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Novel multivariate compositional data’s model for structurally analyzing sub-industrial energy consumption with economic data

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Abstract

Structural prediction and analysis of sub-industrial energy consumption with economic data across three industrial sectors are an important basis for reflecting the coordinated development relationship between energy consumption and industrial development. Empirically, the sub-industrial energy consumption and economic structure have numerous compositional data. The multivariate compositional data’s fractional gray multivariate model on the basis of the Simplex space and its algebraic system is proposed in this study aiming at the multi-dimensional small sample size with high uncertainties. First, the fractional accumulative generation operation sequence of multivariate compositional data is defined according to Aitchison geometry. Then, the novel model with the form of the compositional data vector is obtained. Second, the least square parameter estimation of the model is studied. A derived model is deduced and selected as the time-response expression of the model solution. Moreover, the gray wolf optimizer is introduced and designed to determine the optimal value of the fractional order. Detailed modeling procedures, including the computational steps and the intelligent optimization algorithm, have been clearly presented. Furthermore, 10-year economic structural data of 14 provinces in China are used to validate the effectiveness of the proposed model. The validation presents that the proposed model performs better in fitting, prediction, stability, and applicability, in comparison with the two other models in the Simplex space. Last, from the updated real-time datasets from 2008 to 2018, the proposed model is applied to analyze and forecast the sub-industrial energy consumption structure and industrial structure of Beijing. Results show that the proposed model presents high accuracy and is efficient in addressing the multivariate compositional data in some structural energy and economic issues.

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Acknowledgements

The authors are grateful to the editor for their valuable comments. This research is supported by the National Natural Science Foundation of China (71871174, 61403288) and the Fundamental Research Funds for the Central Universities (WUT: 2019IA005).

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  1. School of Science, Wuhan University of Technology, Wuhan, 430070, China

    Hui Chen, Xinping Xiao & Jianghui Wen

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  1. Hui Chen
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  3. Jianghui Wen
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Correspondence to Xinping Xiao.

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Table 9 Original compositional data of 14 provinces
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Chen, H., Xiao, X. & Wen, J. Novel multivariate compositional data’s model for structurally analyzing sub-industrial energy consumption with economic data. Neural Comput & Applic 33, 3713–3735 (2021). https://doi.org/10.1007/s00521-020-05227-5

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