Virtual sensing of blade strain distribution using tip-timing method

• A novel block-enhanced sparse regularization model is established. • An analytical relationship mapping blade displacement to strain is derived innovatively. • Virtual sensing of blade strain distribution is achieved in the time history. • The periodically changing characteristic of multi-mode strain is revealed innovatively. Vibration measurement and analysis are significant for fault diagnosis of turbomachinery rotor blades. It is hard to sense the blade full-field dynamic strain using traditional strain gauges (SGs). Since the non-contact Blade Tip Timing (BTT) technique enables rotating vibration measurement, this study focuses on the virtual sensing of the rotor blade strain distribution via BTT. A new method, named block-enhanced ℓ 1/2 -norm strain virtual sensing (BLOSS) method was proposed to recover the blade-tip displacement responses and visualize the strain distribution of the rotor blades under multi-mode vibration. This paper includes three novelties. First, a block-enhanced sparse regularization model by using ℓ 1/2 -norm was established to recover the tip response spectrums and identify the vibration parameters. Second, a mapping relationship linking the tip displacement and the strain of the whole blade was analytically expressed based on the system equivalent reduction-expansion process. Third, the periodically changing characteristic of the dynamic strain was revealed under the blade multi-mode vibration superposing the first bending and torsion modes. Based on the BLOSS method, the time-traced displacement response of the blade tip was recovered. The virtual sensing of the blade dynamic strain distribution was achieved at the full field scale based on the mode shapes and the tip displacement of the leading and trailing edges. The strain distribution was perceived and displayed by the contour plots through the updated finite element model of the rotor blade. The proposed method was validated through both a numerical case and a spin test. The strain responses via virtual sensing were compared with those measured by SGs. The comparison showed that the relative errors of frequency identification are within 0.6 % and the mean relative error of the strain amplitude is 6.9 %. The BLOSS method enables the identification of vibration parameters and virtual sensing of the rotor blade strain distribution in a non-contact manner, which is promising to achieve blade online health monitoring.