管道腐蚀深度预测的优化灰色GM(1,1)模型建立及应用

Establishment and application of optimized grey GM(1,1)model for prediction of pipeline corrosion depth

管道腐蚀深度是腐蚀行为研究的重要内容,准确预测管道腐蚀深度变化规律对于保障管道的安全运行意义重大。针对传统GM(1,1)模型背景值计算方法的不足,提出了一种基于二次多项式变换结合背景值优化的改进灰色模型,通过实例对比分析了改进模型和传统模型预测精度的差异。结果表明:当建模样本数为7时,传统模型、改进模型一(采用二次多项式变换方法所建模型)、改进模型二(采用二次多项式变换结合背景值优化方法所建模型)预测所得的平均相对误差分别为5.33%、4.00%和3.731%,因此改进模型二的预测精度高于改进模型一和传统灰色模型;当建模样本数分别为8和9时,改进模型二的预测精度仍最高,因此采用的背景值优化方法有助于提升改进模型一的预测精度;改进模型用于预测管道腐蚀深度完全可行,且所用方法具有计算简单、精度高的优点。

To achieve better prediction accuracy of pipeline corrosion depth,the improved GM(1,1)models are established based on grey theory.By mastering the modeling ideas of the traditional grey GM(1,1)model,an improved grey model(improved model I)is established by introducing the method of function transformation(quadratic polynomial),and an improved grey model II is established using quadratic polynomial transformation combined with background value optimization method.The differences in prediction accuracy between the improved models and the traditional GM(1,1)model are compared and analyzed through examples.The research results show that when the number of modeling samples is 7,the average relative error and root mean square error predicted by the traditional GM(1,1)model is 5.33%and 0.083,respectively.The average relative error and root mean square error predicted by the improved model I are 4.00%and 0.062,respectively.The average relative error and root mean square error predicted by the improved model II are 3.731%and 0.058,respectively.Therefore,the prediction accuracy of improved model II is the highest,followed by the improved model I,while the accuracy of the traditional GM(1,1)model is poor.When the number of modeling samples is 8 and 9,the average relative error predicted by the improved model II is 2.627%and 1.139%,respectively,and the root mean square error is 0.041 and 0.018,respectively.Therefore,its prediction accuracy is still the highest.The function transformation method using quadratic polynomials can help improve the prediction accuracy of the traditional GM(1,1)model,so it is completely feasible to establish an improved model based on this method.In addition,the background value optimization method used in this article overcomes the shortcomings of background value calculation of traditional gray models and can further improve the prediction accuracy of the improved model I.Overall,the improved grey model using quadratic polynomial transformation combined with background value optimization has better predictive performance,and the model is more convenient to apply.