W-H Huang et al. (presented by F-S Wang)
National Chung Cheng University
Almost no lit has so far talked about modelling power-law models with time-varying parameters. In their model formulation, they used a time varying S-Sytem model. The rate coefficients and the kinetic orders are the time-varying parameters. Several basic functions such as block pulse functions, Lagrange polynomials, and orthogonal polynomials can be used to estimate the time-varying parameters. The model parameters for each time scale are constants.
There are two main challenges to parameter estimation: ODE solving and optimization. They developed a modified collocation approach, which is similar to the conventional method except for the approximation technique. Evolutionary algorithms can be applied to overcome drawbacks to optimization using gradient-based methods. They propose a global-local search method. They also describe Hybrid differential evolution (HDE). They did both wet and in silico experiments. For the latter, they found that the time-varying model fits the experiments very closely, much better than the time-invariant models. The wet-lab study was a kinetic model of ethanol fermentation using mixed sugars. The same conclusion, that the time-invariant model did not closely follow the experiment, while the time-varying one did, was found for this experiment.
DEs including constant parameters are commonly used to model biochemical systems. Such a time-invariant model cannot cover all dynamic behaviour – a time-varying S-system model has been developed by them to overcome these limitations. This model is a close fit with experimental data.
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