Multiscale Permutation Entropy Method Research Articles

Disease identification method based on graph features between pulse cycles

The pulse signal at the wrist communicates a range of cardiovascular information and reflects a person’s state of health. In recent years pulse signals have been used extensively in the field of disease identification. As a typical quasi-cyclic physiological signal, many researchers have simply used single-cycle pulse signals for disease diagnosis, ignoring the influence of inter-cycle differences on the diagnosis. In this paper, we propose a disease identification method based on graph features between pulse cycles, to focus on the differences in pulse cycles brought about by the disease. The pulse was pre-processing using a Sliding Window, followed by the construction of the correlation coefficient matrix, the setting of a threshold and the construction of the connection graph to obtain the graph features; the Multiscale Permutation Entropy method was used to extract the pulse’s entropy features. The ReliefF algorithm is then used to select a total of 18 features and a classification algorithm is used to distinguish between patients and healthy people. Both the self-constructed dataset and the open dataset from the PLA 211 Hospital had high recognition rates for the experiments. The accuracy of identifying hypertension was 94.16% with a precision of 90.41%; the accuracy of identifying chronic diseases was 97.23% with a precision of 97.81%. The experimental results from the two datasets demonstrate both the validity of the difference between cycles for disease classification and the applicability of the method proposed in this paper.

Recognition study of denatured biological tissues based on multi-scale rescaled range permutation entropy.

The recognition of denatured biological tissue is an indispensable part in the process of high intensity focused ultrasound treatment. As a nonlinear method, multi-scale permutation entropy (MPE) is widely used in the recognition of denatured biological tissue. However, the traditional MPE method neglects the amplitude information when calculating the time series complexity. The disadvantage will affect the recognition effect of denatured tissues. In order to solve the above problems, the method of multi-scale rescaled range permutation entropy (MRRPE) is proposed in this paper. The simulation results show that the MRRPE not only includes the amplitude information of the signal when calculating the signal complexity, but also extracts the extreme volatility characteristics of the signal effectively. The proposed method is applied to the HIFU echo signals during HIFU treatment, and the support vector machine (SVM) is used for recognition. The results show that compared with MPE and the multi-scale weighted permutation entropy (MWPE), the recognition rate of denatured biological tissue based on the MRRPE is higher, up to 96.57%, which can better recognize the non-denatured biological tissues and the denatured biological tissues.

Biological Tissue Damage Monitoring Method Based on IMWPE and PNN during HIFU Treatment

Biological tissue damage monitoring is an indispensable part of high-intensity focused ultrasound (HIFU) treatment. As a nonlinear method, multi-scale permutation entropy (MPE) is widely used in the monitoring of biological tissue. However, the traditional MPE method neglects the amplitude information when calculating the time series complexity, and the stability of MPE is poor due to the defects in the coarse-grained process. In order to solve the above problems, the method of improved coarse-grained multi-scale weighted permutation entropy (IMWPE) is proposed in this paper. Compared with the MPE, the IMWPE method not only includes the amplitude of signal when calculating the signal complexity, but also improves the stability of entropy value. The IMWPE method is applied to the HIFU echo signals during HIFU treatment, and the probabilistic neural network (PNN) is used for monitoring the biological tissue damage. The results show that compared with multi-scale sample entropy (MSE)-PNN and MPE-PNN methods, the proposed IMWPE-PNN method can correctly identify all the normal tissues, and can more effectively identify damaged tissues and denatured tissues. The recognition rate for the three kinds of biological tissues is higher, up to 96.7%. This means that the IMWPE-PNN method can better monitor the status of biological tissue damage during HIFU treatment.

Fault Recognition of Rolling Bearings Based on Parameter Optimized Multi-Scale Permutation Entropy and Gath-Geva

To extract fault features of rolling bearing vibration signals precisely, a fault diagnosis method based on parameter optimized multi-scale permutation entropy (MPE) and Gath-Geva (GG) clustering is proposed. The method can select the important parameters of MPE method adaptively, overcome the disadvantages of fixed MPE parameters and greatly improve the accuracy of fault identification. Firstly, aiming at the problem of parameter determination and considering the interaction among parameters comprehensively of MPE, taking skewness of MPE as fitness function, the time series length and embedding dimension were optimized respectively by particle swarm optimization (PSO) algorithm. Then the fault features of rolling bearing were extracted by parameter optimized MPE and the standard clustering centers is obtained with GG clustering. Finally, the samples are clustered with the Euclid nearness degree to obtain recognition rate. The validity of the parameter optimization is proved by calculating the partition coefficient and average fuzzy entropy. Compared with unoptimized MPE, the propose method has a higher fault recognition rate.

Refined time-shift multiscale normalised dispersion entropy and its application to fault diagnosis of rolling bearing

Multiscale entropy (MSE) and multiscale permutation entropy (MPE) are two effective nonlinear dynamic complexity measurement methods of time series that have been applied to many areas for complexity feature extraction in recent years. To overcome the inherent defects of sample entropy and permutation entropy, together with the coarse graining process used in MSE and MPE, based on the recently proposed dispersion entropy (DisEn), the refined time-shift multiscale normalised dispersion entropy (RTSMNDE) is proposed here for the complexity measurement of time series. In the RTSMNDE method, first, to expand DisEn to the multiscale framework, the time-shift multiscale method is used to replace the traditional coarse graining multiscale method. The refining approach is adopted to alleviate the fluctuation of DisEns in larger scale factors, and a normalisation operation is implemented on all entropies to restrain the influence of the parameters on RTSMNDE values. Furthermore, the RTSMNDE is compared with the multiscale dispersion entropy (MDE) by analysing synthetic simulation signals to verify its effectiveness. Based on that, an intelligent fault diagnosis method for rolling bearings is proposed by combining the RTSMNDE for fault feature extraction with the particle swarm optimisation support vector machine for feature classification. Finally, the proposed method is applied to rolling bearing experimental data analysis, and the analysis results show that the proposed method can effectively diagnose the locations and degrees of rolling bearing failures and obtain a higher recognition rate than those of the MPE and MDE-based methods.

Fault identification technology for gear tooth surface wear based on MPE method by MI and improved FNN algorithm

Multiscale Permutation Entropy (MPE) is a presented nonlinear dynamic technology for measuring the randomness and detecting the nonlinear dynamic change of time sequences and can be used effectively to extract the nonlinear dynamic wear fault feature of gear tooth surface from vibration signals of gear set. To solve the subjectivity drawback of threshold parameter selection process in MPE method, a joint calculation method based on the Mutual Information (MI) and improved False Nearest Neighbor (FNN) principle for calculating threshold parameters for MPE method was presented in this article. Then, the influence of threshold parameters on the identification accuracy of fault features with the MPE was studied by analyzing simulation data. Through the simulation analysis, the effectiveness of the proposed MPE method is validated. Finally, the wear failure test of spur gear was carried out, and the proposed method was applied to analyze the experimental data of fault signal. Meanwhile, the vibration characteristics of the fault signal are acquired. The analysis results show that the proposed method can effectively realize the fault diagnosis of gear box and has higher fault identification accuracy than the existing methods.

The Optimized Multi-Scale Permutation Entropy and Its Application in Compound Fault Diagnosis of Rotating Machinery.

Multi-scale permutation entropy (MPE) is a statistic indicator to detect nonlinear dynamic changes in time series, which has merits of high calculation efficiency, good robust ability, and independence from prior knowledge, etc. However, the performance of MPE is dependent on the parameter selection of embedding dimension and time delay. To complete the automatic parameter selection of MPE, a novel parameter optimization strategy of MPE is proposed, namely optimized multi-scale permutation entropy (OMPE). In the OMPE method, an improved Cao method is proposed to adaptively select the embedding dimension. Meanwhile, the time delay is determined based on mutual information. To verify the effectiveness of OMPE method, a simulated signal and two experimental signals are used for validation. Results demonstrate that the proposed OMPE method has a better feature extraction ability comparing with existing MPE methods.

Generalized composite multiscale permutation entropy and Laplacian score based rolling bearing fault diagnosis

Abstract Multiscale permutation entropy (MPE) is a recently proposed nonlinear dynamic method for measuring the randomness and detecting the nonlinear dynamic change of time series and can be used effectively to extract the nonlinear dynamic fault feature from vibration signals of rolling bearing. To solve the drawback of coarse graining process in MPE, an improved MPE method called generalized composite multiscale permutation entropy (GCMPE) was proposed in this paper. Also the influence of parameters on GCMPE and its comparison with the MPE are studied by analyzing simulation data. GCMPE was applied to the fault feature extraction from vibration signal of rolling bearing and then based on the GCMPE, Laplacian score for feature selection and the Particle swarm optimization based support vector machine, a new fault diagnosis method for rolling bearing was put forward in this paper. Finally, the proposed method was applied to analyze the experimental data of rolling bearing. The analysis results show that the proposed method can effectively realize the fault diagnosis of rolling bearing and has a higher fault recognition rate than the existing methods.

A Hybrid Generalized Hidden Markov Model-Based Condition Monitoring Approach for Rolling Bearings.

The operating condition of rolling bearings affects productivity and quality in the rotating machine process. Developing an effective rolling bearing condition monitoring approach is critical to accurately identify the operating condition. In this paper, a hybrid generalized hidden Markov model-based condition monitoring approach for rolling bearings is proposed, where interval valued features are used to efficiently recognize and classify machine states in the machine process. In the proposed method, vibration signals are decomposed into multiple modes with variational mode decomposition (VMD). Parameters of the VMD, in the form of generalized intervals, provide a concise representation for aleatory and epistemic uncertainty and improve the robustness of identification. The multi-scale permutation entropy method is applied to extract state features from the decomposed signals in different operating conditions. Traditional principal component analysis is adopted to reduce feature size and computational cost. With the extracted features’ information, the generalized hidden Markov model, based on generalized interval probability, is used to recognize and classify the fault types and fault severity levels. Finally, the experiment results show that the proposed method is effective at recognizing and classifying the fault types and fault severity levels of rolling bearings. This monitoring method is also efficient enough to quantify the two uncertainty components.

A new rolling bearing fault diagnosis method based on multiscale permutation entropy and improved support vector machine based binary tree

A new bearing vibration feature extraction method based on multiscale permutation entropy (MPE) and improved support vector machine based binary tree (ISVM-BT) is put forward in this paper. Local mean decomposition (LMD), a new self-adaptive time–frequency analysis method, is utilized to decompose the roller bearing vibration signal into a set of product functions (PFs) and then MPE method is used to characterize the complexity of the principal PF component in different scales. After the feature extraction, a new pattern recognition approach called ISVM-BT is introduced to accomplish the fault identification automatically, which has the priority of high recognition accuracy compared with other classifiers. Besides, the Laplacian score (LS) is introduced to refine the fault feature by sorting the scale factors. Finally, the rolling bearing fault diagnosis method based on LMD, MPE, LS and ISVM-BT is proposed and the experimental results indicate the proposed method is effective in identifying the different categories of rolling bearings.

Weighted multiscale permutation entropy of financial time series

In this paper, we propose the weighted multiscale permutation entropy (WMPE) as a novel measure to quantify the complexity of nonlinear time series containing amplitude-coded information. WMPE is different from multiscale permutation entropy (MPE) in the sense that it suits better signals having considerable amplitude information and also succeed in accounting for the multiple time scales inherent in the financial systems. We first perform the MPE and WMPE methods on synthetic data showing the power of WMPE. Then, we apply the MPE and WMPE methods to the US and Chinese stock markets and make a comparison to discuss their differences and similarities between these different markets. The WMPE of each US and Chinese stock market points out the necessity of applying permutation entropy on multiple scales and reveals amplitude-coded information contained in the signals and immunity to degradation by noise when $$m = 5-7$$ . Some new conclusions are gotten by the new characteristics we detected in the comparison. WMPE method can distinguish ShangZheng and ShenCheng from these markets and imply that HSI is more similar to the US markets. WMPE moves the fluctuation range of entropy values of different market down differently reflecting more accurate complexity of different stock markets containing amplitude information. Compared WMPE of ShangZheng and ShenCheng with the WMPE of US markets and HSI, US stock market and HSI may have more amplitude information carried by the signals of stock market. Furthermore, compared with MPE, WMPE can reduce the standard deviation which ensures the results more robust. The conclusion that $$m = 7$$ is the best embedding dimension to investigate the WMPE results can be drawn because the WMPE tends to be stable in a certain range and reflects the necessity of investigation on multiscale and advantages of adding different weight, and it can distinguish these markets while reducing the standard deviations of all the markets.

Multi-Scale Permutation Entropy: A Complexity Measure for Discriminating Two-Phase Flow Dynamics

We propose an improved permutation entropy method, i.e., multi-scale permutation entropy (MSPE), for discriminating two-phase flow dynamics. We first take the signals from different typical dynamical systems as examples to demonstrate the effectiveness of the methods. In particular, we compute the MSPE values of sinusoidal signal, logistic, Lorenz and Chen chaotic signals and their signals with white Gaussian noise added. We find that the MSPE method can be an effective tool for analyzing the time series with distinct dynamics. We finally calculate the multi-scale permutation entropy and rate of MSPE from 66 groups of conductance fluctuating signals and find that these two measures can be used to identify different flow patterns and further explore dynamical characteristics of gas-liquid flow patterns. These results suggest that the MSPE can potentially be a useful tool for revealing the dynamical complexity of two-phase flow on different scales.