Evaluation of the Continuous Wavelet Transform for Detection of Single-Point Rub in Aeroderivative Gas Turbines with Accelerometers.

A common fault in turbomachinery is rotor⁻casing rub. Shaft vibration, measured with proximity probes, is the most powerful indicator of rotor⁻stator rub. However, in machines such as aeroderivative turbines, with increasing industrial relevance in power generation, constructive reasons prevent the use of those sensors, being only acceleration signals at selected casing locations available. This implies several shortcomings in the characterization of the machinery condition, associated with a lower information content about the machine dynamics. In this work, we evaluated the performance of Continuous Wavelet Transform to isolate the accelerometer signal features that characterize rotor⁻casing rub in an aeroderivative turbine. The evaluation is carried out on a novel rotor model of a rotor⁻flexible casing system. Due to damped transients and other short-lived features that rub induces in the signals, the Continuous Wavelet Transform proves being more effective than both Fourier and Cepstrum Analysis. This creates the chance for enabling early fault diagnosis of rub before it may cause machine shutdown or damage.

Comparative analysis of some modal reconstruction methods of the shape of the cornea from corneal elevation data.

PURPOSE: A comparative study of the ability of some modal schemes to reproduce corneal shapes of varying complexity was performed, by using both standard radial polynomials and radial basis functions (RBFs). The hypothesis was that the correct approach in the case of highly irregular corneas should combine several bases. METHODS: Standard approaches of reconstruction by Zernike and other types of radial polynomials were compared with the discrete least-squares fit (LSF) by the RBF in three theoretical surfaces, synthetically generated by computer algorithms in the absence of measurement noise. For the reconstruction by polynomials, the maximal radial order 6 was chosen, which corresponds to the first 28 Zernike polynomials or the first 49 Bhatia-Wolf polynomials. The fit with the RBF was performed by using a regular grid of centers. RESULTS: The quality of fit was assessed by computing for each surface the mean square errors (MSEs) of the reconstruction by LSF, measured at the same nodes where the heights were collected. Another criterion of the fit quality used was the accuracy in recovery of the Zernike coefficients, especially in the case of incomplete data. CONCLUSIONS: The Zernike (and especially, the Bhatia-Wolf) polynomials constitute a reliable reconstruction method of a nonseverely aberrated surface with a small surface regularity index (SRI). However, they fail to capture small deformations of the anterior surface of a synthetic cornea. The most promising approach is a combined one that balances the robustness of the Zernike fit with the localization of the RBF.