To address the issue that the fault diagnosis of the gear lubrication system of a nuclear power plant primarily relies on expert knowledge and experience, leading to numerous nuclear accidents, we propose an innovative integrated data-driven machine learning (IDDML) method based on sensor measurements. This IDDML method consists of two major components. The first is the fault tree analysis, which uses fault trees to identify critical fault paths and calculate failure probabilities. The second is the adaptive sparse principal component analysis based on variable projection combined with proximal gradient optimization (VPPGO-ASPCA) method. This method incorporates a modified principal component analysis technique and an optimization algorithm with an adaptive threshold. Compared with traditional diagnostic methods used in gear failure detection, our proposed IDDML method offers higher detection accuracy and improved sensitivity. Additionally, to compare and validate our proposed method, we developed a unique real-time measurement system that integrates multiple high-sensitivity sensors and employs four network architectures for the fault diagnosis of the gear lubrication system in a nuclear power plant. Experimental and computational results demonstrate that the IDDML fault diagnosis method achieves a fault detection success rate of up to 99%.