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

In this paper, the GM(1,1) model with function arccos x transformation and GM(1,1) model with function transformation are established by using arccosine function transformation method and a arccos x function transformation method, and the GM(1,1) model with function cos x 2 transformation is established by using function transformation theory, and GM(1,1) model with function cos x 2 + 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 arccos x transformation, GM(1,1) model with function a arccos x transformation, GM(1,1) model with function cos x 2 transformation, and GM(1,1) model with function cos x 2 + 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 a arccos x transformation on prediction accuracy is discussed, and the influence of c value in GM(1,1) model with function cos x 2 + 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 cos x 2 + 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 cos x 2 + 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 cos x 2 + 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 cos x 2 + 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.