Optimal design of experiments and measurements of the water sorption process of wheat grains using a modified Peleg model
Introduction
Hydration kinetics in food technology are key physicochemical properties. The knowledge of moisture content and moisturizing kinetics is vitally important to determine the chemical and physical properties of food products and their shelf life.
In this work, the water absorption kinetics of wheat grains were investigated and an optimal experimental design was applied. The actual water content of wheat grains due to storage is too low for optimal milling. During the milling process the bran and the germ have to be separated efficiently from the endosperm, because the economic values are related to their purity. The water addition exaggerates the difference of the different parts of the wheat kernel and simplifies the separation process. The hydration kinetics for the endosperm is rather slow compared to the germ and the bran (Delcour and Hoseney, 2010) and a hydrated bran is very flexible and will stay mostly intact during milling and can then be sieved out. Therefore, a hydration step, the tempering, is applied routinely before milling to produce optimal quality. A more detailed knowledge about the hydration kinetics of the components of the wheat grains is therefore required to prepare an optimal separation process.
There are fundamental approaches to water absorption kinetics. Cunningham et al. (2007) and Munson-McGee et al., 2011a, Munson-McGee et al., 2011b used models for water uptake based on Fick’s diffusion laws. However, models based on the diffusion law are usually very complex and not very convenient for computing in most situations. Therefore, Peleg (1988) suggested an empiric two parameter model to describe water absorption curves. For example Sopade et al. (1992) and Maskan (2001) used this model to accurately describe the water absorption of cereal grains and wheat respectively. It is still very common due to its simplicity and ideal for an optimal design of experiments due to its modest computational requirements.
Optimal experimental design is usually carried out to get the maximal amount of information from an experiment with the least amount of effort. This goal is achieved by variation of measurement times and measurement locations or other process variables such temperature or pH. One specific and also quite common goal of an optimal experimental design can be to minimize parameter estimation errors. Ataíde and Hitzmann (2009) used an optimal experimental design to analyze enzyme kinetics in a stirred tank reactor. They proved that fed-batch processes will always result in smaller parameter estimation errors than for normal batch processes. Franceschini and Macchietto (2008) presented a list of various recent model based optimal experimental design applications from chemical kinetics to biological modelling. Sánchez et al. (2012) presented a method for a pareto-optimal design. They showed that it is possible to get a non-optimal but still good experimental design regarding multiple criteria at the same time.
According to Dolan and Mishra (2013), the importance of accurate parameter error estimation is often underestimated in food science. In this work, the optimal design of experiments to improve the parameter estimation error of a modified Peleg model was investigated. To do so, an initial experiment for water sorption of wheat grains was carried out to roughly estimate the parameters. Afterwards these initial parameters were used to carry an optimal experimental designs using the Cramer-Rao lower bound method.
Section snippets
Performing optimal design of experiments
The goal of optimal design of experiments is to determine optimal measurement points or the evolution of process variables (such as batch or fed-batch mode) for an experiment, in a way that the variances of model parameters calculated from corresponding measurements are as small as possible. Therefore, one requirement is a theoretical model describing the process under consideration.
Experiments
Some constraints for the optimal design of experiments had to be specified. Here the maximum duration of the experiments was set to 48 h (2 days) and the number of measurements to be carried out specified to be 12.
Altogether two experiments were performed. First, the initial non-optimal experiment for water absorption whose measurement values are used for the rough estimation of the parameter values of the modified Peleg model. The 12 measurements (in triplicate) were taken at the following
Results & discussion
In Fig. 1 the results of the initial non-optimal water uptake measurements as well as the fitted original 2 parameter Peleg model and the modified 4 parameter Peleg model are shown. All water uptake values are relative to the initial wet weight of the grains. Also shown are the two individual water uptake progressions of the bran layer and the endosperm of the modified model, which correspond to the two major compounds of the grain. The root mean square error of the modified Peleg model is
Conclusion
For an overall process optimization, theoretical models as well as rough values for the model parameters must be known. In this investigation, the water absorption process of wheat grains was considered. At first an experiment with 12 moisture measurements in triplicate was performed and the measurement times were chosen based on experience. It could be shown that the modified Peleg model is very suitable to describe the measured moisturizing process of fresh wheat grains, where the normal
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