Chaotic and multifractal characteristic analysis of noise of thermal variables from rotary kiln

In numbers of industrial fields, many filtering algorithms of industrial signals, mechanism-based modeling methods and control strategies are based on the hypothesis of white noise. However, some researchers propose that the colored noise is closer to the real noise than the white noise. Then, whether the noise is the white noise, the colored noise or other else? And what is the intrinsic dynamic characteristics of the noise? In this paper, noise signals of thermal variables from rotary kiln are extracted and their chaotic, statistical and multifractal characteristics are analyzed to answer the two questions. Based on the experimental results, it is the first time to discover that they are not the white noise or the monofractal colored noise but have the high-dimensional chaotic characteristic, that is, they are determinate and predictable for short term theoretically. However, some models are failed to predict them. Then, further experimental results imply those noise signals have both persistent and anti-persistent multifractal characteristics. In particular, the latter is a reason to failed predictions of noise signals. Moreover, it is firstly discovered that the multifractality of each noise signal is generated mainly by the long-term temporal correlation. Finally, two ideas about modeling multifractality of noise from rotary kiln are proposed as the future work.