Transfer path analysis with real beamforming regularization applied to acoustic modeling of substation transformers

Acoustic modeling of bulky transformers for far-field noise prediction and treatment faces the challenges of computational inefficiency and inaccuracy due to the large model size and complex environment. In this paper, a transfer path analysis (TPA) model is built for two substation transformers by constructing virtual sound sources (VSSs) at a distance in front of the transformer surfaces. A real beamforming regularization (RBR) algorithm is proposed to solve the VSS signals by introducing the beamforming response to regularize the minimization task for the inverse problem. Unlike the original beamforming regularization that uses Green’s functions, the RBR employs measured frequency response functions between the VSSs and near-field receivers to calculate the beamforming response. The noise at far-field receivers 30 m away from the transformers is then predicted by the TPA model using the solved VSSs and validated against the measurement. The proposed TPA-RBR method is computationally efficient and accurate, considering that the maximum prediction error of the prominent noise components is within 3 dB. The noise contributions from different transmission paths are evaluated to provide guidance for further noise treatment. Our study also has potential applications in the localization of sound sources shielded by bulky obstacles.