基于振荡序列的灰色GM(1,1|sin)幂模型及其应用

针对现实中普遍存在的振荡序列预测问题，传统灰色模型的预测效果并不理想。为此，在现有灰色GM(1,1|sin)模型基础上，提出了GM(1,1|sin)幂模型，给出了最小二乘准则下的参数计算公式；构建了以平均模拟相对误差最小化为目标的非线性优化模型，利用粒子群优化算法求得最优参数。最后，将新模型应用于城市交通流和高新技术产品出口额模拟预测，并将预测结果与传统GM(1,1)模型、GM(1,1)幂模型和GM(1,1|sin)模型进行了比较，结果表明，新模型具有更高的模拟精度，更适合对振荡序列的预测分析。

Grey GM(1,1|sin) power model based on oscillation sequences and its application

For the prediction of oscillation sequences in reality, the prediction effect of the traditional grey model is not Satisfactory. Therefore, a new GM(1,1|sin) power model is proposed based on the existing grey GM(1,1|sin) model, and the calculation formula of the parameters of the proposed model under the least square criterion is given. Then we construct a nonlinear optimization model with the objective of minimizing the average simulative relative error and obtain the optimal parameters employing the particle swarm optimization algorithm. The new model is applied to the simulation and prediction of the urban traffic flow and the export of high and new technology products. Compared with the traditional GM(1,1) model, the GM(1,1) power model and the GM(1,1|sin) model, the new model has a higher simulation precision and is more suitable for the prediction and analysis of oscillation sequences.