To address the challenge that early faults of idlers in mining belt conveyors are difficult to accurately identify under complex working conditions, and that strong background noise masks weak features, this paper proposes an online monitoring method based on Distributed Acoustic Sensing. This method integrates physics-model-guided modal reconstruction and cepstral-domain Q-value analysis. First, a "load-clearance" coupled dynamic model for a 6305-type bearing is constructed to simulate vibration modes under various damage conditions, serving as a physical benchmark. Second, Empirical Mode Decomposition is utilized to decompose the collected non-stationary signals into Intrinsic Mode Functions. To overcome the limitations of blind reconstruction, the Bhattacharyya distance is introduced as a similarity criterion. This allows for the screening of effective components that are most similar to the simulated modes from a probability distribution perspective, successfully extracting weak fault features from strong noise. On this basis, the cepstral domain Q-value of the reconstructed signal is calculated as the core discriminative operator. Combined with the quasi-periodic rotation characteristics of the idlers, this significantly amplifies the feature differentiability between healthy and defective idlers. Through continuous field monitoring conducted at a thermal power plant, the system successfully identified a bearing jamming fault in idler #5, issued an early warning for a potential safety hazard in idler #9, and tracked the degradation trend of idler #15. Experimental results demonstrate that the fault identification sensitivity of the reconstructed Q-value is improved by over 30% compared to the original signal. This proposed scheme validates its engineering application value in preventive maintenance, offering a high signal-to-noise ratio and a highly interpretable technical path for the safe operation of belt conveyors.