初始条件优化的近似指数序列灰色建模方法

Grey modeling method for approximate exponential sequence of optimizing initial condition

灰色GM(1,1)预测方法仅针对累加生成满足近似指数特点的原始序列建立预测模型。为了拓宽传统灰色预测模型的应用范围,设计了通过优化初始条件提高灰色GM(1,1)预测精度的新方法——DGM(1,1,c,β)模型。对满足近似指数的原始序列建立DGM(1,1,c,β)模型,利用粒子群算法求解模型参数。最后,通过实例验证了所提出的DGM(1,1,c,β)预测模型的有效性和实用性。

Grey GM（ 1, 1） prediction method is only suitable for the prediction model of the original sequence which satisfies the characteristic of the approximate exponential through the accumulated generating operation.In order to widen the application range of the traditional grey prediction model, a new method, dubbed DGM（ 1, 1, c, β） model（ direct grey model）, was proposed to improve the accuracy of grey GM（ 1, 1） prediction by optimizing initial conditions. DGM（ 1, 1, c, β） model was established for the original sequence conforming to the approximate exponential and the model parameters were obtained by the particle swarm optimization algorithm.Both the simulation and analysis of the example demonstrate that the proposed method is more effective and practical.