The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> C. IMPROVED RÉNYI ENTROPY METHODS <s> We introduce kernel entropy component analysis (kernel ECA) as a new method for data transformation and dimensionality reduction. Kernel ECA reveals structure relating to the Renyi entropy of the input space data set, estimated via a kernel matrix using Parzen windowing. This is achieved by projections onto a subset of entropy preserving kernel principal component analysis (kernel PCA) axes. This subset does not need, in general, to correspond to the top eigenvalues of the kernel matrix, in contrast to the dimensionality reduction using kernel PCA. We show that kernel ECA may produce strikingly different transformed data sets compared to kernel PCA, with a distinct angle-based structure. A new spectral clustering algorithm utilizing this structure is developed with positive results. Furthermore, kernel ECA is shown to be an useful alternative for pattern denoising. <s> BIB001 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> C. IMPROVED RÉNYI ENTROPY METHODS <s> Rolling bearings as vital components are present ubiquitously in manufacturing machines and systems, timely fault diagnosis is of great importance in avoiding serious catastrophe, and a variety of methods have been developed to detect faults of rolling bearings. In this study, we introduce labels to adjust the distance of classes and propose a method called supervised kernel entropy component analysis for fault diagnosis of rolling bearings. The method is developed based on kernel entropy component analysis which attempts to preserve the Renyi entropy of the data set after dimension reduction and presents a good performance for nonlinear feature extraction. Simulation and experiments are carried out to verify the method. The intrinsic geometric features derived from original vibration signals are extracted, and then classified by support vector machine. The results prove the feasibility and effectivity of the supervised kernel entropy component analysis in comparison with other similar methods, demonstrat... <s> BIB002 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> C. IMPROVED RÉNYI ENTROPY METHODS <s> This paper presents a supervised feature extraction method called weighted kernel entropy component analysis (WKECA) for fault diagnosis of rolling bearings. The method is developed based on kernel entropy component analysis (KECA) which attempts to preserve the Renyi entropy of the data set after dimension reduction. It makes full use of the labeled information and introduces a weight strategy in the feature extraction. The class-related weights are introduced to denote differences among the samples from different patterns, and genetic algorithm (GA) is implemented to seek out appropriate weights for optimizing the classification results. The features based on wavelet packet decomposition are derived from the original signals. Then the intrinsic geometric features extracted by WKECA are fed into the support vector machine (SVM) classifier to recognize different operating conditions of bearings, and we obtain the overall accuracy (97%) for the experimental samples. The experimental results demonstrated the feasibility and effectiveness of the proposed method. <s> BIB003
Based on REN, Robert Jenssen developed a novel information-theory-based method for data transformation and dimensionality reduction, called kernel entropy component analysis (KECA) BIB001 . KECA attempts to maintain the maximum estimated Rényi quadratic entropy of the input data set via a kernel-based estimator BIB002 . Zhou et al. developed two fault diagnosis methods based on KECA: supervised kernel entropy component analysis BIB002 and weight kernel entropy component analysis BIB003 for the fault diagnosis of rolling bearings.