Stationary Wavelet-Fourier Entropy and Kernel Extreme Learning for Bearing Multi-Fault Diagnosis

Applications of Entropy in Data Analysis and Machine Learning: A Review

Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and the Theory of Dynamical Systems. Specifically, we are referring to the classical entropies: the Boltzmann-Gibbs, von Neumann, Shannon, Kolmogorov-Sinai and topological entropies. In addition to their common name, which is historically justified (as we briefly describe in this review), another commonality of the classical entropies is the important role that they have played and are still playing in the theory and applications of their respective fields and beyond. Therefore, it is not surprising that, in the course of time, many other instances of the overarching concept of entropy have been proposed, most of them tailored to specific purposes. Following the current usage, we will refer to all of them, whether classical or new, simply as entropies. In particular, the subject of this review is their applications in data analysis and machine learning. The reason for these particular applications is that entropies are very well suited to characterize probability mass distributions, typically generated by finite-state processes or symbolized signals. Therefore, we will focus on entropies defined as positive functionals on probability mass distributions and provide an axiomatic characterization that goes back to Shannon and Khinchin. Given the plethora of entropies in the literature, we have selected a representative group, including the classical ones. The applications summarized in this review nicely illustrate the power and versatility of entropy in data analysis and machine learning.

A review on extreme learning machine

Extreme learning machine (ELM) is a training algorithm for single hidden layer feedforward neural network (SLFN), which converges much faster than traditional methods and yields promising performance. In this paper, we hope to present a comprehensive review on ELM. Firstly, we will focus on the theoretical analysis including universal approximation theory and generalization. Then, the various improvements are listed, which help ELM works better in terms of stability, efficiency, and accuracy. Because of its outstanding performance, ELM has been successfully applied in many real-time learning tasks for classification, clustering, and regression. Besides, we report the applications of ELM in medical imaging: MRI, CT, and mammogram. The controversies of ELM were also discussed in this paper. We aim to report these advances and find some future perspectives.

A Novel End-To-End Feature Selection and Diagnosis Method for Rotating Machinery

Feature selection is to obtain effective features from data, also known as feature engineering. Traditional feature selection and predictive model learning are separated, and there is a problem of inconsistency of criteria. This paper presents an end-to-end feature selection and diagnosis method that organically unifies feature expression learning and machine prediction learning into one model. The algorithm first combines the prediction model to calculate the mean impact value (MIVs) of the feature and realizes primary feature selection for the prediction model by selecting the feature with a larger MIV. In order to take into account the performance of the feature itself, the within-class and between-class discriminant analysis (WBDA) method is proposed, and combined with the feature diversity strategy, the feature-oriented secondary selection is realized. Eventually, feature vectors obtained by two selections are classified using a multi-class support vector machine (SVM). Compared with the modified network variable selection algorithm (MIVs), the principal component analysis dimensionality reduction algorithm (PCA), variable selection based on compensative distance evaluation technology (CDET), and other algorithms, the proposed method MIVs-WBDA exhibits excellent classification accuracy owing to the fusion of feature selection and predictive model learning. According to the results of classification accuracy testing after dimensionality reduction on rotating machinery status, the MIVs-WBDA method has a 3% classification accuracy improvement under the low-dimensional feature set. The typical running time of this classification learning algorithm is less than 10 s, while using deep learning, its running time will be more than a few hours.

Vibrations in CDFW

Continuous drive friction welding is a solid-state welding process that has been experimentally proven to be a fast and reliable method. This is a complex process; deformations in the viscosity of a material alter the friction between the surfaces of the pieces. All these dynamics cause changes in the vibration signals; the interpretation of these signals can reveal important information. The vibration signals generated during the friction and forging stages are measured on the stationary part of the structure to determine the influence of the manipulated variables on the time domain statistical characteristics (root mean square, peak value, crest factor, and kurtosis). In the frequency domain, empirical mode decomposition is used to characterize frequencies. It was observed that it is possible to identify the effects of the manipulated variables on the calculated statistical characteristics. The results also indicate that the effect of manipulated variables is stronger on low-frequency signals.