一种改进灰色预测模型在变形预测中的应用

针对传统的单一模型和非线性GM(1,1)-AR组合模型无法实现对非平稳、含噪时间序列信号进行优化处理的问题,该文提出了一种新的基于小波的GM(1,1)-AR模型预测算法。采用小波变换原理对监测数据进行消噪处理和不同频带的分离,有效地获取了实际变形量;利用GM(1,1)模型和AR时序分析模型对具有确定性的趋势项和不确定性的随机项进行建模组合,较好地综合了灰色模型拟合功能强大和时间序列善于处理细节信息两者优势。通过工程实例对比分析结果表明:基于小波的GM(1,1)-AR模型不仅有效剔除了多余噪声,还利用各种模型有机嵌套组合实现优势互补,新算法预测结果比各单一模型、非线性GM(1,1)-AR模型结果更为精确。

The application of GM(1, 1)-AR forecasting model based on Wavelet in deformation forecast

For the traditional single model and nonlinear GM (1,1)-AR composite model can not achieve the optimal processing of the non-stationary and noisy time series signals,a new GM(1,1)-AR model prediction algorithm based on wavelet was proposed in this paper.Wavelet transform was used to eliminate noise and separate different frequency bands and the actual deformation was effectively extracted;The deterministic trends and stochastic term of uncertainties were used finishing the modeling combination through GM(1,1)model and AR time series analysis model.The advantages that the gray model with powerful fitting function and time series adept at handling details were well integrated.The results based on the test examples showed that:The GM(1,1)-AR model based on wavelet was not only effective to eliminate the excess noise,but also achieved complementary advantages using a variety of models of organic combination.The results of the new algorithm were more accurate than those of the single models and the nonlinear GM(1,1)-AR model.