预测水泥砒砂岩强度的Markov灰色残差模型

Markov grey residual model for predicting strength of cement Pisha sandstone

为了研究Markov-灰色残差GM(1,1)模型预测水泥固化砒砂岩抗压强度的精准度和适用性,先对抗压强度数据进行了一系列的处理,建立灰色GM(1,1)模型和灰色残差GM(1,1)模型,然后基于马尔克夫过程构建Markov-灰色残差GM(1,1)模型,并以此模型来估算水泥固化砒砂岩的抗压强度.结果表明,灰色残差GM(1,1)模型的检验精度得到了很大的提升且各项检验指标基本上都达到了1级,明显优于灰色GM(1,1)模型.马尔克夫过程便于确定残差修正值的正、负号,采用Markov-灰色残差GM(1,1)模型对不同水泥掺量下90 d龄期的水泥固化砒砂岩的抗压强度进行了预测,相对误差由原来的1.77%~4.01%降低至0.60%~2.36%,平均相对误差由2.63%减小至1.25%,模型的预测精度明显提高.该研究可以为水泥固化砒砂岩以及其他水泥基工程材料抗压强度的预测提供一种简易且可靠的新方法.

In order to study the accuracy and applicability of Markov grey residual GM(1,1)model in predicting compressive strength of cement pisha sandstone,after a series of processings of compressive strength data,the grey GM(1,1)model and grey residual GM(1,1)model were established.Then the Markov grey residual GM(1,1)model was constructed based on the Markov process,and the compressive strength of cement-cured pasha sandstone was estimated by this model.The results show that the test accuracy of the grey residual GM(1,1)model is greatly improved and all the test indexes basically reach level 1,which is obviously better than that of the grey GM(1,1)model.The Markov process is convenient to determine the positive and negative signs of residual correction,and then the compressive strength of cement solidified Pisha sandstone with different cement contents at 90 days was predicted by the Markov grey residual GM(1,1)model.The relative error is reduced from 1.77%-4.01%to 0.60%-2.36%,and the average relative error is reduced from 2.63%to 1.25%.The prediction accuracy of the model is improved obviously.This study can provide a simple and reliable new method for predicting the compressive strength of cement-cured Pisha sandstone and other cement-based engineering materials.