This paper originated from an investigation of sparsity indexes for fault diagnosis of rotating machinery. Although various sparsity indexes have been widely applied in machinery fault feature extraction, there is little information on the guideline available for the selection of the best sparsity index for the specified scenarios with different interferences. To solve the problem, this article firstly analyzes the performance of the representative sparsity indexes, containing Gini index, l₂/l₁ norm, Hoyer measure and kurtosis. Aiming at the feature of the machinery fault signal, three performance attributes, including data-length independency, random-impulse resistance and fault-impulse discernibility, are originally proposed to quantitatively evaluate the sparsity index. Based on the comparison results, a guideline for the selection of the optimal sparsity measure is summarized. After that, this guideline is used for the improvement of kurtogram and protrugram, and the results are evaluated. Finally, the comparison result, using both simulated and experimental bearing fault signals, confirms that an optimal scheme can be designed for the sparsity-based improvement under the proposed guideline.

本文源于稀疏性指标的研究，用于旋转机械的故障诊断。尽管各种稀疏性指标已广泛应用于机械故障特征提取中，但对于针对具有不同干扰的特定场景选择最佳稀疏性指标的指南，信息很少。为了解决这个问题，本文首先分析了代表稀疏性指标的性能，其中包含基尼系数l ₂ / l ₁规范，Hoyer度量和峰度。针对机械故障信号的特点，最初提出了数据长度独立性，随机脉冲抗性和故障脉冲可分辨性三个性能属性，以定量评估稀疏性指标。根据比较结果，总结了最佳稀疏度量的选择指南。之后，将本指南用于改进峰度图和程序图，并对结果进行评估。最后，使用模拟和实验轴承故障信号进行的比较结果证实，可以在建议的指导原则下为基于稀疏性的改进设计最佳方案。