Research On Reliable Interpolation Reconstruction Methods For Blade Tip Timing Signal

Monitoring aero-engine blades online is conducive to early detection of blade damage,and is of great significance for ensuring operational safety.Blade tip timing(BTT)measurement is a non-contact online measurement technology for blade vibration.It is low-cost and can monitor all blades simultaneously,opening up a broad prospect for detecting blade damage online.However,detecting small damages of blades online requires high reliability,(i.e.,accuracy and stability)of BTT measurement results.There are still many problems to be solved among the established analytical methods for BTT signals.Therefore,this thesis proposes the wideband interpolation method and multiband interpolation method.They can reconstruct BTT signals accurately and stably with the support of prior information,which is of great importance to the detection of small damages of blades.Aiming at the difficulty of obtaining prior information in complex systems,this thesis proposes a real signal-based multiple signal classification(RSMUSIC)algorithm to provide prior information of frequency for the wideband interpolation method and multiband interpolation method,so as to have the ability of blind interpolation to a certain extent.The main work of this thesis includes:(1)The wideband interpolation method is proposed.For the situation where the blade vibration frequency is concentrated,a wideband signal is used to represent blade tip displacement.The connection between the original signal and the sampled signal(blade tip displacement sequence)is established via the unsolved interpolation function.By letting the signal bandwidth be an integral multiple of the sampling rate,the spectrum aliasing of the sampled wideband signal shows a regular sub-band division.Focusing on the goal of eliminating aliasing,an anti-aliasing matrix equation is constructed according to the range of each sub-band,and the corresponding interpolation function can be obtained by solving the equation,thereby reconstructing the signal.The theoretical and simulation results show that the maximum allowable bandwidth of the wideband interpolation method is half the product of the rotational frequency and the number of sensors,therefore breaking the bandwidth limitation of the second-order bandpass interpolation method.With the support of prior information of frequency,it can accurately and stably reconstruct BTT signals,including nonlinear blade vibration,thereby obtaining rich and reliable time-domain information.Moreover,it has low requirements for the accuracy of prior information of frequency.(2)The multiband interpolation method is proposed.For the situation where the blade vibration frequency is dispersed,a signal with multiple narrow frequency bands is used to represent blade tip vibration displacement.The original signal and the sampled signal are also connected by an unknown interpolation function.The spectrum of the original signal is decomposed according to the range of each frequency band.By letting each frequency band to have equal bandwidth and not overlap with each other,the spectrum aliasing of the sampled multi-band signal is simplified.The anti-aliasing matrix equation is constructed according to the range of each band,respectively.The interpolation function is derived from this equation for signal reconstruction.The theoretical and simulation results show that the multiband interpolation method is not restricted by the distance of frequencies,and can process the frequency bands whose number is half the number of sensors simultaneously.It can accurately and stably reconstruct multi-frequency BTT signals under the condition that the prior information is known.Moreover,it does not require high accuracy of prior information of frequency.(3)The blind interpolation method is proposed.Since the multiple signal classification algorithm has good anti-noise performance and frequency identification effect,this thesis proposes the RSMUSIC algorithm based on the existing similar algorithms and the real-valued characteristic of BTT signals.The frequencies identified by the RSMUSIC algorithm not only provide a basis for the selection of the above two interpolation methods,but also provide necessary prior information for them to further reconstruct BTT signals,thereby having the ability of blind interpolation to a certain extent.The simulation results show that without prior information,the RSMUSIC algorithm can accurately identify the frequencies of multi-frequency blade vibration,and the blind interpolation method can identify frequency spectrums accurately.Both methods have good stability.This thesis carries out experimental researches on the proposed methods.The experimental results are consistent with the theoretical and simulation results,which verifies the accuracy and stability of the wideband interpolation method and multiband interpolation method.The results also demonstrate the effectiveness and feasibility of the RSMUSIC algorithm and the blind interpolation method.In conclusion,this thesis provides reliable analytical methods for BTT signals,and a methodological support for identifying small damages of blades.