Cross-radius independent dictionary sparse method for blade vibration reconstruction

Aircraft engine blades are critical components, and Blade Tip Timing (BTT) is widely used due to its non-contact measurement capability. However, conventional BTT can only measure a single point at the blade tip, making it difficult to capture higher-order modes such as torsional modes. In addition, due to the under-sampling characteristics of BTT signals, increasing the number of measurement points would require a substantial increase in the number of probes. To address these issues, this paper proposes a sensor installation scheme in which probes are mounted on the casing with an inclination angle, so that different probes measure points at different radial positions along the blade leading edge. To address the fact that signals at different measurement points share the same frequency but have different amplitudes and phases, a cross-radius independent dictionary and coupled constraint (CR-IDCC) method is proposed. Based on this method, the amplitudes and phases at multiple radial positions are estimated, enabling reconstruction of the blade vibration mode shapes. This method requires only one probe at each radial position, using a total of five probes, and leverages the cross-radial coupling to recover the blade mode shapes. To verify the effectiveness of the proposed method, numerical simulations constrained by finite element modal data are conducted, and the estimated mode shapes are compared with the finite element results. Finally, experimental validation is performed on a test rig, and the results are compared with strain gauge measurements. The error analysis further supports the feasibility of the proposed method.