Sparse reconstruction for blade tip timing signal using generalized minimax-concave penalty
Sparse reconstruction for blade tip timing signal using generalized minimax-concave penalty
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DOI：
10.1016/j.ymssp.2021.107961
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发表时间：
2021
影响因子：
8.4
通讯作者：
Jinghui Xu;Baijie Qiao;Junjian Liu;Chunyan Ao;Guangrong Teng;Xuefeng Chen
中科院分区：
文献类型：
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作者：
Jinghui Xu;Baijie Qiao;Junjian Liu;Chunyan Ao;Guangrong Teng;Xuefeng Chen
基于非接触式叶尖定时（BTT）技术的转子叶片健康监测已经被证明是经典接触式应变测量方法的替代方法。然而，由BTT系统采样的信号通常由于有限的BTT传感器而欠采样。本文提出了一种基于稀疏正则化的叶片振动参数识别方法。然而，标准的稀疏正则化的基础上，1-范数惩罚通常会产生一个低估的解决方案。广义极小极大凹罚作为一种非凸罚，与广义极小极大凹罚相比，具有幅度改善的特性。本文提出了一种基于GMC罚函数的非凸优化模型，用于重构欠采样的BTT信号，以获得精确的叶尖位移和叶片固有频率。提出了基于GMC罚函数的优化模型，即使GMC罚函数是一个非凸正则化子，也能找到BTT信号稀疏表示的全局最优解。此外，通过叶尖定时仿真器提供了正则化参数的选择策略。建立了噪声水平与正则化参数之间的关系，为实验中正则化参数的选择提供了策略。最后，进行了叶片旋转试验，用BTT和应变片系统测量叶片振动。将重建的BTT信号的振幅和频率与应变计的测量值进行比较，通过使用从有限元模型获得的转换系数，将应变计的测量值从叶片根部的应变转换为叶片尖端的位移。仿真和实验结果均表明，与传统的101-范数罚函数相比，GMC罚函数能更准确地重构叶尖位移和叶片固有频率。
Rotor blade health monitoring based on the non-contact blade tip timing (BTT) technique has already been proved to be an alternative method to the classical contact strain measurement method. However, the signal sampled by the BTT system is usually undersampled due to the limited BTT sensors. Sparse regularization in the framework of ℓ 1-norm has been introduced to identify the blade vibration parameter from the undersampled BTT data. However, the standard sparse regularization based on ℓ 1-norm penalty generally generates an underestimated solution. Compared with ℓ 1-norm penalty, generalized minimax-concave (GMC) penalty as a non-convex penalty has the promising property of amplitude improvement. In this paper, a non-convex optimization model based on GMC penalty is developed for reconstructing the undersampled BTT signal to obtain the accurate blade-tip displacement and blade natural frequency. The optimization model based on GMC penalty is presented to find the global optimal solution for the sparse representation of the BTT signal even if GMC penalty turns out to be a non-convex regularizer. Additionally, the strategy of regularization parameter selection is provided through the blade tip timing simulator. The relationship between the noise level and the regularization parameter is established to provide the strategy of regularization parameter selection in experiment. Finally, the blade spin testing is carried out for measuring the blade vibration by BTT and strain gauge systems. Amplitudes and frequencies of reconstructed BTT signals are compared with the measurements of the strain gauge, which are transferred from the strain at the blade root to the displacement at the blade tip by using the conversion coefficient obtained from the finite element model. Both simulation and experiment demonstrate that compared with the ℓ 1-norm penalty, GMC penalty can reconstruct the blade-tip displacement and blade natural frequency with high accuracy.