Monitoring friction interfaces is essential for evaluating system health. However, direct force sensing is often not feasible in real applications. Sound and vibration signals offer an alternative, but their relationship with the coefficient of friction (COF) remains unclear. And most studies focus only on predicting the mean COF and ignore its fluctuation characteristics. In this study, a multi-source acquisition platform was built to synchronously record COF, sound pressure, and bidirectional vibration signals during dry sliding tests. Correlation analysis shows that the fluctuation features of COF exhibit strong correlations with resonance frequencies of sound and vibrational signals, while the mean value of COF lacks clear direct correspondence with these signals. Based on these findings, we propose a two-step prediction method with clear physical meaning. First, fluctuation features of COF (e.g., standard deviation, peak-to-peak, waveform factor) are predicted from sound and vibration features using multiple regression models and ensemble strategies. Second, these fluctuation features are used to predict the mean and root mean square (RMS) of COF through statistical modeling and Random Forest regression. The proposed method achieves high accuracy, over 95% for most fluctuation indicators and above 98% for mean and RMS predictions. By separating the modeling of fluctuation and central tendency, this method improves both interpretability and prediction performance. It provides a practical approach for early fault warning and long-term monitoring in tribological systems.