A microbial growth kinetics model driven by hybrid stochastic colored noises in the water environment

Abstract

This study develops three microbial growth models in the sewage biodegradation process driven by white noise, colored noise and hybrid noises, respectively. The proposed models are more universal in reflecting the impact of uncertainty on microbial systems, compared with the previous efforts. An improved Box–Mueller algorithm is used to solve the model. The modeling results show that the different noise types have remarkable effects on microbial growth kinetics. To better understanding the insights of various noises affecting the system, the growth process of microbial in the sewage biodegradation process is discussed under different conditions with varied noise properties (i.e. intensity and correlation time). The results indicate that the effect of noise on the microbial growth kinetics decreases with the reduction of the noise intensity and the correlation time. Therefore, a known noise can be relieved by changing the noise intensity or the correlation time. As the model driven by noises is capable of addressing the system’s uncertainty, it is useful in supporting stochastic simulation, risk analysis, and process design of a sewage biological treatment system. Future works may focus on the development of more effective statistical-inference methods for the noises based on observed data.