matrix takes into account the heterogeneity of the errors in random distribution throughout the planning area. In this paper, studies of the synthesis of optimal experimental designs using proven proposition and consequence under various conditions of computational experiments are presented. The results of calculating the efficiency function using the obtained relation and using the known relation for the normal distribution of errors are compared, it is found that the results coincide. Optimal experimental designs are constructed for various distributions of random components. The results of the synthesis of optimal experimental design showed that when function of efficiency is constant throughout the planning area then the optimal experimental design is equilibrium plan. When there are differences in the values of the efficiency function in the planning area, the optimal plan ceases to be equilibrium

scholarly journals Optimal Experimental Design Using a Consistent Bayesian Approach

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Scott N. Walsh ◽  
Tim M. Wildey ◽  
John D. Jakeman
Keyword(s):  
Experimental Design ◽  
Computational Model ◽  
Probability Density ◽  
Bayesian Approach ◽  
Information Gain ◽  
Optimal Experimental Design ◽  
Model Parameters ◽  
Computationally Efficient ◽  
Push Forward ◽  
Expected Information Gain

We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent Bayesian approach for solving stochastic inverse problems, which seeks a posterior probability density that is consistent with the model and the data in the sense that the push-forward of the posterior (through the computational model) matches the observed density on the observations almost everywhere. Given a set of potential observations, our optimal experimental design (OED) seeks the observation, or set of observations, that maximizes the expected information gain from the prior probability density on the model parameters. We discuss the characterization of the space of observed densities and a computationally efficient approach for rescaling observed densities to satisfy the fundamental assumptions of the consistent Bayesian approach. Numerical results are presented to compare our approach with existing OED methodologies using the classical/statistical Bayesian approach and to demonstrate our OED on a set of representative partial differential equations (PDE)-based models.

Sign in / Sign up

Export Citation Format

Share Document