含有时间幂次项的加权一致性分数阶离散灰色模型构造及其应用

Construction and Application of Weighted Conformable Fractional Discrete Grey Model with Time Power Term

一致性分数阶累加生成算子由于其良好的性能受到广泛关注,但仍存在适应性不足的问题.本文给出了加权一致性分数阶累加生成算子的构造过程,将含有时间幂次项的灰色模型进行离散化,构造了加权一致性分数阶离散时间幂次项灰色模型,即WCFDGM(1,1,t^(α))模型,并给出模型的具体求解过程和其无偏性的证明过程.在模型超参数求解方面,本文运用海洋捕食算法(MPA)实现最优搜索.最后,运用构建的模型对我国供水总量和生产用供水总量进行实证分析,结果表明,构建的WCFDGM(1,1,t^(α))模型具有更高的拟合精度和预测精度.

Conformable fractional-order grey prediction models have attracted considerable attention due to their versatile modeling techniques.Nevertheless,existing models often suffer from limitations in adaptability.This paper presents the construction process of the weighted conformable fractional-order and discretizes the grey model with time power term,constructing the Weighted Conformable Fractional Discrete Grey Model with Time Power Term WCFDGM(1,1,t^(α)),along with its specific solution process and proof of unbiasedness.In terms of solving model hyperparameters,the Marine Predation Algorithm(MPA)is utilized for optimal search.Finally,the constructed model is empirically analyzed for China's total water supply and production water supply,showing that the constructed WCFDGM(1,1,t^(α))model has higher fitting and prediction accuracy.