Experimental Study on the Optimization of the Sensor Arrangement for Blade Tip Timing Measurement

As a means of non-contact measurement of blade vibrations, blade tip timing (BTT) has good application prospects for blade design verification and health monitoring. In BTT, the sensor arrangement directly determines the effectiveness of the extracted signal and ultimately affects the quality of the identified vibration parameters. In previous research on optimizing sensor arrangements, the position of each sensor is often selected from among multiple uniformly distributed virtual positions, which limits the optimization space. Moreover, to verify the performance of a sensor arrangement, a high-precision experimental calibration platform is required. However, it is often difficult for the precision to meet the requirements for a benchmark due to an inability to measure the actual blade vibrations. This paper optimized the sensor arrangement by simultaneously considering the mutual coherence and the approximate distance between sensing matrices for an equiangular tight frame in arbitrary-angle compressive sensing method. To avoid the uncertainty in blade displacement conversion in traditional calibration, such as with strain gauges, a laser displacement sensor connected to a slip ring was used to measure directly the displacement of the blade due to vibration. Besides, a macro-fiber composite was used to apply an excitation with a precise frequency to the blade at different speeds to make the blade vibrate synchronously or asynchronously. Then the performance of sensor arrangements optimized by the proposed method as well as other methods, such as mutual coherence, were verified on the self-developed BTT experimental calibration platform. The experimental results show that the signals identified with the optimized sensor arrangements are in good agreement with measurements made by the laser displacement sensor. The amplitude accuracy was more than 76.5% and 91.3% for synchronous and asynchronous vibrations, respectively. Moreover, the identification results were stable after data from 1 or 2 random sensors were removed. This shows the method has good reconstruction accuracy and sensor redundancy.