基于压缩感知的叶端定时信号参数辨识方法

Parameter identification of blade tip timing signal using compressed sensing

叶端定时技术作为一种非接触式测量手段,在实际应用中的主要问题之一是测量信号欠采样。压缩感知方法是解决信号欠采样问题的有效手段,但由于求解过程中引入了正则化项,在提高稀疏度时,降低了幅值重构精度,而转子叶片振动幅值参数的准确辨识对于叶片动应力重构具有重要意义。将叶片振动方程设计矩阵与压缩感知字典相结合,在不依赖先验信息的条件下对叶片振动参数进行辨识。首先,根据振动方程设计矩阵形式及关注的最大振动频率,构造压缩感知字典;其次,通过叶端定时信号稀疏表示中的非零元素所在位置,从压缩感知字典中提取对应原子构成设计矩阵进而求得振动参数;接着,叶端定时(BTT)模拟仿真结果表明,所提方法可有效辨识叶片单模态、多模态振动参数;最后,开展旋转叶片振动测试试验,同时利用应变片和叶端定时系统采集振动信号,结果表明,与应变片测量结果相比,提出的方法振动频率辨识相对误差仅为0.14%;对比4个叶片的位移-应变传递比,其中偏离均值的最大百分比仅为2.15%。

Despite the wide application of the blade tip timing as a non-contact measurement technique,its acquired displacement signal is undersampled in many situations.Compressed sensing is an effective means to reconstruct the undersampled signal.However,the reconstruction process introduces the regularization penalty to achieve sparsity,reducing the amplitude accuracy of the reconstructed signal at the same time,and affecting the accurate identification of blade vibration amplitude,which is highly significant in reconstructing the dynamic stress of the blade.This paper combines the design matrix of the blade vibration equation and the compressed sensing dictionary to identify parameters of the blade vibration equation without prior information.First,a compressed sensing dictionary is constructed according to the form of design matrix elements and the maximum vibration frequency of interests.Second,atoms are extracted from the dictionary according to the indices of non-zero elements in the sparse representation of the blade tip timing signal,and parameters of the vibration equation are calculated.Third,Blade Tip Timing(BTT)simulation results demonstrate that the proposed method can accurately identify parameters of the vibration equation with both single-mode and multi-mode vibrations.Finally,experimental results of rotor blades show that the relative error of the identified natural frequency between using strain gage and using blade tip timing with compressed sensing is only 0.14%;the transmissibility of blade tip displacement to certain points strain of the four blades is compared and the maximum percentage of deviation from the mean is only 2.15%.