Gear transmission is one of the most commonly used transmission methods in mechanical equipment. By analyzing the vibration data of gearbox, an improved deep belief network (DBN) algorithm for gear fault diagnosis based on wavelet packet energy entropy (WPEE) and multiscale permutation entropy (MPE) is proposed. Firstly, the vibration data of gearbox with various fault types under multiple working conditions are collected. Secondly, the energy entropy of wavelet packet and the entropy distribution of multiscale permutation are calculated respectively to form a combined feature matrix. Then, the improved threshold adaptive DBN is used to further extract the fault signal features, and finally the deep layer features are classified. By analyzing the vibration data of multi-platform gearbox, a high and stable diagnostic accuracy is obtained.

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An Intelligent Fault Diagnosis Method of Variable Condition Gearbox Based on Improved DBN Combined With WPEE and MPE

The Fisher-DisEn plane: A novel approach to distinguish different complex systems

In economic (financial) time series analysis, prediction plays an important role and the inclusion of noise in the time series data is also a common phenomenon In particular, stock market data are highly random and non-stationary, thus they contain much noise Prediction of the noise-free data is quite difficult when noise is present Therefore, removal of such noise before predicting can significantly improve the prediction accuracy of economic models Based on this consideration, this paper proposes a new shrinkage (thresholding) function to improve the performance of wavelet shrinkage denoising The proposed thresholding function is an arctangent function with several parameters to be determined and the optimal parameters are determined by ensuring that the thresholding function satisfies the condition of continuously differentiable The closing price data with the Shanghai Composite Index from January 1991 to December 2014 are used to illustrate the application of the proposed shrinkage function in denoising the stock data The experimental results show that compared with the classical shrinkage (hard, soft, and nonnegative garrote) functions, the proposed thresholding function not only has the advantage of continuous derivative, but also has a very competitive denoising performance

A Continuous Differentiable Wavelet Shrinkage Function for Economic Data Denoising

The ordinal pattern is an essential tool to extract the information in time series. However, little attention has been paid to the transition probability matrix of ordinal patterns, which affects the accuracy and comprehensiveness of the extracted information. In this article, we propose a transition permutation entropy (TPE) and a transition dissimilarity measure (TDM) through the transition matrix. The TPE can evaluate the complexity of systems. The TDM measures the dissimilarity between systems through the dynamic transition and the probability distribution of ordinal patterns. The proposed methods are comprehensively evaluated by simulation experiments and vehicle dynamic response data. The results show that both the TPE and the TDM can distinguish complex systems and locate the rail corrugation. The combination of the TDM, multidimensional scaling, and neural networks can be used for fault detection and is better than other distance calculation methods. 

Transition Permutation Entropy and Transition Dissimilarity Measure: Efficient Tools for Fault Detection of Railway Vehicle Systems

This chapter aims at presenting entropy measures that are now widely used in health informatics. Entropy measures have been introduced in 1990s and are derived from the theory of chaos. The traditional entropy-based analysis methods evaluate the degree of regularity of signals. We therefore present, first, the very well-known entropy measures used in the biomedical field: their theoretical background is detailed and some medical applications are presented. Then, more and very recent entropy measures are exposed and some of their used in health informatics are listed. This is performed from two points of view: for time series (uni-dimensional data) and for images (bi-dimensional data).

Entropy Analysis in Health Informatics

Discussing the complexity of time series has been a long-standing problem, including the use of information entropy to determine the complexity of the sequence. Permutation entropy (PE) has been regarded as a learning process to investigate the complexity of time series, such as financial time series and physiological time series. The permutation entropy, which is based on the Shannon entropy (SE), has undeniable shortcomings in dealing with some specific problems. Hence in this paper, we propose the multiscale Tsallis permutation entropy (MTPE) as an improved measuring tool for assessing the hidden temporal correlations in time series. The modified method not only presents a different way showing clear characteristics but also provides more significant results compared with the SE. Robustness of the hypothesis is proved by the correlation between Tsallis permutation entropy (TPE) and HURST exponent obtained from the sequences which are generated from fractional brownian motion stochastic model. Experimental results of autoregressive sequences (AR) and electroencephalograph time series (EEG) make the advantages of Tsallis permutation entropy more obvious, which also well validate the efficiency and integrity of principle of maximum entropy (PME). Multiscale analysis provides us with another perspective to analyze permutation entropy, which also allows us to better analyze the complexity of the sequence.

Multiscale Tsallis permutation entropy analysis for complex physiological time series

In this paper, a new modified method is proposed as a measure to investigate the correlation between past price and future volatility for financial time series, known as the complexity analysis based on generalized deviation. In comparison with the former retarded volatility model, the new approach is both simple and computationally efficient. The method based on the generalized deviation function presents us an exhaustive way showing the quantization of the financial market rules. Robustness of this method is verified by numerical experiments with both artificial and financial time series. Results show that the generalized deviation complexity analysis method not only identifies the volatility of financial time series, but provides a comprehensive way distinguishing the different characteristics between stock indices and individual stocks. Exponential functions can be used to successfully fit the volatility curves and quantify the changes of complexity for stock market data. Then we study the influence for negative domain of deviation coefficient and differences during the volatile periods and calm periods. after the data analysis of the experimental model, we found that the generalized deviation model has definite advantages in exploring the relationship between the historical returns and future volatility.

Chao li

Papers

Multiscale Tsallis permutation entropy analysis for complex physiological time series

Complexity analysis based on generalized deviation for financial markets