提出快速短时根MUSIC算法，实现高速主轴微小故障实时检测。
A novel fast short-time root music method for vibration monitoring of high-speed spindles
- 基于傅里叶加速的龙格-巴迪斯分解，降低计算复杂度至SNlog₂N级别。
- 可检测150μm微缺陷，频率分辨率达1.2 Hz，-5 dB信噪比下识别率93%。
- 单帧处理仅需2.4毫秒，适合嵌入式设备部署，适合精密加工领域。
超高速主轴轴承因宽带噪声、非平稳性和有限时频分辨率，难以用传统方法监测。本文提出一种快速短时根MUSIC（fSTrM）算法，利用FFT加速的Lanczos双对角化方法，将计算复杂度从O(N³)降至SNlog₂N + S²(N+S) + M²(N+M)，同时保持参数超分辨率能力。该方法对16毫秒信号帧构造汉克尔矩阵，并在单位圆上进行多项式求根以提取故障频率。在意大利都灵理工大学轴承数据集上的实验表明，该算法具备突破性微缺陷检测能力：可可靠识别此前无法检测的150μm缺陷，提供超过72小时的预警时间。相比STFT和小波方法，fSTrM实现1.2 Hz频率分辨率（对比12.5 Hz），在-5 dB信噪比下达到93%检测率，并通过谐波含量分析量化缺陷严重程度。关键在于，该算法在嵌入式ARM Cortex-M7硬件上每帧处理仅需2.4毫秒，支持实时部署。此项进展使轴承监测从故障预防转向持续退化评估，为航空航天与精密加工领域的预测性维护树立新范式。
原文摘要 · Abstract (English)
Ultra-high-speed spindle bearings challenge traditional vibration monitoring due to broadband noise, non-stationarity, and limited time-frequency resolution. We present a fast Short-Time Root-MUSIC (fSTrM) algorithm that exploits FFT-accelerated Lanczos bidiagonalization to reduce computational complexity from $\mathcal{O}(N^3)$ to $SN\log_2N+S^2(N+S)+M^2(N+M)$ while preserving parametric super-resolution. The method constructs Hankel matrices from 16 ms signal frames and extracts fault frequencies through polynomial rooting on the unit circle. Experimental validation on the Politecnico di Torino bearing dataset demonstrates breakthrough micro-defect detection capabilities. The algorithm reliably identifies 150 $μ$m defects -- previously undetectable by conventional methods -- providing 72+ hours additional warning time. Compared to STFT and wavelet methods, fSTrM achieves 1.2 Hz frequency resolution (vs. 12.5 Hz), 93\% detection rate at $-$5 dB SNR, and quantifies defect severity through harmonic content analysis. Critically, the algorithm processes each frame in 2.4 ms on embedded ARM Cortex-M7 hardware, enabling real-time deployment. This advancement transforms bearing monitoring from failure prevention to continuous degradation assessment, establishing a new paradigm for predictive maintenance in aerospace and precision machining.
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