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Chaotic characteristics analysis of the sintering process system with unknown dynamic functions based on phase space reconstruction and chaotic invariables

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Abstract

Because the sintering process system (SPS) of the rotary kiln is influenced by many uncertain factors, such as the composition of raw materials, the structure of the kiln crust, and the mode of operation, it displays complex nonlinear dynamic characteristics. In addition, its dynamic functions are unknown. Thus, data-based chaotic analysis methods are used to study the dynamic characteristics of the SPS. First, three sintering temperature (ST) data with different timescales are extracted, respectively, from the three SPSs. Second, the reasons why the dynamic characteristics of the SPS can be analyzed by the ST based on the phase space reconstruction (PSR) method are explained, and several potential PSR forms (reconstructed systems) are achieved. Third, the three optimal PSR forms of the three ST data (SPSs) are determined by chaotic invariables-based quantitative analysis. We determined that the three SPSs are all five-order chaotic systems. Finally, the optimal PSR forms are further verified by predicting the practical ST. The highly accurate predictions show that not only are the three optimal PSR forms applicable but also the chaotic methodologies are effective. Thus, the results in this paper not only provide extensive theoretical research values for subsequent studies of the SPS but also provide extensive industrial application value for other industries such as the nonferrous metallurgy, cement, steel, and chemical industries, in which the SPS is applied. Specifically, the PSR-based and chaotic invariables-based chaotic analysis methods can be used to analyze other industrial systems with unknown dynamic functions.

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Acknowledgements

We gratefully acknowledge the financial support from the National Natural Sciences Foundation of China under Grants 61672216 and 61673162. We thank three anonymous reviewers and the editor for valuable comments that improved this article. We also thank Ph.D Branko Pecar, Professor Charles L. Webber, and Professor Marisa Faggini for offering their profound insights about the PSR method.

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Authors and Affiliations

  1. College of Computer Science and Electronic Engineering, Hunan University, Lushan South Road, Changsha, 410082, People’s Republic of China

    Xiaogang Zhang, Mingyang Lv, Hua Chen, Bowang Dai & Yuebing Xu

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  1. Xiaogang Zhang
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  2. Mingyang Lv
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  3. Hua Chen
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Correspondence to Hua Chen.

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Zhang, X., Lv, M., Chen, H. et al. Chaotic characteristics analysis of the sintering process system with unknown dynamic functions based on phase space reconstruction and chaotic invariables. Nonlinear Dyn 93, 395–412 (2018). https://doi.org/10.1007/s11071-018-4200-7

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  • DOI: https://doi.org/10.1007/s11071-018-4200-7

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