Abstract: Detecting bridge plug position and leakage volume is crucial for understanding bridge plug operational status and enabling real-time quantitative monitoring during staged multi-cluster hydraulic fracturing operations. This is of significant importance for evaluating the effectiveness of fracturing and optimizing fracturing processes. This paper focuses on the core objectives of precise bridge plug position detection and effective identification of leakage volume. Combining numerical simulation with numerical signal processing methods, the following research is conducted: First, by analyzing bridge plug operation conditions, an acoustic monitoring approach is proposed. Then, based on the k-ω turbulence model and convective wave theory, a numerical model for real-time monitoring of bridge plug conditions is established. Second, leveraging equipment principles and numerical signal processing, Empirical Mode Decomposition (EMD) is employed to extract signal feature parameters. Finally, Principal Component Analysis (PCA) is used for dimensionality reduction, and Random Forest (RF) is applied for digital signal processing-based leakage volume identification. Supported by the equipment design and digital signal processing methods introduced herein, plug position detection accuracy exceeds 96%. Under limited dataset conditions, the Random Forest algorithm achieves an R2 value exceeding 0.9 for plug leakage volume identification, with an absolute mean error of only 0.0105 m3/min. These research outcomes hold significant theoretical and practical value for enhancing fracturing efficiency, optimizing fracturing design, and mitigating operational risks.