Nonlinear time transformation-based vibration signal reconstruction for blade tip-timing under rotation speed fluctuations

Blade tip-timing (BTT) is a promising method to monitor blade vibrations of aero engines. Since blade tip-timing signals are typically under-sampled, how to reconstruct vibration characteristics from under-sampled signals is a big challenge. Existing signal reconstruction methods are mainly based on the assumption of constant rotation speeds and equally mounted sensors. However, fluctuation of blade rotation speed is inevitable in engineering applications. In this case, the BTT sampling process should be non-uniform, which causes conventional reconstruction methods to be unavailable. In order to solve this problem, this paper presents an improved under-sampled reconstruction method under rotation speed fluctuations by using three equally-mounted BTT sensors. Firstly, speed fluctuations are defined as random variations of sampling times. Here, both Gaussian and uniform distributions are considered. Then, a nonlinear time transformation equation is proposed to project BTT sampling times to another timeline so that non-uniform BTT sampling times become uniform ones. The key is to fit the discrete-time time variations to a continuous-time function and linear interpolation is used here. Based on the above uniform sampled signals, an interpolation function using the six-order B-spline function is built to reconstruct vibration signals. Finally, numerical simulations are done to verify the proposed method. The results demonstrate that this method can eliminate the effects of rotation speed fluctuations and improve the accuracy of BTT signal reconstruction under rotation speed fluctuations.