Modeling Of Microbial Growth Kinetics Driven In Water Environment By The Noises

In recent years, the bioremediation techniques become the research focuses because of the low cost and pollution-free characteristic, with the increasing of the water pollution situation. Being a kind of bioremediation techniques, microorganism remediation techniques mainly use the disintegrating capacity of the microbial cell itself to transfer the organic contaminants into steady compounds in water remediation processes such as oxidation, reduction, assimilation, dissimilation etc., so as to ensure the normal operation and water quality. Because the process of microbial cells growth is complicated and has many restrictions, the researchers often use mathematical models to describe it in natural environment. However, the random noise cannot be avoided in nonlinear stochastic systems as the environment is not in an isolated condition. The irregular disturbance may have negative effects to the random system, but may also have positive effects in some conditions.The nonlinear stochastic systems driven by noises have drawn broad attentions in recent years. The noises have been widely used in physics, chemistry and biology fields. The environmental factors mainly include:temperature, oxygen, pH and additive agents in microbial growth models. However, there are a lot of uncertain factors in real natural environments, such as the lack of nutrients, living competition between different microbial cells, abrupt environmental accidents, etc. They have great impacts on the microbial growth process and may lead to random errors between the simulation and true values. Therefore, the noise can be introduced into microbial growth models in order to describe the growth process of microbial cells more accurately.Based on the Box-Muller algorithm, the paper develops three microbial growth models in water environment driven by white noise, colored noise and recombination noises, respectively. Then the effects of various noises on the growth process of microbial cells will be analyzed based on the modeling results. Different intensities and correlation time of noises are also investigated. The results show that the microbial model can be significantly affected by noises; the influence of noise level and intensity (or correlation time) is positively correlated; when the noise intensity is less than 10"4 or the correlation time is less than 0.1, the noise will not affect the model. This phenomenon means the model can simulate the growth process of the microbial cell in the real environment.According to the characteristics of the noise, the paper uses the Fractional Fourier transform algorithm to characterize the property of noise (e.g. intensity, correlation time). Based on the transform algorithm, the estimate proportion of noise intensity and correlation time can be obtained. The results show that the transform algorithm can well estimate noise parameters. Multiple simulation samples are obtained under different running times. The results indicate that a well-identified running number is helpful in improving the estimation accuracy.16 scenarios are set through combing four groups of intensity and correlation time real values. The major findings include:the larger the true values of the noise intensity and correlation time, the more uncertain factors, and the lower the estimation accuracy is.In general, this paper studies the microbial growth model driven by white noises, colored noise and recombination noises and analyzes the effect of different intensities and correlation time of noises on the model. In addition, the property of noise are estimated by the Fractional Fourier transform algorithm. Moreover, the noises in real-world cases may be more complex than the ones in this study, and thus more researches related to various types of noises can be accomplished in the near future.