A real-time hybrid method based on blade tip timing for diagnostics and prognostics of cracks in turbomachine rotor blades

Abstract

This dissertation proposes hybrid models for (i) diagnosis and (ii) remaining useful life estimation of a single fatigue crack in a low-pressure turbine blade. The proposed hybrid methods consist of physics-based methods and data-driven methods. In this dissertation, blade tip timing is used to measure the relative tip displacement of a rotor blade. The natural frequency of the blade is determined by detecting the critical speeds of the blade using a newly derived least squares spectral analysis method. The method shares its origin from the Lomb-Scargle periodogram and can detect resonance frequencies in the blade’s displacement while the rotor is in operation. A Campbell diagram is then used to convert the critical speed into a natural frequency. Two kinds of shaft transients are considered, a run-up run-down crossing the same critical speed, is used to test the new method. This dissertation shows that the relative displacement of the blade tip is comparable to those simulated from an analytical single degree of freedom model. It is also shown that the newly proposed resonance detection method estimates the natural frequency of the blade to a high degree of accuracy when compared to the measurements from a modal impact hammer test. The natural frequency obtained from the real time measurement is then used in a pre-constructed hybrid diagnostics model. The diagnostics model provides a probability density function estimation of the surface crack length given the measured natural frequency. A Gaussian Process Regression model is trained on data collected during experiments and finite element simulations of a fatigue crack in the blade. The final part of this dissertation is a sequential inference model for improving the estimation of the crack length and the prediction of the crack growth. The suggested model uses an unscented Kalman filter that improves estimations of the crack length and the rate of crack growth from Paris’ Law coefficients. The model is updated each time a diagnosis is performed on the blade. The RUL of the blade is then determined from an integration of Paris’s Law given the uncertainty estimates of the current damage in the blade. The result of the algorithm is an estimation of the remaining number of cycles to failure. The algorithm is shown to improve the overall estimation of the RUL; however, it is suggested that future work looks at the convergence rate of the method.