Optimization of sensor arrangement for radial mode analysis of fan noise using compressed sensing

Mode analysis has played a significant role in the study of aero-engine noise. Accurate understanding of the mode wave patterns within the fan duct can provide theoretical support for noise reduction designs. Wall-flush mounted sensors are commonly used in Radial Mode Analysis (RMA), due to the advantage of not interfering with the flow field. This paper applies the compressed sensing (CS) method to RMA. The performance of sparse sensor arrays in a hard-wall circular duct are studied through numerical experiments. Firstly, based on the mutual coherence of the sensing matrix, the upper limit for the axial spacing dz of the sensor array and the lower limit for the total length L are discussed. Random arrays with low condition numbers and low mutual coherence are generated through non-uniform placement in both azimuthal and axial directions. Secondly, the random arrays are further filtered based on the equiangular tight frame (ETF) index J and the mutual coherence μ. The accuracy, noise immunity, sensor failure tolerance, and spatial robustness of the proposed layout are discussed using the Monte Carlo method. In summary, a sparse wall-flush mounted sensor array suitable for CS-RMA can be obtained through the two parts of optimization in this paper.