稀疏测度和复杂性测度及其在设备健康监测中的研究进展

doi:10.3901/JME.2025.01.123

摘要/Abstract

摘要： 机械设备健康监测对于保障机械设备的健康运行起着至关重要的作用，其核心技术之一为故障特征提取。由于机械故障信号时域和频域具有稀疏性，因此基于稀疏测度和复杂性测度的故障特征提取被广泛应用于机械设备健康监测中。过去在机械设备健康监测领域主要是通过实验研究手段对稀疏测度和复杂性测度进行研究，缺乏足够的理论基础支撑。本研究主要总结和回顾了近年来稀疏测度和复杂性测度理论基础研究方面的新进展，并把其与设备健康监测研究结合进行阐述，利于机械设备监测领域的研究人员充分理解：①稀疏测度广义数学框架；②准算数均值比构建新型故障特征统计量；③新型稀疏测度与故障特征统计量构造；④稀疏测度性能比较；⑤改进稀疏测度；⑥稀疏测度与复杂性测度理论差异。通过稀疏测度与复杂性测度应用案例对比了稀疏测度和复杂性测度的应用效果。最后，研究展望给出了稀疏测度和复杂性测度在机械设备健康监测领域的未来发展方向。

关键词: 稀疏测度, 复杂性测度, 峭度, 熵, 基尼指数, 相关维度, 近似熵, 模糊熵, 样本熵, 设备健康监测

Abstract: Machine health monitoring plays a crucial role in ensuring machine health operation, and one of its core technologies is fault feature extraction. Due to the sparsity of mechanical fault signals in both the time and frequency domains, sparsity and complexity measures based fault feature extraction is widely used in machine health monitoring. In the past years, in the domain of machine health monitoring, research on sparsity and complexity measures was mainly conducted through experimental studies, lacking enough theoretical supports. This article mainly summarizes and reviews some new progresses in the theoretical foundation research of sparsity and complexity measures in recent years, and elaborates on their integration with machine health monitoring, which is beneficial for researchers in the field of machine health monitoring to fully understand: (1) The generalized mathematical framework of sparsity measures; (2) Constructing a new type of fault feature statistics based on the ratio of quasi-arithmetic means; (3) Construction of new sparsity measures and fault feature statistics; (4) Sparsity measure performance comparison; (5) Improved sparsity measures; (6) The difference between sparsity and complexity measures. The application effects of sparsity and complexity measures are compared through case studies. Finally, research outlook provides some future development directions of sparsity and complexity measures in the field of machine health monitoring.

Key words: sparsity measure, complexity measure, kurtosis, entropy, Gini index, correlation dimension, approximate entropy, fuzzy entropy, sample entropy, machine health monitoring

中图分类号:

TH17

王冬, 侯炳昌, 王玉婷, 夏唐斌, 彭志科, 奚立峰. 稀疏测度和复杂性测度及其在设备健康监测中的研究进展[J]. 机械工程学报, 2025, 61(1): 123-139.

WANG Dong, HOU Bingchang, WANG Yuting, XIA Tangbin, PENG Zhike, XI Lifeng. Advances in Sparsity Measures and Complexity Measures for Machine Health Monitoring[J]. Journal of Mechanical Engineering, 2025, 61(1): 123-139.

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