An Adaptive Setting Optimization Algorithm for Debris Flow Early Warning Threshold Integrating Chaotic Gray Wolf Optimization and Internal Model Repetitive Control

The effectiveness of early warning thresholds for debris flows is concurrently constrained by geological spatial heterogeneity and the cumulative effects of rainfall duration, with the coupling mechanisms between the two being complex and difficult to adapt dynamically. To address this issue, an adaptive optimization algorithm for debris flow early warning thresholds is proposed, integrating Chaotic Grey Wolf Optimization (CGWO) with Internal Model Repetitive Control (IMRC). This algorithm establishes a dual-layer linkage architecture of “offline global optimization + online periodic compensation”: CGWO solves for the optimal baseline thresholds for different types of susceptibility zones offline based on historical disaster data, while IMRC performs periodic compensation on the baseline thresholds according to real-time rainfall duration, thereby synergistically generating dynamic critical rainfall thresholds that account for both spatial zonation differences and rainfall temporal evolution. The method is validated in a debris-flow-prone mountainous watershed in Southwest China. The results indicate that the IMRC compensation exhibits clear duration dependence and zonation differentiation. Under short-duration rainstorm conditions, IMRC provides positive compensation, with compensation amounts of +3.5 mm, +1.5 mm, and +12.0 mm for high, moderate, and low susceptibility zones, respectively. Under medium-duration rainfall conditions, the compensation amounts are −2.0 mm, −1.5 mm, and +7.0 mm, respectively. Under long-duration sustained rainfall conditions, the compensation amounts are differentially output according to zonal geological conditions, being +2.5 mm, −3.0 mm, and −1.0 mm, respectively. Based on the above dynamic thresholds, the three-tier yellow, orange, and red early warning intervals exhibit a comprehensive early warning efficiency index that steadily improves with the accumulation of historical samples, eventually converging to 0.98–0.99. These results fully demonstrate the adaptive optimization capability of the proposed algorithm in both spatial zonation and temporal evolution dimensions, providing a reliable quantitative basis for refined graded early warning of debris flows at the watershed scale.