Symbolic Dynamic Entropy Research Articles

A Fault Diagnosis Approach for Rolling Bearing Integrated SGMD, IMSDE and Multiclass Relevance Vector Machine.

The vibration signal induced by bearing local fault has strong nonstationary and nonlinear property, which indicates that the conventional methods are difficult to recognize bearing fault patterns effectively. Hence, to obtain an efficient diagnosis result, the paper proposes an intelligent fault diagnosis approach for rolling bearing integrated symplectic geometry mode decomposition (SGMD), improved multiscale symbolic dynamic entropy (IMSDE) and multiclass relevance vector machine (MRVM). Firstly, SGMD is employed to decompose the original bearing vibration signal into several symplectic geometry components (SGC), which is aimed at reconstructing the original bearing vibration signal and achieving the purpose of noise reduction. Secondly, the bat algorithm (BA)-based optimized IMSDE is presented to evaluate the complexity of reconstruction signal and extract bearing fault features, which can solve the problems of missing of partial fault information existing in the original multiscale symbolic dynamic entropy (MSDE). Finally, IMSDE-based bearing fault features are fed to MRVM for achieving the identification of bearing fault categories. The validity of the proposed method is verified by the experimental and contrastive analysis. The results show that our approach can precisely identify different fault patterns of rolling bearings. Moreover, our approach can achieve higher recognition accuracy than several existing methods involved in this paper. This study provides a new research idea for improvement of bearing fault identification.

Health condition identification for rolling bearing based on hierarchical multiscale symbolic dynamic entropy and least squares support tensor machine–based binary tree

Bearing health condition identification plays a crucial role in guaranteeing maximum productivity and reducing maintenance costs. In this article, a novel tensorial feature extraction approach called hierarchical multiscale symbolic dynamic entropy is developed, which can be used to assess the dynamic characteristic of the measured vibration data at different hierarchical layers and different scales. Besides, the influence of parameters in hierarchical multiscale symbolic dynamic entropy is investigated so as to select the optimal parameters. Then, a new multi-fault classifier called least squares support tensor machine–based binary tree is presented to achieve the fault identification automatically. In the least squares support tensor machine–based binary tree method, the divisibility measure strategy is constructed by two new separability measures (i.e. the average center distance of samples in one class, the center distance of samples between sub-class and global class). Finally, a novel intelligent fault diagnosis scheme based on hierarchical multiscale symbolic dynamic entropy and least squares support tensor machine–based binary tree is developed, which is applied to analyze the experimental data of rolling bearing. The results indicate that the proposed scheme has a superior performance in health condition identification. Compared with the existing symbolic dynamic entropy–based fault diagnosis methods, the proposed method has higher diagnostic accuracy and better stability.

Refined composite multivariate multiscale symbolic dynamic entropy and its application to fault diagnosis of rotating machine

Accurate and efficient identification of various fault categories, especially for the big data and multisensory system, is a challenge in rotating machinery fault diagnosis. For the diagnosis problems with massive multivariate data, extracting discriminative and stable features with high efficiency is the significant step. This paper proposes a novel feature extraction method, called Refined Composite multivariate Multiscale Symbolic Dynamic Entropy (RCmvMSDE), based on the refined composite analysis and multivariate multiscale symbolic dynamic entropy. Specifically, multivariate multiscale symbolic dynamic entropy can capture more identification information from multiple sensors with superior computational efficiency, while refine composite analysis guarantees its stability. The abilities of the proposed method to measure the complexity of multivariate time series and identify the signals with different components are discussed based on adequate simulation analysis. Further, to verify the effectiveness of the proposed method on fault diagnosis tasks, a centrifugal pump dataset under constant speed condition and a ball bearing dataset under time-varying speed condition are applied. Compared with the existing methods, the proposed method improves the classification accuracy and F-score to 99.81% and 0.9981, respectively. Meanwhile, the proposed method saves at least half of the computational time. The result shows that the proposed method is effective to improve the efficiency and classification accuracy dealing with the massive multivariate signals.

Evaluation of heart rate dynamics during meditation using Poincaré phase plane symbolic measures

Meditation has long been known to affect human physiology which is mediated through autonomic nervous system. The main objective of this study was to assess dynamic changes in cardiac inter-beat intervals and autonomic nervous system during meditation hypothesising that Poincare plots in conjunction with symbolic dynamics can lead to better understanding of the dynamics of the underlying physiological mechanisms. The Poincare phase plane standard descriptors can measure only linear gross variability of the heart rate time series. Moreover, these descriptors exhibit limitations where the occurrence of nonlinear behaviour may be responsible to distinguish the phase plane patterns. We captured the changes in Poincare phase plane patterns resulting from nonlinear processes, during two meditation techniques, employing two complexity measures, symbolic dynamics entropy and forbidden words, which are appropriate to distinguish between the two states. Findings show that symbolic dynamics entropy, also a marker of parasympathetic activity, reveals that during premeditation state, there is parasympathetic dominance while during meditation state there is sympathetic dominance in both the meditation techniques. We also show the presence of nonlinear deterministic structures in the meditation inter-beat interval time series and appropriateness of the application of our nonlinear approach through surrogate data analysis.

A method based on refined composite multi-scale symbolic dynamic entropy and ISVM-BT for rotating machinery fault diagnosis

Multiscale symbolic dynamic entropy (MSDE) has been recently proposed to characterize the dynamical behavior of time series, which has merits of high computational efficiency and robustness to noise comparing with multiscale sample entropy (MSE) and multiscale permutation entropy (MPE). However, the variance of the MSDE values increases as the length of a time series becomes shorter using multiscale analysis. To address this shortcoming, a new method, namely refined composite multi-scale symbolic dynamic entropy (RCMSDE), is proposed to extract the fault information of rotating machinery. Then, Laplacian score (LS) is utilized to reduce the dimension of eigenvectors. In the end, the selected features are taken as the input of the improved support vector machine based on binary tree (ISVM-BT) for fault type identification. The effectiveness of the proposed method is validated using both the simulation and two experimental tests. Results demonstrate that the proposed method generates highest classification accuracy in comparison with existing methods such as MSDE, refined composite multiscale sample entropy (RCMSE) and refined composite multiscale permutation entropy (RCMPE).

Health condition identification of planetary gearboxes based on variational mode decomposition and generalized composite multi-scale symbolic dynamic entropy

This paper proposes a novel fault diagnosis method based on variational mode decomposition (VMD) and generalized composite multi-scale symbol dynamic entropy (GCMSDE) to identify the different health conditions of planetary gearboxes. First, VMD is adopted to remove the noises and highlight the fault symptoms. Second, GCMSDE is utilized to extract the fault features from the denoised vibration signals. Third, the Laplacian score (LS) approach is employed to refine the fault features. Finally, the new features are fed into Softmax regression to identify the health conditions of planetary gearboxes. The proposed method is numerically and experimentally demonstrated to be able to differentiate seven localized fault types on the sun gear, planet gear and ring gear of planetary gearboxes.

Early fault diagnosis of rolling bearings based on hierarchical symbol dynamic entropy and binary tree support vector machine

Early fault diagnosis of rolling bearings is crucial to operating and maintenance cost reduction of the equipment with bearings. This paper aims to propose a novel early fault feature extraction method based on the proposed hierarchical symbol dynamic entropy (HSDE) and the binary tree support vector machine (BT-SVM). Multiscale symbolic dynamic entropy (MSDE) has been recently proposed to characterize the dynamical behavior of time series. MSDE has several merits comparing with multiscale sample entropy (MSE) and multiscale permutation entropy (MPE), such as high computational efficiency and robustness to noise. However, MSDE only utilizes the fault information in the low frequency components and consequently the fault information hidden in the high frequency components is discarded. To address this shortcoming, a new method, namely HSDE, is proposed to extract the fault information in the high frequency components. Then, the BT-SVM is utilized to automatically complete the fault type identification. The effectiveness of the proposed method is validated using simulated and experimental vibration signals. Meanwhile, a comparison is conducted between MPE, hierarchical permutation entropy (HPE), MSE, hierarchical sample entropy (HSE), MSDE and HSDE. Results show that the proposed method performs best to recognize the early fault types of rolling bearings.

A fault diagnosis scheme for planetary gearboxes using modified multi-scale symbolic dynamic entropy and mRMR feature selection

Health condition identification of planetary gearboxes is crucial to reduce the downtime and maximize productivity. This paper aims to develop a novel fault diagnosis method based on modified multi-scale symbolic dynamic entropy (MMSDE) and minimum redundancy maximum relevance (mRMR) to identify the different health conditions of planetary gearbox. MMSDE is proposed to quantify the regularity of time series, which can assess the dynamical characteristics over a range of scales. MMSDE has obvious advantages in the detection of dynamical changes and computation efficiency. Then, the mRMR approach is introduced to refine the fault features. Lastly, the obtained new features are fed into the least square support vector machine (LSSVM) to complete the fault pattern identification. The proposed method is numerically and experimentally demonstrated to be able to recognize the different fault types of planetary gearboxes.

Spatiotemporal imaging of complexity

What are the functional neuroimaging measurements required for more fully characterizing the events and locations of neocortical activity? A prime assumption has been that modulation of cortical activity will inevitably be reflected in changes in energy utilization (for the most part) changes of glucose and oxygen consumption. Are such a measures complete and sufficient? More direct measures of cortical electrophysiological activity show event or task-related modulation of amplitude or band-limited oscillatory power. Using magnetoencephalography (MEG), these measures have been shown to correlate well with energy utilization sensitive BOLD fMRI. In this paper, we explore the existence of state changes in electrophysiological cortical activity that can occur independently of changes in averaged amplitude, source power or indices of metabolic rates. In addition, we demonstrate that such state changes can be described by applying a new measure of complexity, rank vector entropy (RVE), to source waveform estimates from beamformer-processed MEG. RVE is a non-parametric symbolic dynamic informational entropy measure that accommodates the wide dynamic range of measured brain signals while resolving its temporal variations. By representing the measurements by their rank values, RVE overcomes the problem of defining embedding space partitions without resorting to signal compression. This renders RVE-independent of absolute signal amplitude. In addition, this approach is robust, being relatively free of tunable parameters. We present examples of task-free and task-dependent MEG demonstrating that RVE provides new information by uncovering hidden dynamical structure in the apparent turbulent (or chaotic) dynamics of spontaneous cortical activity.

Periodic Orbits, Symbolic Dynamics and Topological Entropy for the Restricted 3-Body Problem

This paper concerns the restricted 3-body problem. By applying topological methods we give a computer assisted proof of the existence of some classes of periodic orbits, the existence of symbolic dynamics and we give a rigorous lower estimate for the topological entropy.

Symbolic Dynamics and Topological Entropy of Henon Map11The project supported by National Natural Science Foundation of China.

By using the method with which the trajectories of dissipative maps can be derived from the Hamiltonian, we study the symbolic dynamics of Henon map and its relation with the symbolic dynamics of unimodal map, and compute the topological entropy as a function of the parameter and . Finally, the boundary of the region where the topological entropy exists on the parameter plane is given.