Parameter Inversion of Probability Integral Model Based on GA–BFGS Hybrid Algorithm

The probability integral method is the primary technique for predicting mining-induced subsidence in China, and its predictive accuracy strongly depends on the precision of the model parameters. To improve the accuracy and stability of parameter inversion and to overcome the convergence randomness of the Genetic Algorithm (GA) in global search, as well as the tendency of the BFGS quasi-Newton method (BFGS) to converge to local optima in non-convex optimization problems, a hybrid GA–BFGS optimization algorithm is proposed for inverting the parameters of the probability integral model. This hybrid approach combines the global exploration capability of GA with the fast local refinement of BFGS, resulting in a more efficient and robust parameter optimization process. Simulation results under ideal conditions without model error demonstrate that the proposed GA–BFGS algorithm outperforms pattern search (PS), GA, and BFGS in terms of inversion accuracy, convergence stability, and robustness to noise and outliers. In engineering applications, the inversion accuracy is reduced compared with simulation experiments, which can be attributed to complex geological conditions and inherent model uncertainties. Therefore, further improvements in subsidence prediction accuracy require not only refined inversion algorithms but also the development of more accurate prediction models that explicitly account for site-specific geological and mining conditions.