Real-time monitoring of vibration acceleration of civil infrastructure is imperative for effective management and safe operation of structures. Although the triboelectric nanogenerator (TENG) shows potential for self-powered sensing, it faces challenges in correlating limited experimental electrical amplitudes to structural responses, thereby hindering comprehensive performance analysis of civil infrastructure. Herein, a self-driven acceleration TENG sensor (A-TENG) is designed and manufactured, comprising an outer shell and an inner mass-spring-damper system. By establishing a sensing model based on vibration theory and the TENG mechanism, the electrical signals generated by the sensors can be correlated with structural acceleration, enabling self-driven real-time quantitative characterization. Indoor and on-site experiments demonstrate that the A-TENG sensor is capable of continuously monitoring the acceleration profile with excellent consistency compared to commercial sensors. The non-contact free-standing sliding mode design and ultra-lightweight construction of the A-TENG sensor (~8   g) enhance its start-up sensitivity (~0.1   m/s2), long-term stability (~30000 loading cycles) while minimizing mass interference. The proposed sensing theory renders a novel approach to offering complete time-domain information, which is vital for the precise analysis of structural behavior. This work facilitates understanding of self-driven sensors utilizing TENG technology and provides a useful tool for long-term real-time quantitative structural health monitoring.