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 $L_1$ 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, $L_1$ norm optimization has been shown to be suboptimal and cannot enforce further sparsity. A fan noise radial mode detection method based on $L_{1/2}$ regularization algorithm is proposed in this paper to improve its robustness and dynamic range. This method employs the $L_{1/2}$ regularization to directly solve the in-duct sound propagation model. Synthesized simulations indicates that the $L_{1/2}$ 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 $L_{1/2}$ regularizer. It is demonstrated that the new $L_{1/2}$ 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 $L_{1/2}$ regularization method, which makes it an effective and robust fan noise radial mode detection technique in practical applications.