Spatial transformation of general sampling-aliasing frequency region for rotating-blade parameter identification with emphasis on single-probe blade tip-timing measurement

Blade-health monitoring is intensely required for turbomachinery because of the high failure risk of rotating blades. Blade-Tip Timing (BTT) is considered as the most promising technique for operational blade-vibration monitoring, which obtains the parameters that characterize the blade condition from recorded signals. However, its application is hindered by severe undersampling and stringent probe layouts. An inappropriate probe layout can make most of the existing methods invalid or inaccurate. Additionally, a general conflict arises between the allowed and required layouts because of arrangement restrictions. For the sake of economy and safety, parameter identification based on fewer probes has been preferred by users. In this work, a spatial-transformation-based method for parameter identification is proposed based on a single-probe BTT measurement. To present the general Sampling-Aliasing Frequency (SAFE) map definition, the traditional time–frequency analysis methods are extended to a time-sampling frequency. Then, a SAFE map is projected onto a parameter space using spatial transformation to extract the slope and intercept parameters, which can be physically interpreted as an engine order and a natural frequency using coordinate transformation. Finally, the effectiveness and robustness of the proposed method are verified by simulations and experiments under uniformly and nonuniformly variable speed conditions.