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Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

机译：分数阶累积的NDGM模型的稳定性及其优化研究。

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摘要

The grey forecasting model has been successfully applied in numerous fields since it was proposed. The nonhomogeneous discrete grey model (NDGM) was approximately constructed based on the nonhomogeneous index trend; it increased the applicability of discrete grey model. However, the NDGM required accurate data and better effect when the original data did not meet the conditions and fitting and prediction errors were larger. For this, the NDGM with the fractional order accumulating operator (abbreviated as NDGM (p/q)) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGM (p/q) and the NDGM (p/q) can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGM (p/q) was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGM (p/q) and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGM (p/q) was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.
机译：自提出以来，灰色预测模型已成功应用于许多领域。基于非均匀指数趋势，近似构建了非均匀离散灰色模型（NDGM）。它增加了离散灰色模型的适用性。但是，当原始数据不满足条件且拟合误差和预测误差较大时，NDGM需要准确的数据和更好的效果。为此，具有分数阶累加运算符（缩写为NDGM（p / q））的NDGM具有更高的性能。本文使用参数的矩阵摄动界来分析NDGM（p / q）的稳定性，NDGM（p / q）可以减小扰动界。随后，研究了NDGM（p / q）的参数估计方法，并采用粒子群优化算法对NDGM（p / q）的阶数进行了优化，并提供了一些步骤。另外，两个实例的结果表明，与传统的NDGM模型和DGM模型相比，NDGM的扰动（p / q）小于NDGM的扰动，并提供了卓越的预测性能。

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  • 来源
    《Mathematical Problems in Engineering》 |2017年第6期|9728587.1-9728587.10|共10页
  • 作者

    Duan Huiming; Shao Kailiang; Xiao Xinping; Yang Jinwei;

  • 作者单位

    Chongqing Univ Post & Telecommun, Coll Sci, Chongqing 400065, Peoples R China|Wuhan Univ Technol, Coll Sci, Wuhan 430070, Peoples R China;

    Chongqing Univ Post & Telecommun, Coll Sci, Chongqing 400065, Peoples R China;

    Wuhan Univ Technol, Coll Sci, Wuhan 430070, Peoples R China;

    Wuhan Univ Technol, Coll Sci, Wuhan 430070, Peoples R China;

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