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分数阶累加时滞GM(1,N,τ)模型及其应用
Fractional order accumulation time-lag GM(1,N,τ) model and its application
基于系统的时滞性, 本文建立了时滞灰色GM(1,N,τ)模型, 给出了模型的最小二乘参数估计公式以及模型的解析解.在引入分数阶累加生成算子后, 将原模型扩展为分数阶累加GM(1,N,τ) 模型, 当时滞值为非整数情况时, 采用相邻整数点加权构造法, 完善了模型; 通过粒子群算法确定模型最优的分数阶累加生成阶数. 最后本文结合武汉市1995-2008年14 年科技投入及经济增长的实际背景, 分别建立了经典时滞GM(1,N,τ)和分数阶累加时滞GM(1,N,τ) 模型对GDP数据做了预测, 比较了两个模型预测结果, 发现分数阶累加时滞GM(1,N,τ) 模型具有更高的建模精度.
Based on the time lag effect of system, this paper constructs the time-lag GM(1,N,τ) model, and provides its least squares parameter estimation formula and analytical solution. Then introducing fractional order accumulation generation operator, GM(1,N,τ) is transformed into fractional order accumulation time-lag GM(1,N,τ), offering adjacent integer points weighted method when time-lag value is not integer, determining the time-lag value via particle swarm optimization. Finally, we test the original GM(1,N,τ) and fractional order accumulation time-lag GM(1,N,τ) by using the real data of R&D investment and GDP in Wuhan from 1995 to 2008. The example indicates that the accuracy of fractional order accumulation time-lag GM(1,N,τ) is more satisfactory.
灰色模型 / GM(1,N,τ / )模型 / 分数阶累加生成 / 时滞 / 粒子群算法 {{custom_keyword}} /
grey model / GM(1,N,τ / ) model / fractional order accumulation / time-lag / particle swarm optimization {{custom_keyword}} /
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教育部人文社会科学基金(11YJC630155); 中国博士后科学基金特别资助(2013T60755);中国博士后科学基金(2012 M521487); 中央高校自主创新研究基金(2012-Ia-034)
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