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| 摘要: |
| 针对振荡序列的预测问题,在已有GM(1,1|sin)模型的基础上,首先利用分数阶累加算子,对原始数据序列进行分数阶累加生成。然后为了尽量减少模型从离散到连续的转换误差,对白化微分方程进行了推导,提出了分数阶累加GM(1,1|sin)模型。为达到最优的模拟预测效果,构建了以平均相对误差最小化为目标的非线性优化模型,利用粒子群算法求解最优参数。最后以城市交通流的模拟预测为例,结果表明：分数阶累加GM(1,1|sin)模型的平均模拟相对误差为0.8280%,显著低于GM(1,1|sin)模型的4.4651%。 |
| 关键词: 灰色系统 分数阶累加 GM(1,1|sin)模型 振荡序列 |
| DOI： |
| 分类号:O175.2 |
| 基金项目:广东省普通高校特色创新资助项目(2016KTSCX164)；广东理工学院科研资助项目(GKJ2017025)；广东理工学院科研资助项目(GKJ2016002). |
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| Research on GM (1,1|sin) Model Based on Fractional Order Accumulationand Its Application |
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LI Ya-nan
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| Abstract: |
| Aiming at the problem of prediction of oscillation sequence, based on the existing GM(1,1|sin) model, the original data sequence is accumulated by fractional order. Then, to minimize the transformation error of the model from discrete to continuous, the whitening differential equation is derived, and the GM (1,1|sin) model based on fractional order accumulation is proposed. In order to achieve the best simulation and prediction effect, a nonlinear optimization model based on minimizing mean relative error is constructed, and particle swarm optimization is applied to solve the optimal parameters. Finally, taking the simulation and prediction of urban traffic flow as an example, the results show that the average relative error of the GM(1,1|sin) model based on fractional order accumulation is 0.8280%, which is significantly lower than 4.4651% of the GM(1,1|sin) model. |
| Key words: grey model fractional order accumulation GM(1,1|sin) model oscillation sequence |
