Research on 3D-BTC Signals Fractal Dimension Reconstruction Method of Aero-Engine

Turbine blades are key components of aero-engines. To comprehensively reflect the three-dimensional characteristics of the blades, the concept of three-dimensional blade tip clearance(3D-BTC) was proposed in our previous research. However, the 3D-BTC measurement signals is severely under-sampled due to the limitations of sensor installation and is prone to noise interference during the measurement process. Therefore, to reduce the impact of noise on the reconstruction effect, this paper proposes a 3D-BTC signals fractal dimension reconstruction method based on compressed sensing to reconstruct the 3D-BTC signals and obtain the multi-frequency response of the blade. Firstly, a measurement equivalent sampling model of 3D-BTC signals considering measurement noise is constructed, and a compressed sensing model of 3D-BTC dynamic response considering noise interference is established based on compressed sensing theory. Then, an improved generalized backtracking regularized adaptive matching pursuit (IGBRAMP) algorithm is proposed, and the reconstructible conditions of 3D-BTC signals are analyzed. Finally, the optimal installation quantity and position of 3D-BTC sensors are determined through finite element simulation signals, and the IGBRAMP algorithm is used for reconstruction to verify the reconstruction effect, laying the foundation for subsequent blade fault monitoring and diagnosis.