Fan noise radial mode detection based on L1/2 regularization method

Radial mode detection has been widely employed in fan noise research. Many radial mode detection algorithms by conducting the convex L1 norm optimization have been proposed by taking advantage of the fact that the fan noise sound field is usually dominated by a limited set of radial modes. Nevertheless, L1 norm optimization has been shown to be suboptimal and cannot enforce further sparsity. A fan noise radial mode detection method based on L1/2 regularization algorithm is proposed in this paper to improve its robustness and dynamic range. This method employs the L1/2 regularization to directly solve the in-duct sound propagation model. Synthesized simulations indicates that the L1/2 regularization method can detect the correct radial mode order and amplitude under low signal-to-noise ratio. Moreover, the new method is insensitive to regularization parameter. An experimental system of radial rake is implemented to validate the new method. It is shown that the L-curve method, which do not require any prior information of the acoustic mode distribution or contaminating measurement noise, is an appropriate choice of the regularization parameter determination method for the L1/2 regularizer. It is demonstrated that the new L1/2 regularization method can enhance the mode sparsity, especially under low signal-to-noise ratio. Moreover, the resolution and dynamic range can be improved by the L1/2 regularization method, which makes it an effective and robust fan noise radial mode detection technique in practical applications.