Fractional derivative multivariable grey model for nonstationary sequence and its application

Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.

Combined model based on optimized multi-variable grey model and multiple linear regression

The construction method of background value is improved in the original multi-variable grey model （MGM（1,m）） from its source of construction errors. The MGM（1,m） with optimized background value is used to eliminate the random fluctuations or errors of the observational data of all variables, and the combined prediction model together with the multiple linear regression is established in order to improve the simulation and prediction accuracy of the combined model. Finally, a combined model of the MGM（1,2） with optimized background value and the binary linear regression is constructed by an example. The results show that the model has good effects for simulation and prediction.

基于改进MGM的省级用电量中长期预测

当前中国用电环境随全球经济呈非线性、非规律性波动。以往所用电量中长期预测方法难以适应现在的精准规划要求,无论是传统GM(1,1)还是MGM(1,n),由于其自然属性,已经不再适应当前的新规律。基于某省级电网不同产业全社会用电总量及GDP变化趋势,分析了数据间的逻辑关系及变化规律。通过构造与当前变化相适应的背景优化函数,对MGM进行相关改进,以满足当前精准规划的用电量预测要求。预测了某省2010—2018年的全社会用电总量,预测结果可靠性高,预测精度满足当前规划需要。

Epidemic Prediction of Hemorrhagic Fever with Renal Syndrome Using Grey Multivariable Model

In this paper,we set up a grey multivtriable model to predict the HFRS morbidity.Forecasting test results show that this new model is of general use in the prediction Of the disease.It is particularly appropriate for HFRS investigations and controls.

基于灰色马尔可夫模型的变压器油中溶解气体体积分数预测

准确预测变压器油中溶解故障特征气体的体积分数对发现变压器早期潜伏性故障,实现电力系统安全经济运行具有重要意义。将灰色多变量预测方法和马尔可夫链理论有机结合,提出了一种适合变压器故障特征气体体积分数预测的灰色马尔可夫组合预测模型。利用优化的背景值构造公式建立灰色多变量模型对变压器故障特征气体时间序列的宏观发展规律进行动态预测,在此基础上,建立故障特征气体时间序列的状态转移概率矩阵,以归一化的各阶自相关系数作为权重值,通过加权马尔可夫链模型修正灰色多变量模型预测值,实现变压器故障特征气体体积分数的预测,预测精度较高。实际算例分析验证了该模型的实用性和有效性。

The Novel Triangle MGM(1,m,N)Model and Its Applications

The MGM(1,m,N)model is an effective grey multi-variate forecasting model that considers multiple system characteristic sequences affected by multiplefactors.Nevertheless,it isregularly inaccurate in the application This is because the model requires a strong correlation between the system characteristic sequences That reduces the applicability of the model.To solve this problem,this paper proposes a novel multi-variate grey model.This model does not require a certain correlation between system characteristic sequences and has higher applicability Through numerical integration,a two-point trapezoidal formula,and a recursive method,thetime-response expressions ofthetwo model forms are obtained Some properties of the proposed model are further discussed Finally,the validity of the proposed model is evaluated by using two real cases related to China's invention patent development.Theresultsshow that the novel models outperformother models inbothsimulation and prediction applications.

基于新型核与灰度序列的MGM(1,m,N)模型及其应用

雾霾是空气质量重要评判标准之一,对其进行准确预测能为相关政府部门及时做出正确决策提供理论支持,因此预测雾霾具有实际意义。本文针对区间灰数分布信息已知的序列,构建多个影响因素作用于多个系统行为变量的灰色MGM(1,m,N)模型。首先根据可能度函数计算得到区间灰数的新型核与灰度序列,然后对新型核与灰度序列分别建立MGM(1,m,N)模型以求得模拟值和预测值,最后通过还原得到区间灰数序列的上、下界。为进一步验证该模型的可行性,本文将该模型应用于雾霾相关数据并与基于传统核与灰度序列的MGM(1,m,N)模型进行比较,结果表明本文构建的新模型的模拟预测精度都较传统模型更好。