基于新维无偏灰色马尔可夫模型的大坝沉降预测研究

Dam settlement prediction based on metabolism unbiased Grey-Markov model

【目的】基于组合预测思想,结合灰色理论与马尔可夫预测方法的特点构建一种新的预测模型,为大坝沉降量的中长期预测提供支持。【方法】通过对传统灰色系统模型的优化改进,简化建模步骤并提高模型预测精度。在此基础上,借助于马尔可夫模型处理时间序列的随机性波动,克服灰色模型对随机波动性大的序列预测精度较低的局限性,并利用新信息优先原理,构建新维无偏灰色马尔可夫组合预测模型。将构建的新维无偏灰色马尔可夫组合模型应用于大坝沉降量的预测。【结果】构建的模型预测平均误差由原来的1.7%降低为1.0%,且预测误差的变化波动性减小。同时,随着预测期数的增加,相对于传统灰色模型,改进后的组合模型的预测精度进一步提高。【结论】与传统计算方法相比,所建立的新维无偏灰色马尔可夫组合预测模型计算量小、预测精度较高,且该模型保留了传统灰色模型短期预测精度高的优点,提高了模型的中长期预测能力,适用于大坝沉降量的中长期预测。

【Objective】 Based on Grey system theory and Markov chain prediction method,a combined prediction model was developed to support the prediction of dam settlement in medium and long-term.【Method】 Firstly improvements were implemented to diminish the inherent bias of the conventional Grey model,simplify the modeling procedure and make it more suitable for long term prediction.Then,Markov chain prediction method was used to modify the prediction of the improved Grey model to capture the prediction errors and improve the prediction accuracy.Additionally considering the principle that new information has higher priority in prediction process,a combined model,named metabolism unbiased Grey-Markov（MUBGM（1,1）-Markov） model,was developed.The combined model was used to predict the settlement of a dam.【Result】 Results of empirical study indicated that the average prediction error of MUBGM（1,1）-Markov model was 1.0%,less than that of the traditional Grey model（the average prediction error was 1.7%） with the volatility of the prediction error decreased.At the same time,with the prediction period increased,the prediction error of MUBGM（1,1）-Markov model decreased to be even more stable than the traditional Grey model.【Conclusion】 Compared with the traditional method,the MUBGM（1,1）-Markov model had the higher prediction accuracy with less amount of calculation resource consumption.It improved the long period prediction accuracy of the dam settlement,while kept the short period prediction accuracy using the traditional Grey model.This model is capable of predicting accurately the settlement of dam in medium and long-term.