A Novel Approach for Accurate Surface Subsidence Forecasting: Combining Tanh Time Function with Adaptive Weighted Models

To address the challenges of insufficient accuracy and stability in surface subsidence prediction, especially in mined-out areas with complex temporal and spatial variations, a two-parameter hyperbolic tangent (tanh) time function was introduced. This approach aimed to analyze the influences of its parameters and establish two advanced predictive models: a variance reciprocal equivalence combination (VREC) model and an error squared sum reciprocal variable-weight combination (ESSR-VWC) model. This study thoroughly examines how the parameters of the tanh function affect the morphology of subsidence curves and proposes a method for parameter identification. Subsequently, two combined prediction models were constructed and validated through a case study conducted at the mined-out areas of 1176 East Working Face in China. Results show that the tanh function accurately captures the spatiotemporal variation patterns of surface subsidence. Furthermore, the ESSR-VWC model stands out for its computational simplicity and superior performance compared to the VREC model, exhibiting higher prediction accuracy and stability. Notably, in intervals with complex changes, the predicted values from the ESSR-VWC model closely match the measured data. Overall, the integration of the tanh time function with the ESSR-VWC model significantly enhances the reliability of surface subsidence prediction, offering a valuable tool for mining engineering and geotechnical applications.