A Non-Uniformly Under-Sampled Blade Tip-Timing Signal Reconstruction Method for Blade Vibration Monitoring

Abstract

High-speed blades are often prone to fatigue due to severe blade vibrations. In particular, synchronous vibrations can cause irreversible damages to the blade. Blade tip-timing methods (BTT) have become a promising way to monitor blade vibrations. However, synchronous vibrations are unsuitably monitored by uniform BTT sampling. Therefore, non-equally mounted probes have been used, which will result in the non-uniformity of the sampling signal. Since under-sampling is an intrinsic drawback of BTT methods, how to analyze non-uniformly under-sampled BTT signals is a big challenge. In this paper, a novel reconstruction method for non-uniformly under-sampled BTT data is presented. The method is based on the periodically non-uniform sampling theorem. Firstly, a mathematical model of a non-uniform BTT sampling process is built. It can be treated as the sum of certain uniform sample streams. For each stream, an interpolating function is required to prevent aliasing in the reconstructed signal. Secondly, simultaneous equations of all interpolating functions in each sub-band are built and corresponding solutions are ultimately derived to remove unwanted replicas of the original signal caused by the sampling, which may overlay the original signal. In the end, numerical simulations and experiments are carried out to validate the feasibility of the proposed method. The results demonstrate the accuracy of the reconstructed signal depends on the sampling frequency, the blade vibration frequency, the blade vibration bandwidth, the probe static offset and the number of samples. In practice, both types of blade vibration signals can be particularly reconstructed by non-uniform BTT data acquired from only two probes.

Undersampled Blade Tip‐Timing Vibration Reconstruction under Rotating Speed Fluctuation: Uniform and Nonuniform Sensor Configurations

“…proposed an undersampled BTT signal reconstruction method of monitoring synchronous vibrations using nonuniformly mounted BTT sensors [14]. In this section, the authors will advance the previous work [14] to consider both uniform and nonuniform BTT sensor configurations under rotating speed fluctuation.…”

“…Interestingly, it can be seen from equation (17) that nonuniformly sampled vibration signals is equivalent to the sum of I uniformly sampled signal streams. Furthermore, the reconstruction process of d(t) is represented in Figure 3, which is formulated as follows [14]:…”

“…e goal of this paper is to advance the previous works [11,13,14] and explore a new BTT vibration reconstruction method under rotating speed fluctuation. Firstly, the effect of rotating speed fluctuation on BTT measurements is equivalent to a random nonuniform sampling process.…”

Non-Contact Measurement of Blade Vibration in an Axial Compressor

“…This approach saves a lot of work related to configuring the conventional tip-timing solver.Sensors 2020, 20, 68 2 of 18 models for this can be simplistic sine fitting [10] or more complex ones derived from the finite element method (FEM) during the calibration and validation process used with BTT.Alternative methods introduced in the previous decade such as auto-regressive [11], spectral estimation using nonuniform sampling [12], or full-signal analysis using many points per blade pass [13], were too complex or not efficient enough to leave the labs and be widely used by the community. These alternative methods provide little additional capability to the BTT technology but are often revisited by researchers [14][15][16] in the hope of finding methods for in-service blade health monitoring (BHM), where the blade sets are already well understood.A significant number of papers, introducing new BTT models and algorithms such as a new two-parameter plot method [17], convolutional neural networks [18], aliasing reduction [19,20], sparse representation, and compressed sensing [21], were published recently, but they can be applied in real life to a limited extent. Several newly introduced algorithms work well only with simulated or rig acquired data, usually with a single response of the first mode.…”

“…A significant number of papers, introducing new BTT models and algorithms such as a new two-parameter plot method [17], convolutional neural networks [18], aliasing reduction [19,20], sparse representation, and compressed sensing [21], were published recently, but they can be applied in real life to a limited extent. Several newly introduced algorithms work well only with simulated or rig acquired data, usually with a single response of the first mode.…”