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【目的】针对复杂旋转机械在变工况运行下振动信号呈现出的强非线性、非平稳多分量以及瞬时频率非比例演变等物理特征，传统时频分析方法难以有效解析紧密相连且演化规律各异的非比例瞬时频率轨迹，严重制约了设备运行状态的精准评估与故障的早期检测.为突破复杂非平稳信号时频解析的分辨率瓶颈，该文提出一种新型时频分析方法——局部熵选择尺度提取调频小波变换(LESSECT),旨在全面提升多分量非比例信号的时频表示分辨率、结构可读性与能量聚集度，为精密机械装备的可靠故障诊断提供坚实的理论与算法支撑.【方法】该文提出的LESSECT方法融合了多维调频率缩放机制、基于Rényi熵的调频率选择策略及同步能量再提取技术.首先，构建多组覆盖不同调频演化趋势的子时频表示空间，以全面捕捉信号的多样化局部特征；其次，在各个局部时间中心，创新性地以Rényi熵最小化为优化准则，自适应地筛选最优调频率组合，从而实现多个非比例且相距极近的瞬时频率成分的同步剥离与高保真保留；最后，结合同步能量局部重提取算子，对目标时频区域内的能量进行二次深度聚焦，彻底消除交叉项干扰与能量模糊扩散现象，重构出高度集中的精细化时频结构.为系统评估该方法的性能，该文开展了包含多谐波仿真合成信号、蝙蝠回声定位实测信号、滚动轴承内圈故障模拟信号以及风电行星齿轮箱振动数据在内的多场景综合实验.将LESSECT与短时傅里叶变换(STFT)、连续小波变换(CWT)、同步提取变换(SET)、广义线性调频小波变换(GLCT)、尺度基调频小波变换(SBCT)和熵匹配调频小波变换(EMCT)6种前沿基线方法进行深度对比.【结果】数值与实验结果表明：在处理具有复杂非比例瞬时频率轨迹的非平稳信号时，LESSECT所生成的时频表示获得了最低的Rényi熵值，即极优的能量聚集性以及最高的结构相似性指数(SSIM).即使在强背景噪声与严苛的非比例多分量干扰下，该方法依然能够清晰、连续地分离并还原信号的关键物理本征频率及其各阶高频谐波特征.【结论】所提出的LESSECT方法具备卓越的时频结构自适应解析能力，从根本上克服了现有时频分析工具在处理复杂非比例瞬时频率信号时的能量泄漏与分量混叠难题.该技术不仅显著增强了时频特征的可视化表达与物理可解释性，更为复杂旋转机械在变工况下的微弱故障精准检测、状态劣化评估及高可靠性智能诊断提供了极具价值的新型分析框架，展现出广阔的工程应用前景.
Abstract：【Objective】 To address the challenges in analyzing vibration signals from complex rotating machinery under time-varying conditions, which inherently exhibit strong non-linearity, multi-component interactions, and non-proportional instantaneous frequency(IF) evolutions. Conventional time-frequency analysis(TFA) methods struggle to effectively resolve closely spaced and asynchronously evolving IF trajectories, thereby limiting accurate state evaluation and early fault detection. To overcome these resolution bottlenecks, this paper proposes a novel TFA method named Local Entropy Selection Scale-Extracting Chirplet Transform(LESSECT). This method aims to comprehensively enhance the resolution, structural readability, and energy concentration of time-frequency representations for multi-component non-proportional signals, providing a robust theoretical and algorithmic foundation for precise machinery fault diagnosis. 【Method】The proposed LESSECT integrates a multi-dimensional chirp rate scaling mechanism, a Rényi entropy-based optimal chirp rate selection strategy, and a synchronous local energy re-extraction technique. Firstly, multiple sub-time-frequency representations(sub-TFRs) with varied chirp rates are constructed to thoroughly capture diverse local frequency evolution patterns. Secondly, at each local time center, Rényi entropy minimization is innovatively applied as an optimization criterion to adaptively select the optimal combination of chirp rates. This enables the synchronous separation and high-fidelity retention of multiple non-proportional and closely spaced IF components. Finally, a synchronous local re-extraction operator is incorporated to achieve secondary deep focusing of the energy within target time-frequency regions, effectively eliminating cross-term interference and energy blurring to reconstruct a highly concentrated and refined time-frequency structure. To systematically evaluate the performance of the proposed method, comprehensive experiments were conducted utilizing synthetic multi-harmonic signals and three experimental datasets: bat echolocation calls, rolling bearing inner race fault data, and wind turbine planetary gearbox vibration signals. LESSECT was extensively compared against six mainstream TFA methods: short-time Fourier transform(STFT), continuous wavelet transform(CWT), synchroextracting transform(SET), general linear chirplet transform(GLCT), scale-based chirplet transform(SBCT), and entropy-matched chirplet transform(EMCT). 【Result】Numerical and experimental results consistently demonstrate that when processing non-stationary signals with complex non-proportional IF trajectories, the time-frequency representations generated by LESSECT yield the lowest Rényi entropy values(indicating superior energy concentration) and the highest structural similarity index(SSIM). Even under severe background noise and complex non-proportional multi-component interference, the method clearly and continuously separates and restores the critical physical intrinsic frequencies and their high-order harmonic features. 【Conclusion】The proposed LESSECT method exhibits exceptional adaptive structural resolution capabilities, fundamentally overcoming the energy leakage and component aliasing dilemmas faced by existing TFA tools when handling complex non-proportional IF signals. This technique not only significantly enhances the visual expression and physical interpretability of time-frequency features but also provides a highly valuable and novel analytical framework for the precise detection of weak faults, degradation assessment, and highly reliable intelligent diagnosis of complex rotating machinery under variable conditions, demonstrating profound engineering application potential.
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基本信息:
DOI：10.13715/j.issn.2096-644X.20250704.0001
中图分类号:TH17
引用信息:
[1]牛渝礼,谭建鑫,王天杨,等.基于局部熵选择尺度提取调频小波变换的非平稳机械振动信号时频分析方法[J].湘潭大学学报(自然科学版),2026,48(02):21-46.DOI:10.13715/j.issn.2096-644X.20250704.0001.
基金信息:
国家自然科学基金(52161135101)
2025-07-04
2025
2026-04-15
2026-05-18
2026
1
2025-09-11
2025-09-11
2025-09-11