Browsing by Subject "Parameter estimation"

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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.
Regionalising a soil-plant model ensemble to simulate future yields under changing climatic conditions
(2023) Bendel, Daniela Silke; Streck, Thilo
Models are supportive in depicting complex processes and in predicting their effects. Climate models are applied in many areas to assess the possible consequences of climate change. Even though Global Climate Models (GCM) have now been regionalised to the national level, their resolution of down to 5x5 km2 is still rather coarse from the perspective of a plant modeller. Plant models were developed for the field scale and work spatially explicitly. This requires to make adjustments if they are applied at coarser scales. The regionalisation of plant models is reasonable and advantageous against the background of climate change and policy advice, both gaining in importance. The higher the spatial and temporal heterogeneity of a region, the greater the computational need. The (dis)aggregation of data, frequently available in differing resolutions or quality, is often unavoidable and fraught with high uncertainties. In this dissertation, we regionalised a spatially-explicit crop model ensemble to improve yield projections for winter wheat under a changing climate. This involved upscaling a crop model ensemble consisting of three crop models to the Stuttgart region, which has an area of 3,654 km2. After a thorough parameter estimation performed with a varying number of Agricultural Response Units on a high-performance computing cluster, yield projections up to the year 2100 were computed. The representative concentration pathways of the Intergovernmental Panel on Climate Change (IPCC) RCP2.6 (large reduction of CO2 emissions) and RCP8.5 (worst case scenario) served as a framework for this effort. Under both IPCC scenarios, the model ensemble predicts stable winter wheat yields up to 2100, with a moderate decrease of 5 dt/ha for RCP2.6 and a small increase of 1 dt/ha for RCP8.5. The variability within the model ensemble is particularly high for RCP8.5. Results were obtained without accounting for a potential progress in wheat breeding.