With a view to solving the defect that multiscale amplitude-aware permutation entropy (MAAPE) can only quantify the low-frequency features of time series and ignore the high-frequency features which are equally important, a novel nonlinear time series feature extraction method, hierarchical amplitude-aware permutation entropy (HAAPE), is proposed. By constructing high and low-frequency operators, this method can extract the features of different frequency bands of time series simultaneously, so as to avoid the issue of information loss. In view of its advantages, HAAPE is introduced into the field of fault diagnosis to extract fault features from vibration signals of rotating machinery. Combined with the pairwise feature proximity (PWFP) feature selection method and gray wolf algorithm optimization support vector machine (GWO-SVM), a new intelligent fault diagnosis method for rotating machinery is proposed. In our method, firstly, HAPPE is adopted to extract the original high and low-frequency fault features of rotating machinery. After that, PWFP is used to sort the original features, and the important features are filtered to obtain low-dimensional sensitive feature vectors. Finally, the sensitive feature vectors are input into GWO-SVM for training and testing, so as to realize the fault identification of rotating machinery. The performance of the proposed method is verified using two data sets of bearing and gearbox. The results show that the proposed method enjoys obvious advantages over the existing methods, and the identification accuracy reaches 100%.

中文翻译：

---

基于分层幅度感知排列熵和成对特征接近的旋转机械故障诊断方法

为了解决多尺度幅度感知置换熵（MAAPE）只能量化时间序列低频特征而忽略同等重要的高频特征的缺陷，一种新颖的非线性时间序列特征提取方法，分层提出了幅度感知排列熵（HAAPE）。该方法通过构造高频和低频算子，可以同时提取时间序列不同频段的特征，避免信息丢失的问题。鉴于其优点，将HAAPE引入故障诊断领域，从旋转机械的振动信号中提取故障特征。结合成对特征邻近（PWFP）特征选择方法和灰狼算法优化支持向量机（GWO-SVM），提出了一种新的旋转机械智能故障诊断方法。在我们的方法中，首先采用HAPPE提取旋转机械的原始高频和低频故障特征。之后利用PWFP对原始特征进行排序，对重要特征进行过滤，得到低维敏感特征向量。最后将敏感特征向量输入GWO-SVM进行训练和测试，实现旋转机械故障识别。使用轴承和齿轮箱的两个数据集验证了所提出方法的性能。结果表明，该方法与现有方法相比具有明显优势，识别准确率达到100%。采用HAPPE提取旋转机械原有的高频和低频故障特征。之后利用PWFP对原始特征进行排序，对重要特征进行过滤，得到低维敏感特征向量。最后将敏感特征向量输入GWO-SVM进行训练和测试，实现旋转机械故障识别。使用轴承和齿轮箱的两个数据集验证了所提出方法的性能。结果表明，该方法与现有方法相比具有明显优势，识别准确率达到100%。采用HAPPE提取旋转机械原有的高频和低频故障特征。之后利用PWFP对原始特征进行排序，对重要特征进行过滤，得到低维敏感特征向量。最后将敏感特征向量输入GWO-SVM进行训练和测试，实现旋转机械故障识别。使用轴承和齿轮箱的两个数据集验证了所提出方法的性能。结果表明，该方法与现有方法相比具有明显优势，识别准确率达到100%。最后将敏感特征向量输入GWO-SVM进行训练和测试，实现旋转机械故障识别。使用轴承和齿轮箱的两个数据集验证了所提出方法的性能。结果表明，该方法与现有方法相比具有明显优势，识别准确率达到100%。最后将敏感特征向量输入GWO-SVM进行训练和测试，实现旋转机械故障识别。使用轴承和齿轮箱的两个数据集验证了所提出方法的性能。结果表明，该方法与现有方法相比具有明显优势，识别准确率达到100%。