Acoustic dynamic modal analysis through Bayesian inference with Hamiltonian Monte Carlo method

Aerodynamic acoustic radiation is present throughout an aircraft’s flight. Identifying the dynamic modes of such noise is crucial for understanding the mechanisms of sound generation within the airflow and its propagation. However, the validity of the mode parameters identified by modal decomposition methods faces significant challenges due to the inherent random nature of aerodynamic noise sources. Moreover, the limited number of sensors in experiments constrains high-resolution spatial measurements of the noise. This paper proposes a Bayesian data-driven modal decomposition method, based on Hamiltonian Monte Carlo, for the valid and high-resolution identification of aerodynamic noise modes, with applications to microphone array measurements. This Bayesian framework for dynamic mode decomposition is constructed using Koopman eigen-decomposition theory. Subsequently, analytic gradient expressions, which serve as driving forces for the Markov chains, are derived for the mode parameters. The posterior distributions of these parameters are then estimated using the HMC sampler. Finally, the set of mode parameters is iteratively updated based on the relationship between the Koopman eigenvalues and eigenfunctions, significantly reducing computational complexity. The reconstruction of transient dynamics in the noise-driven Kuramoto–Sivashinsky equation shows that the proposed method attains a root mean square error below 15%, reflecting its effectiveness in modal decomposition. Further computational aeroacoustic simulations and non-synchronous wind tunnel measurements were conducted on the trailing-edge noise of the NACA 0012 airfoil to obtain the acoustic modes. The results show that this method can effectively visualize the dynamic behavior of sound waves, offering a novel perspective for exploring the mechanisms of aerodynamic noise generation and propagation.