Bayesian Compressed Sensing for the Rotating Flow Mode Analysis in a Transonic Fan

The conventional compressive sensing (CS) based on l1-norm can reconstruct the azimuthal modes for the rotating flow in compressors when the data is undersampled spatially. However, the signal noise and outlier can greatly affect its accuracy. The present work presents the application of the Bayesian compressive sensing (BCS) in the azimuthal mode reconstruction for the rotating flow in a transonic fan. To improve the anti-outlier ability during the mode reconstruction, a Heterogeneous Noise Model (HNM) is introduced to consider the signal outlier encountered at some specific probes. Mode reconstructions for the azimuthal components with different undersampling ratios are carried out to examine the performance of the above methods. It is found that the signal outlier can reduce the dominant mode amplitude and result in the formation of aliasing modes for the BCS and the conventional CS methods. In contrast, the BCS-HNM method can accurately identify the dominant mode order and further recover the mode amplitude in the presence of amplitude or phase outlier. If the undersampling becomes severe, the overall accuracy tends to deteriorate for all the three methods. However, the BCSHNM still exhibits the highest probability to achieve a successful mode reconstruction and find the probes with signal outlier. The robustness of the BCS-HNM has also been demonstrated, and it is revealed that the performance of the BCS-HNM method can be maintained over a wider range of signal outlier compared to the other two methods.