基于傅里叶变换的质量预测动态残差修正模型

Research on the dynamic model of error amendment for quality prediction based on Fourier transform

针对生产过程中的动态性和预测的非零误差性,在传统灰色模型的基础上,遵循数据"重近轻远"的原则,综合数据新陈代谢动态反映系统目前特征和傅里叶变换强大的降噪功能的优势,提出循环傅里叶修正新陈代谢GM(1,1)模型(CFGM(1,1)),并给出相应的步骤和算法。该模型通过傅里叶变换对新陈代谢模型的预测残差进行动态修正补偿,提高了对系统随机误差的预测能力,从而提高了预测精度。对具体实例的Matlab仿真,表明,CFGM(1,1)模型预测精度较高,建模与计算速度快且不需要大量的数据,为动态生产过程的在线控制提供了有利条件。

The dynamics of the production process and the non-zero error of quality prediction are considered, and by taking advantage of the metabolic gray model（1, 1） and prediction error amendment, the cycling Fourier gray model （CFGM （1,1）） is put forward based on the traditional gray model, and the corresponding steps and algorithm are given. Unlike the gray model （1,1）, this model follows the principle of ＂attaching much weight to the near data but taking the far data lightly＂. The prediction residual error obtained by the metabolic gray model is amended dynamically by way of the Fourier transform,which can filter out the noise of data, and the random error is considered on the basis of system errors during the quality predicting process, so the prediction accuracy is greatly improved. A specific example of this model is proved by the Matlab emulator, and the results show that the model CFGM （1, 1） has the advantages of rapid modeling and calculating, and the prediction accuracy is high. Besides, this model does not need a large amount of data and provides favorable conditions for on-line control of the dynamic production process.