基于函数cot(x^(α))变换的加权非等间隔灰色GM(1,1)模型及其应用

Weighted Non-equal Interval Gray GM(1,1)Model Based on Function cot(x^(α)) Transformation and Its Application

针对建筑物累计沉降监测数据量少、信息贫乏、非等间隔、光滑性差且呈近似指数增长等特点,建立了非等间隔灰色GM(1,1)预测模型.采用函数cot(x^(2))对原始建模监测数据进行光滑度提升变换,再按作用和地位不同对建模监测数据赋予不同权重,以此提高了模型的预测精度.实证分析表明加权非等间隔灰色cot(x^(2))-GM(1,1)模型具有较高的预测精度,可用以工程实践.

Aiming at the characteristics of building accumulated settlement monitoring data,such as less data,lack of information,non-equal intervals,poor smoothness and approximate exponential growth,a non-equal interval gray GM(1,1)prediction model was established.The function cot(x^(2))is used to improve the smoothness of the original modeling monitoring data,and then different weights are assigned to the modeling monitoring data according to different functions and positions,to improving the prediction accuracy of the model.The empirical analysis shows that the weighted non-equal interval gray cot(x^(2))-GM(1,1)model has high prediction accuracy and can be used in engineering practice.