Research on the Markov-Chain State Interval Division Based on Predicted Data Correction

Abstract

By 2022, the total length of roads in Tibet Autonomous Region reached 121,447 kilometers. Due to the unique geological conditions in Tibet, various natural disasters such as earthquakes, mudslides, landslides, avalanches, and strong winds frequently occur. Along the Sichuan-Tibet Highway alone, over 300 disasters happen each year, significantly impacting the region’s economic development. This study focuses on the complexity and randomness of natural disaster mechanisms and combines Markov chain theory to improve the accuracy of prediction data for mudslides, landslides, and earth subsidence etc. The main method is to modify the state interval of the prediction model parameter-Markov chain based on the distribution of discrete points on the number axis. The following state interval division methods are proposed: (1) If the relative error of the predicted value exceeds 50%, adjust the prediction model. (2) Obtain the lower bound of state E1 by taking the floor value downward. (3) The width of each interval does not need to be uniform. (4) Arrange continuous, dense, and close points on the number line in the same side in batches, and represent a state continuously, dividing it into one suitable interval or batches. Using this method, an improved RMSE of 0.28mm and MAPE of 0.87% were obtained for engineering examples, outperforming other models such as GM(1,1), Verhulst, DGM(2,1) with corresponding RMSE values of 0.86 mm, 0.69 mm, and 1.38 mm, and MAPE values of 2.75%, 2.53%, and 5.99%. The combined prediction results for five sets of data yielded an RMSE of 0.14 mm and MAPE of 0.56%, which are quite close to the results obtained using Markov selection correction with an RMSE of 0.37 mm and MAPE of 1.01%. Furthermore, comparing the four sets of case, the average reduction in RMSE and MAPE is 3.56mm and 1.72%, respectively, demonstrating that this method can further improve the performance of Markov chain prediction.