Surface movement monitoring and dynamic prediction system based on the optimized Knothe time function

Aiming at the engineering application problem that software development for surface subsidence prediction induced by coal mining lags behind the optimization of prediction models, this study established a dynamic prediction model for surface movement based on probability integration theory and an optimized Knothe time function and developed a corresponding surface movement prediction system. The composite trapezoidal formula method was employed to integrate surface point subsidence calculations, combined with time function values computed for dynamic units, ultimately predicting the total subsidence at any surface location. Developed in Java and Python, the system implements monitoring, prediction, and 2D/3D visualization functions. Taking 21 404 working face of a mine as an engineering example, the error analysis shows that the measured data of surface monitoring points of 105d, 276d, 346d, 458d, 654d, and 753d are compared and analyzed with the dynamic prediction results: The average value of relative error of dynamic prediction is 12.22%, which indicates that the proposed model has well stability in the dynamic prediction of surface movement. This research provides a practical and efficient solution for the dynamic prediction of coal mining subsidence.