Acoustic sensing faces inherent challenges in balancing sensitivity and bandwidth for weak acoustic signal detection under extreme environmental conditions. This study proposes a self-assembled gradient acoustic metamaterial driven by shape memory alloy, which optimizes sound pressure enhancement through dynamic regulation of material parameters and geometric characteristics. By establishing an analytical acoustic field model using effective medium theory and Wentzel-Kramers-Brillouin (WKB) approximation, the research reveals the synergistic regulation mechanisms of material elastic modulus, density gradient, and frequency characteristics on acoustic wave propagation properties. Multiphysics-coupled simulations verify the acoustic pressure amplification patterns across the 1~13 kHz broadband range. Results indicate that adjusting geometric gradient parameters to modify effective refractive index can overcome the sensitivity-bandwidth trade-off in conventional sensors: large-taper-angle structures (60°) achieve rapid acoustic energy amplification in high-frequency ranges (9.7~12.9 kHz), while small-taper-angle designs (30°) effectively extend the gain coverage for low-frequency waves (2.1~5.3 kHz). The developed metamaterial with dynamic reconfigurability provides a novel technical approach for weak acoustic signal detection in industrial equipment, offering theoretical foundations and experimental validation to resolve performance contradictions in traditional acoustic sensors. This advancement holds significant implications for enhancing fault diagnosis reliability in complex operational conditions.