We address the problem of the reconstruction of time-frequency characteristics of sparse multi-band signals by using the discrete multi-coset sampling (DMCS) model. In this article, the signal is characterized by complicated time-variable components. According to the feature of the short-time Fourier transform (STFT) analysis method, we obtain the rewritten matrix form of the discrete STFT. Then, an analysis method of the multi-coset sliding window (MCSW) is proposed, and the discrete multi-coset sampling sequence is locally windowed. The sparse signal reconstruction algorithm is used to obtain the optimal time-frequency reconstruction value of the original signal. Numerical simulations show the feasibility of this method. We simulate the effects of measurement noise, sampling rate, and time-frequency analysis parameters on the reconstruction accuracy. Our method can carry out time-frequency reconstruction for undersampled signals obtained from multi-coset sampling to ensure the time-varying feature of the original signals, which can well highlight the characteristics of signals. The method is of great significance to the research and development of the sub-Nyquist sampling technique.

Blade tip timing (BTT) technology is a research hotspot and can directly estimate the blade vibration, which is of great significance to blade fault diagnosis. However, the traditional once per revolution (OPR) method has greatly limited the application of this technology due to the installation problem of the sensor and low measurement accuracy. In order to overcome the disadvantages of the OPR method, this article proposes a shifting straight-line fitting (SSLF) method to accurately calculate the blade vibration. The principle of the SSLF method is to obtain the expected arrival time of the optimal fitting point by shifting the straight-line fitting (SLF), and the vibration of the blade can be obtained according to the time. In this article, first, a brief introduction of BTT technology and the OPR method is given. Then, theoretical analysis and experimental investigations are used to verify the effectiveness of the SSLF method. In the end, the SSLF method is applied to the large centrifugal compressor, which can be concluded that the SSLF method can be used for blade monitoring of the compressor based on the investigation of experiments.

The impeller is one of the core components of a large-scale centrifugal compressor, and its performance directly affects the stability and safety of the centrifugal compressor. The non-contact measurement technology, blade tip timing (BTT), has attracted generous attention in the blade vibration monitoring of rotating impellers. Based on the existing BTT technique, the blade vibration displacement and the blade vibration effective value was used to evaluate the running status of the centrifugal compressor, and a novel rotation speed-based surge identification (RSSID) method was proposed to analyze the surge frequency. Moreover, the cracked blade was detected by monitoring the natural frequency of the blade. A healthy impeller (ky96) and a fault impeller (ky50) with a cracked blade were monitored at the large-scale centrifugal compressor test rig. The blade vibrational alarm threshold for the surge condition is established in agreement with the experimental results, and the surge frequency obtained by the RSSID method matches well with the conclusions of the pressure pulsation signal. The results of the experiments with varying speed show that the natural frequency of the cracked blade deviates significantly from those of the other blades, and the conclusion can be more persuasive by considering the effect of the cracked blade on the standard deviation of the natural frequencies of the other blades. This study is of great importance for running status monitoring and rotating blade fault diagnosis of large-scale centrifugal compressors.