基于SPOQ正则项的叶端定时信号稀疏重构

doi:10.3901/JME.260372

机械工程学报 ›› 2026, Vol. 62 ›› Issue (7): 208-220.doi: 10.3901/JME.260372

• 机械动力学 • 上一篇

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基于SPOQ正则项的叶端定时信号稀疏重构

雷卓^1,2, 乔百杰^1,2, 王亚南^1,2, 杜军³, 梁俊³, 刘元是³, 伏宇³, 陈雪峰^1,2

1. 西安交通大学机械工程学院西安 710049;
2. 西安交通大学航空动力系统与等离子体技术全国重点实验室西安 710049;
3. 中国航空发动机集团有限公司四川燃气涡轮研究院成都 610500

收稿日期:2024-12-15 修回日期:2025-09-29 发布日期:2026-05-25
作者简介:雷卓，男，2001年出生。主要研究方向为航空发动机叶片振动参数辨识。E-mail:leizhuo0709@stu.xjtu.edu.cn
乔百杰(通信作者)，男，1985年出生，博士，教授，博士研究生导师。主要研究方向为航空发动机叶片健康监测。E-mail:qiao1224@xjtu.edu.cn
基金资助:
国家自然科学基金资助项目(52075414)。

Sparse Reconstruction for Blade Tip Timing Signal Based on SPOQ Regularization Term

LEI Zhuo^1,2, QIAO Baijie^1,2, WANG Yanan^1,2, DU Jun³, LIANG Jun³, LIU Yuanshi³, FU Yu³, CHEN Xuefeng^1,2

1. School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049;
2. National Key Lab of Aerospace Power System and Plasma Technology, Xi'an Jiaotong University, Xi'an 710049;
3. Sichuan Gas Turbine Establishment, Aero Engine Corporation of China, Chengdu 610500

Received:2024-12-15 Revised:2025-09-29 Published:2026-05-25

摘要/Abstract

摘要： 利用叶端定时技术进行旋转叶片的非接触测量是公认的叶片振动监测的有效方法。然而，受到机匣可布置传感器数目的限制，叶端定时系统获取的振动信号存在严重的欠采样问题。目前的凸松弛和非凸松弛方法均未考虑到$\ell_0$范数重要的尺度不变性，导致幅值重构精度受到限制，无法获得最稀疏的解。为解决这一问题，首先引入具有尺度不变性的范数比函数来逼近$\ell_0$范数，针对其非凸非光滑性，构建平滑近似的代理函数(Smooth $\ell_p$ over $\ell_q$, SPOQ)以避免陷入局部最小值，再基于SPOQ函数构建叶端定时信号稀疏表示模型，并使用变步长前向后向算法对该模型进行求解。叶端定时仿真和试验的结果表明，与现有的$\ell_1$正则化和GMC正则化方法比较，该方法不仅能更精确地重构信号幅值，还能有效滤除干扰频率成分，促使频谱更稀疏。

关键词: 叶端定时, 欠采样, 稀疏重构, 尺度不变性

Abstract: Non-contact measurement of rotating blades using blade tip timing technology is recognized as an effective method for blade vibration monitoring. However, due to the limitation on the number of sensors that can be arranged in the casing, the vibration signal acquired by the blade tip timing system has a serious under-sampling problem. The current convex relaxation and non-convex relaxation methods do not take into account the important scale invariance of $\ell_0$ norm, which limits the reconstruction accuracy and makes it impossible to obtain the sparsest solution. To solve this problem, a scale-invariant norm ratio function is first introduced to approximate $\ell_0$ norm. For its non-convex and non-smooth properties, a smooth approximation proxy function(Smooth $\ell_p$ over $\ell_q$,SPOQ) is constructed to avoid falling into the local minimum. Then, a sparse representation model of blade tip timing signals is constructed based on the SPOQ function, and the model is solved using a variable metric forward–backward algorithm. The results of blade tip timing simulation and test show that, by comparing with $\ell_1$ regularization and GMC regularization, this method can not only accurately reconstruct the signal amplitude, but also effectively filter out the interference frequency components, making the solution sparser.

Key words: blade tip timing, undersampling, sparse reconstruction, scale-invariant

中图分类号:

TG156

雷卓, 乔百杰, 王亚南, 杜军, 梁俊, 刘元是, 伏宇, 陈雪峰. 基于SPOQ正则项的叶端定时信号稀疏重构[J]. 机械工程学报, 2026, 62(7): 208-220.

LEI Zhuo, QIAO Baijie, WANG Yanan, DU Jun, LIANG Jun, LIU Yuanshi, FU Yu, CHEN Xuefeng. Sparse Reconstruction for Blade Tip Timing Signal Based on SPOQ Regularization Term[J]. Journal of Mechanical Engineering, 2026, 62(7): 208-220.

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基于SPOQ正则项的叶端定时信号稀疏重构

Sparse Reconstruction for Blade Tip Timing Signal Based on SPOQ Regularization Term

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