The connection between digital-twin model and physical space for rotating blade: an atomic norm-based BTT undersampled signal reconstruction method

Digital twin that shows great potential in different fields may serve as the enabling technology for the health monitoring of aero-engine blade. However, due to the harsh conditions inside the aero-engine, one of the most challenging issues for the implementation of digital-twin-based blade health monitoring is the lack of an accurate connection method between the digital-twin model and the physical entity for rotating blade. Wherein, the key is how to measure the blade data accurately. The emerging blade tip timing (BTT), an effective non-contact measurement method for blades, has received extensive attention recently. Whereas, due to the limited probes that are allowed to be installed on the engine casing, the BTT signal is generally incomplete and under-sampling, which makes it very difficult to reconstruct the blade vibration parameters from the measured data. In this study, a novel paradigm for blade vibration parameter reconstruction with super-resolution from the undersampled BTT signal is proposed based on atomic norm soft thresholding (AST), which may offer accurate blade vibration information for the construction and updating of blade digital-twin model. Unlike the conventional reconstruction method that generally needs the interested signal to be sparse under a finite discrete dictionary for successful reconstruction, the proposed AST-based blade vibration parameter reconstruction method can take any continuous value in the frequency domain from the measurement data with fewer sampling numbers and higher under-sampling rate. Both numerical simulation and experimental verification are utilized to verify the validity of the proposed method. The comparative results indicate that the proposed method performs well in resisting “incomplete.” Meanwhile, the proposed method performs better than state-of-the-art methods under conditions with fewer data.