From Theory to Practice: Chinese Remainder Theorem-Based Blade Tip Timing Measurement

Blade tip timing (BTT) is a promising noncontact vibration measurement technique for rotating blades owing to its high measurement efficiency and long service life. However, due to the mismatch between the high vibration frequency of blades and the low achievable sampling frequency, the vibration data measured by BTT is inherently undersampled and thus results in difficulties for subsequent frequency identification. Chinese remainder theorem (CRT) is an efficient theory that can estimate the target frequency from undersampled waveforms. Nevertheless, its application in BTT encounters two issues: excessive probes in multirate sampling and remainder ambiguity in real-valued signals. This article proposes a practical method to overcome the two issues and identify the frequency from the undersampled BTT data, which involves two key steps: active aliasing technique and selective translation operation. The former is a practical alternative to multirate sampling since it requires fewer probes. The latter is a symbolic-graphic combination operation that eliminates the remainder ambiguity by utilizing the prior of opposite frequencies in real-valued signals. Both simulations and experiments validate the effectiveness of the proposed method. In addition to the low number requirement for probes, the proposed method shows high computational efficiency. That is, it is user-friendly for probe installation and online computing in BTT. In short, the proposed method opens new avenues for frequency estimation of undersampled BTT data.