Blade Tip Timing (BTT), an emerging technology poised to replace strain gauges, enables contactless measurement of rotor blade vibration. However, the blade vibration signals measured by BTT systems often suffer from significant undersampling. Sparse reconstruction methods are instrumental in addressing the challenge of undersampled signal reconstruction. However, traditional approaches grounded in regularization tend to underestimate the amplitude of the true solution. This underestimation is particularly pronounced in the resonance state of the rotor blade, hindering effective prediction of the blade’s operational state. To overcome this limitation, this paper introduces a novel non-convex regularized BTT model, employing a non-convex penalty term with convex-preserving properties to achieve nearly unbiased reconstruction accuracy. Additionally, we propose a new threshold iteration algorithm designed for the swift solution of this model. The accuracy and robustness of the proposed method in identifying the multimodal vibration parameters of rotor blades are validated through simulations and experiments. Comparatively, the proposed method closely aligns with the Orthogonal Matching Pursuit (OMP) method in recognizing blade multimodal vibration amplitude, showcasing significant improvement over the regularization method. Furthermore, it demonstrates lower sensitivity to changes in BTT probe layout when compared to the OMP and regularization methods.

中文翻译：

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通过叶尖正时的凸优化进行非凸稀疏正则化


叶尖正时 (BTT) 是一项有望取代应变计的新兴技术，可实现转子叶片振动的非接触式测量。然而，BTT 系统测量的叶片振动信号经常遭受严重的欠采样。稀疏重建方法有助于解决欠采样信号重建的挑战。然而，基于正则化的传统方法往往会低估真实解的幅度。这种低估在转子叶片的共振状态下尤其明显，阻碍了对叶片运行状态的有效预测。为了克服这一限制，本文引入了一种新颖的非凸正则化 BTT 模型，采用具有保凸特性的非凸惩罚项来实现几乎无偏的重建精度。此外，我们提出了一种新的阈值迭代算法，旨在快速解决该模型。通过仿真和实验验证了该方法识别转子叶片多模态振动参数的准确性和鲁棒性。相比之下，所提出的方法在识别叶片多模态振动幅度方面与正交匹配追踪（OMP）方法紧密结合，显示出比正则化方法的显着改进。此外，与 OMP 和正则化方法相比，它对 BTT 探针布局变化的敏感性较低。