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为了提高灰色GM(2,1)模型的预测精度,本文首先对灰色GM(2,1)模型的向前、向后差分进行线性组合出灰色GM(2,1,λ)模型,利用参数λ修正背景值;然后引入参数ρ对原始数列进行数乘变换,进一步将模型拓展为灰色GM(2,1,λ,ρ)模型.由于参数λ,ρ与误差之间为明显的非线性关系,难以解析,本文基于微粒群算法(PSO),给出PSO-GM(2,1,λ,ρ)优化方法.在该方法中,用λ,ρ构成一个二维的微粒群,以绝对的平均相对误差作适应度函数,以其最小为目标,求解最优的λ,ρ值.实例计算表明,该方法收敛速度快,预测精度高于普通模型,而且可满足实际需要.
In order to improve the prediction accuracy of the gray GM (2,1) model, a gray GM (2,1, λ) model is linearly combined with the forward and backward difference of the gray GM (2,1) model. Then modify the background value, and then introduce the parameter ρ to multiply the original sequence by number, and further expand the model to gray GM (2,1, λ, ρ) model.As the parameters λ, ρ and the error are obvious nonlinear relationship, In this method, we use λ and ρ to form a two-dimensional particle swarm with absolute average The relative error is taken as fitness function, and the optimal λ and ρ values are solved with the minimum as objective.Examples show that the method has the advantages of fast convergence and high prediction accuracy compared with ordinary models, and can meet the actual needs.