Browsing by Subject "Optimal design of experiments"

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Improved methods in optimal design of experiments for determination of water absorption kinetics of cereal grains
(2016) Paquet-Durand, Olivier; Hitzmann, Bernd
In this thesis, the optimal design of experiments was applied to determine hydration kinetics of wheat grains. In the first study the used mathematical model was the Peleg model for which the optimal design of experiments was carried out while investigating how the optimization criterion will influence the result. The parameter estimation errors could be reduced by up to 62% compared to a non-optimal equidistant experimental design. It has been shown that the individual parameter estimation errors vary significantly depending on the used criterion. In this application only the D-optimal experimental design can reduce the parameter estimation errors of both parameters. In case of the A, Pr and E criterion at least one of the two parameter error could be reduced significantly. As the numerical optimization is computationally demanding, an alternative method for the entire optimal experimental design was developed. This alternative method is based on a mathematical function which depends on the rough initial parameter values. This function allows optimal measuring points to be calculated directly and therefore much faster, than the usual optimal design approach using numerical optimization techniques. In case of the very commonly used D-optimality criterion, the derived function is the exact solution. The deviation of the parameter estimation errors acquired by using the approximate optimal design instead of a normal optimal design are mostly around 0.01 % and therefore negligible. In the second study, the suitability of the Peleg model for water absorption kinetics of wheat grains was investigated closer. Cereal grains usually consist of three major components, bran layer, endosperm and germ. All these components have different water absorption kinetics. Therefore, the normal two parameter Peleg model might be insufficient to describe the water absorption process of cereal grains properly. To address this, the Peleg model was enhanced and a second Peleg like term was added to account for the two biggest fractions of the grain, namely the endosperm and the bran layer. Two experiments were carried out, an initial experiment to get rough parameter values and a second experiment, which was then optimally designed. The modified Peleg model had now four parameters and could be used to describe the hydration process of wheat grains much more accurate. Using the parameters calculated from the initial experiment the optimal measurement points where calculated in a way that the determination of the parameters of the modified Peleg model was as accurate as possible. The percentage parameter errors for the four parameters in the initial experiment were 669%, 24%, 12%, and 2.4%. By applying the optimal design, they were reduced to 38% 5.4%, 4.5% and 1.9% respectively. The modified Peleg model resulted in a very low root mean square error of prediction of 0.45% where the normal Peleg model results in a prediction error of about 3%. In the third study, it was investigated if bootstrapping could be used as a feasible alternative method for optimal experimental design. The classical procedure to determine parameter estimation errors is based on the Cramér-Rao lower bound but bootstrapping or re-sampling can also be used for the estimation of parameter variances. The newly developed method is more computationally demanding compared to the Cramér-Rao lower bound approach. However, bootstrapping is not bound to any restrictive assumptions about the measurement and parameter variations. An optimal experimental design based on the bootstrap method was calculated to determine optimal measurement times for the parameter estimation of the Peleg model. The Cramér-Rao based optimal design results were used as a benchmark. It was shown, that a bootstrap based optimal design of experiments yields similar optimal measurement points and therefore comparable results to the Cramér-Rao lower bound optimal design. The parameter estimation errors obtained from both optimal experimental design methods deviate on average by 1.5%. It has also been shown, that the probability densities of the parameters are asymmetric and not at all normal distributions. Due to this asymmetry, the estimated parameter errors acquired by bootstrapping are in fact likely to be more accurate. So bootstrapping can in fact be used in an optimal design context. However, this comes at the cost of a high computational effort. The computation time for a bootstrap based optimal design was around 25 minutes compared to only 5 seconds when using the Cramér-Rao lower bound method. But compared to the time required to carry out the experiments this is neglectable. Furthermore, as computers get faster and faster over time, the computational demand will become less relevant in future.
Modeling microbial regulation of pesticide turnover in soils
(2022) Chavez Rodriguez, Luciana; Streck, Thilo
Pesticides are widely used for pest control in agriculture. Besides their intended use, their long-term fate in real systems is not well understood. They may persist in soils, thereby altering ecosystem functioning and ultimately affecting human health. Pesticide fate is assessed through dissipation experiments in the laboratory or the field. While field experiments provide a close representation of real systems, they are often costly and can be influenced by many unknown or uncontrollable variables. Laboratory experiments, on the other hand, are cheaper and have good control over the governing variables, but due to simplification, extrapolation of the results to real systems can be limited. Mechanistic models are a powerful tool to connect lab and field data and help us to improve our process understanding. Therefore, I used mechanistic, process-based models to assess key microbial regulations of pesticide degradation. I tested my model hypotheses with two pesticide classes: i) chlorophenoxy herbicides (MCPA (2-methyl-4-chlorophenoxyacetic acid) and 2,4-D (2,4-Dichlorophenoxyacetic acid)), and ii) triazines (atrazine (AT)), in an ideal scenario, where bacterial degraders and pesticides are co-localized. This thesis explores some potential controls of pesticide degradation in soils: i) regulated gene expression, ii) mass-transfer process across the bacterial cell membranes, iii) bioenergetic constraints, and iv) environmental factors (soil temperature and moisture). The models presented in this thesis show that including microbial regulations improves predictions of pesticide degradation, compared to conventional models based on Monod kinetics. The gene-centric models achieved a better representation of microbial dynamics and enable us to explore the relationship between functional genes and process rates, and the models that used transition state theory to account for bioenergetic constraints improved the description of degradation at low concentrations. However, the lack of informative data for the validation of model processes hampered model development. Therefore, in the fourth part of this thesis, I used atrazine with its rather complex degradation pathway to apply a prospective optimal design method to find the optimal experimental designs to enable us identifying the degradation pathway present in a given environment. The optimal designs found suggest to prioritize determining metabolites and biomass of specific degraders, which are not typically measured in environmental fate studies. These data will lead to more robust model formulations for risk assessment and decision-making. With this thesis, I revealed important regulations of pesticide degradation in soils that help to improve process understanding and model predictions. I provided simple model formulations, for example the Hill function for gene expression and transition state theory for bioenergetic growth constraints, which can easily be integrated into biogeochemical models. My thesis covers initial but essential steps towards a predictive pesticide degradation model usable for risk assessment and decision-making. I also discuss implication for further research, in particular how mechanistic process-based modeling could be combined with new technologies like omics and machine learning.