分数阶离散灰色GM(1,1) 幂模型及其应用

针对GM(1,1)幂模型时间响应式由离散估计到连续预测所存在的固有误差,建立离散灰色GM(1,1)幂模型,并将该模型扩展为分数阶离散灰色GM(1,1)幂模型；以最小化平均相对误差为目标、参数之间的关系为约束条件,构建关于序列累加阶数和幂指数的优化模型,并运用量子遗传算法确定模型的最优累加阶数和幂指数。通过对高速公路地基沉降和中国高新技术产业R&D发展两个实例的预测结果表明,分数阶离散灰色GM(1,1)幂模型具有良好的建模精度。

Fractional order discrete grey GM(1, 1) power model and its application

To overcome the problems of model error and initialized value of the existing GM(1,1) power model, the grey discrete power GM(1,1) model is constructed, and grey discrete power GM(1,1) is transformed into fractional order grey discrete power GM(1,1). An optimization model is constructed with the objective of minimum average relative error, the constraints of relationships between parameters in order to optimize the power exponent and the accumulation order, and the optimization values of accumulation order and power exponential are determined by using the quantum genetic algorithm. Finally, two application examples, named settlement volume of subgrade and chinese high technology enterprises, show that the proposed model has higher precision accuracy.