Physics-Informed Fuzzy Regression for Aeroacoustic Prediction Using Clustered TSK Systems

Efficient aero-acoustic regression is critical for unmanned aerial vehicle (UAV) design and urban air mobility operations, where noise mitigation is essential for regulatory compliance and public acceptance. While data-driven fuzzy Takagi–Sugeno–Kang (TSK) systems have shown potential for modeling complex aero-acoustic behaviors in UAV applications, their performance is strongly affected by input dimensionality and rule-base complexity. This work extends previous research on dimensionality reduction for genetic algorithm-optimized fuzzy systems by conducting a comparative benchmark on an aero-acoustic database regression task relevant to drone propulsion noise prediction. Several TSK architectures are evaluated, including zero- and first-order models, different membership function granularities, and clustering-based rule-generation strategies. In addition, a physics-based heuristic TSK rule system incorporating aero-acoustic knowledge is introduced and compared against data-driven fuzzy configurations. Model performance is primarily assessed through graphical regression analysis and optimization convergence behavior, with a focus on computational efficiency, structural complexity, and qualitative prediction trends—critical considerations for onboard UAV systems and real-time acoustic monitoring. The results highlight the trade-offs between data-driven learning and physics-informed rule construction, demonstrating that physics-based heuristics can reduce optimization complexity while preserving physically consistent behavior. This study provides practical insights into the design of interpretable and efficient fuzzy regression models for UAV aero-acoustic applications, supporting next-generation drone acoustic signature management.