基于灰色关联分析和PSO改进的多变量GM(1,N)模型

Improved GM(1,N)Model Based on Grey Correlation Analysis and Particle Swarm Optimization Algorithm

GM(1,N)模型是一种重要的因果关系预测模型,建模过程充分考虑了相关因素对系统变化的影响,但GM(1,N)模型存在建模机理和模型结构上的不足,因此在实际应用中常常导致模型误差大于GM(1,1)模型。为了解决传统灰色模型预测精度不高的问题,论文以OGM(1,N)预测模型为研究基础,采用灰色关联分析方法计算筛选与参考序列关联度较高的序列组成自变量输入序列,同时根据OGM(1,N)模型预测原理优化模型初始条件,基于PSO算法和变量数目直接对OGM(1,N)模型参数进行优化求解。论文提出的模型将灰微分方程背景值的寻优过程转化为利用PSO寻找最小模型还原值与实际值误差平方和的问题,有效避免了背景值寻优过程或直接定义背景值再对模型参数值进行求解产生的偏差。最后,论文通过在两个预测数据集上的实验证明了所提模型的预测准确性和价值性。

GM(1,N)model is an important causality prediction model.And its modeling process fully takes into account the impact of relevant factors on system changes.However,GM(1,N)model has some shortcomings in modeling mechanism and model structure,which often leads to model errors greater than GM(1,1)model in practical applications.In order to solve the problem that the prediction accuracy of traditional grey model is not high,this paper takes OGM(1,N)prediction model as the research basis,and uses grey correlation analysis method to filter the sequence with high correlation with reference sequence and compose it into independent variable sequence.Meanwhile,this paper optimizes the initial conditions of the model based on the prediction principle of OGM(1,N)model,and directly solves and optimizes the parameter values of OGM(1,N)model based on the PSO algorithm and the number of variables.The model proposed in this paper transforms the optimization process of background value of grey differential equation into the problem of finding the square sum of error between the minimum model reduction value and the actual value by using PSO,which effectively avoids the deviation caused by the optimization process of background value or the error caused by directly defining the background value to solve the model parameter values.Finally,the paper proves the prediction accuracy and value of the proposed model through experiments on two prediction data sets.