Function x&lt;sup&gt;-ln x&lt;/sup&gt; (x &amp;#x2265; e) transformation for improving smooth degree and its application in grey modeling

Zhang, Huanyong; Yang, Aiping; Dai, Wei

doi:10.1109/gsis.2007.4443491

Cited by 1 publication

(1 citation statement)

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“…The accuracy of the improved model is higher than that of the traditional GM(1,1) model, and the reasonable translation variables make the improved GM(1,1) model have higher prediction accuracy. Literatures (Xu et al, 2021;Jin et al, 2022;Zhang et al, 2016;Huanyong et al, 2007;Liu et al, 2013;Shao et al, 2010;Yao-guo et al, 2009) proposed the cotangent function transformation, logarithmic function transformation, inverse cotangent function transformation, exponential logarithmic function transformation, cosine function transformation, sine function transformation, and linear transformation to improve the smoothness of the original sequence and thus improve the model prediction accuracy, respectively.…”

Section: Introductionmentioning

confidence: 99%

Prediction of wax deposit thickness in waxy crude oil pipelines using improved GM(1,1) model

Fan²,

Song³

et al. 2022

Front. Chem. Eng.

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In this paper, the GM(1,1) model with function arccosx transformation and GM(1,1) model with function transformation are established by using arccosine function transformation method and aarccosx function transformation method, and the GM(1,1) model with function cosx2 transformation is established by using function transformation theory, and GM(1,1) model with function cosx2+c transformation is established by using translational transformation theory on the basis of this model. The prediction accuracy of GM(1,1) model, GM(1,1) model with function arccosx transformation, GM(1,1) model with function aarccosx transformation, GM(1,1) model with function cosx2 transformation, and GM(1,1) model with function cosx2+c transformation are compared by modeling with the field pipeline data and the indoor loop data. The influence of a value in GM(1,1) model with function aarccosx transformation on prediction accuracy is discussed, and the influence of c value in GM(1,1) model with function cosx2+c transformation on prediction accuracy is discussed. With the increase of a and c values, the average relative error show a trend of decreasing and then increasing, by comparing the average relative errors under different a and c values, the optimal a value and c value and the optimal prediction accuracy are obtained. The results show that the GM(1,1) model with function cosx2+c transformation in the indoor loop has an average relative error of 0.6490% when c=0.114, which is the minimum average relative error compared to other models and achieves the highest prediction accuracy. The GM(1,1) model with function cosx2+c transformation in the field pipeline has an average relative error of 1.94156% when c=−0.555, which is the minimum average relative error compared to other models and achieves the highest prediction accuracy. Among the five models, only the GM(1,1) model with function cosx2+c transformation has fitted and predicted values that are closer to the actual thickness values in the indoor loop experimental data and the field pipeline data, and the predicted values are more consistent with the actual conditions in the field pipeline. This paper verifies the feasibility of using the GM(1,1) model with function cosx2+c transformation to predict the wax deposition thickness of the pipe wall, and provides a reference for subsequent research on accurate prediction of wax deposition thickness.

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Section: Introductionmentioning

confidence: 99%