Application of Newton–Raphson-based optimizer in <i>K</i>-means clustering and random forest optimization for hydropower unit operation state monitoring

Abstract This study addresses the need for precise analysis and fault prediction in hydropower units by introducing an enhanced framework that integrates the Newton–Raphson-Based Optimizer (NRBO) with K -means clustering and random forest (RF) models. This framework dynamically optimizes both cluster numbers and hyperparameters, yielding significant improvements in clustering accuracy. The findings demonstrate that the NRBO-optimized K -means model achieves precise operational state classification without predefined cluster numbers, thereby enhancing intra-cluster compactness and inter-cluster separation. Experimental validation confirms the effectiveness of the proposed method in complex operational scenarios. Furthermore, the optimized RF model identifies critical features such as Active Power and Guide Vane Opening, which are crucial for risk detection under high-load conditions. This approach provides strong support for advanced state analysis and intelligent management of hydropower units, highlighting substantial potential for real-world applications.