改进三角模糊数灰模型在变形监测中的应用

Application of Improved Triangular Fuzzy Number Gray Model in Deformation Monitoring

灰色系统理论是一种研究少数据、先验信息贫乏问题的预测方法。目前以GM(1,1)模型为代表的灰色预测模型只适用于精确序列,但变形监测数据往往存在模糊性和关联性,这种关联性对结果的影响可大可小。传统三角模糊数GM(1,1)模型,简称TFGM(1,1)模型,把数据的模糊性融入模型,扩大了灰模型的应用范围,但上述模型没有考虑数据的关联性和整体性。在此基础上,给出一种改进TFGM(1,1)模型,该模型对发展系数做了权重比处理。结合传统TFGM(1,1)模型,给出了改进TFGM(1,1)模型的建立以及预测过程。实例验证表明,考虑数据之间相关性后的改进TFGM(1,1)模型的拟合与预测精度优于传统TFGM(1,1)模型。

Gray system theory is a kind of forecasting method for studying the problem of less data and a priori information. The gray forecasting model represented by GM （1,1） model is only suitable for precise sequence, but deformation monitoring data often exist fuzzy. The traditional triangular fuzzy GM （1,1） model （referred to as TFGM （1,1） model） integrating the fuzziness of data into mode, expanding the application range of grey model. But the above model does not take into account the correlation and integrity of the data. On this basis, an improved TFGM （1, 1） model, which combines the weight of the development coefficient is presented. The traditional TFGM （1,1） model is given to improve the establishment and prediction of the TFGM （1,1） model. The example shows that the improved TFGM （1,1） model is considered and predicted after the correlation between the data, the accuracy is superior to the traditional TFGM （1,1） model.