摘要
2020年突发传染病严重威胁人们的生命健康,精准的预测对于传染病的管理有重要意义。基于传染病发展的不确定性,建立传统灰色NGM(1,1)模型,而NGM(1,1)模型初始值的选取、背景值的构造以及参数估计方法是导致该模型精度不稳定的重要原因。首先,本文以三参数的紧邻均值背景值来优化传统NGM(1,1)模型背景值为基础,以平均相对误差最小为目标,利用粒子群优化算法求最优初始值的取值,然后将三参数的紧邻均值背景值改为加权的三参数背景值,利用粒子群优化算法寻求最优的加权权数,最后将参数估计方法最小二乘法改为加权最小二乘法求模型的灰参数,构成NGM(1,1)模型初始值的选取、背景值的构造和参数估计方法的组合优化。通过算例来验证优化后的灰色NGM(1,1)模型性能,并将改进的模型应用于传染病的预测。
The outbreak of infectious diseases in 2020 is a serious threat to people’s life and health, and accu-rate prediction is important for the management of infectious diseases. Based on the uncertainty of infectious disease development, the traditional gray NGM(1,1) model is established, and the selec-tion of initial values of NGM(1,1) model, the construction of background values and the parameter estimation methods are important reasons for the unstable accuracy of this model. Firstly, this pa-per optimizes the background value of the traditional NGM(1,1) model based on the three-parameter tight-neighborhood mean background value, and uses the particle swarm optimi-zation algorithm to find the optimal initial value with the objective of minimizing the average rela-tive error, then changes the three-parameter tight-neighborhood mean background value to a weighted three-parameter background value, and uses the particle swarm optimization algorithm to seek the optimal weighting weights, as well as finally changes the parameter estimation method least squares Finally, the least squares method of parameter estimation is changed to the weighted least squares method to find the gray parameters of the model, which constitutes the optimization of the combination of the initial value selection, background value construction and parameter es-timation method of the NGM(1,1) model. The performance of the optimized gray NGM(1,1) model is verified by arithmetic examples, and the improved model is applied to the prediction of infectious diseases.
出处
《建模与仿真》
2023年第4期3794-3806,共13页
Modeling and Simulation
