Permutation Entropy Algorithm Research Articles

Operation conditions monitoring of flood discharge structure based on variance dedication rate and permutation entropy

There has been a growing concern on how to monitor the operation conditions of flood discharge structure in recent decades. However, the online monitoring process is always interfered by ambient excitation which leads to inaccurate and uncertain structural characteristic evaluation. To mitigate the interference, a valid operation conditions monitoring method based on variance dedication rate (VDR) and permutation entropy (VDR-PE) is proposed. Firstly, a de-noising method combining wavelet threshold and empirical mode decomposition is used to remove heavy background noises, reducing the interference of ambient excitation to structural characteristic information. Then VDR method is used to realize the dynamic fusion of multi-channel vibration signals, extracting the vibration characteristic of the overall structure in an accurate and comprehensive way. Finally, permutation entropy is used to extract the entropy value of the fused signal. Through evaluating the operation conditions with coefficient of variation, the online monitoring of flood discharge structure can be realized. The effectiveness of permutation entropy algorithm on signal dynamic monitoring is validated by a simulation experiment. Furthermore, VDR-PE method is applied to Three Gorges dam to compare differences between analytical simulation and finite element simulation. The comparison results show that VDR-PE method can be applied to detect the dynamic changes and reveal the vibration characteristic of the overall structure accurately, which provides a new direction for the online monitoring of flood discharge structure.

A Quantitative Analysis for EEG Signals Based on Modified Permutation-Entropy

PurposeElectroencephalogram (EEG) is a record of brain electrical activities along the scalp which contains precious information related to different brain states. The aim of this study is to investigate the complexity of EEG signals and distinguish the EEG signals with different rhythm. Material and methodsThe EEG time series data used in this study come from single neural mass model. The model with the different parameters produces the EEG signals with different rhythm such as normal EEG signals and epileptiform spikes. The modified permutation-entropy is used to extract the complexity features of the normal EEG signals and epileptiform spikes and is compared with the permutation-entropy algorithm and Rényi permutation-entropy algorithm. The statistical analysis is used to characterize the differences between the signals. ResultsThe signals corresponding to A=3.25 mV and A=3.6 mV are easy to distinguish according to the average values and the standard deviations of the modified permutation-entropy. The statistical results reveal that group differences of the modified permutation-entropy values for the signals corresponding to A=3.25 mV and A=3.4 mV are significant, manifested as F>1 and p<0.05. Compared with the permutation-entropy and Rényi permutation-entropy, F-values of the modified permutation-entropy are the greatest and p-values of the modified permutation-entropy are the smallest. ConclusionThere are significant differences between the complexity features of normal EEG signals and epileptiform spikes signals. The signals can be distinguished under different lengths of time series, embedding dimensions and delay times by using the modified permutation-entropy. The modified permutation-entropy is an effective complexity measure to quantify the EEG signals. Compared with the permutation-entropy and Rényi permutation-entropy, the modified permutation-entropy is more effective to distinguish the EEG signals with different rhythm.

Dynamical properties and complexity in fractional-order diffusionless Lorenz system

In this paper, dynamics and complexity of the fractional-order diffusionless Lorenz system which is solved by the developed discrete Adomian decomposition method are investigated numerically. Dynamical properties of the fractional-order diffusionless Lorenz system with the control parameter and derivative order varying is analyzed by using bifurcation diagrams, and period-doubling route to chaos in different cases is observed. The complexity of the system is investigated by means of Lyapunov characteristic exponents, multi-scale spectral entropy algorithm and multiscale Renyi permutation entropy algorithm. It can be observed that the three methods illustrate consistent results and the system has rich complex dynamics. Interestingly, complexity decreases with the increase of derivative order. It shows that the fractional-order diffusionless Lorenz system is a good model for real applications such as information encryption and secure communication.

A hybrid automated detection of epileptic seizures in EEG records

The paper introduces a new automated seizure detection model that integrates Weighted Permutation Entropy (WPE) and a Support Vector Machine (SVM) classifier model to enhance the sensitivity and precision of the detection process. The proposed system utilizes the fact that entropy based measures for the EEG segments during epileptic seizure are lower than in normal EEG. The new suggested model better tracks abrupt changes in the signal and assigns less complexity to segments that exhibit regularity or are subjected to noise effects. The Weighted Permutation Entropy algorithm relies on the ordinal pattern of the time series along with the amplitudes of its sample points. The proposed technique is implemented and tested on hundreds real EEG signals and the performance is compared based on sensitivity, specificity and accuracy. Various experiments have been applied in different scenarios including healthy with eyes open, healthy with eyes closed, epileptic patients during no-seizure state from two different location of the brain. Other scenarios have been applied accompanied by background simulated noise resulting from physiological and environmental artifacts. Results showed outstanding performance and revealed promising results in terms of discrimination of seizure and seizure-free segments. It also manifests high robustness against noise sources.

IMPROVING THE COMPLEXITY OF CHAOTIC SEQUENCE BASED ON THE PCA ALGORITHM

The principal component analysis (PCA) is an effective statistical analysis method in statistical data analysis, feature extraction and data compression. The method simplifies multiple related variables into a linear combination of several irrelevant variables, through the less-comprehensive index as far as possible to replace many of the original data, and can reflect the information provided by the original data. This paper studies the signal feature extraction algorithm based on PCA, and extracts sequences’ feature which generated by Logistic mapping. Then we measured the complexity of the reconstructed chaotic sequences by the permutation entropy algorithm. The testing results show that the complexity of the reconstruction sequences is significantly higher than the original sequences.

Modified multiscale permutation entropy algorithm and its application for multiscroll chaotic systems

To analyze the complexity of continuous chaotic systems better, the modified multiscale permutation entropy (MMPE) algorithm is proposed. Characteristics and parameter choices of the MMPE algorithm are investigated. The comparative study between MPE and MMPE shows that MMPE has better robustness for identifying different chaotic systems when the scale factor τ takes large values. Compared with MPE, MMPE algorithm is more suitable for analyzing the complexity of time series as it has τ time series. For its application, MMPE algorithm is used to calculate the complexity of multiscroll chaotic systems. Results show that complexity of multiscroll chaotic systems does not increase as scroll number increases. Discussions based on first‐order difference operation present a reasonable explanation on why the complexity does not increase. This complexity analysis method lays a theoretical as well as experimental basis for the applications of multiscroll chaotic systems. © 2014 Wiley Periodicals, Inc. Complexity 21: 52–58, 2016

Multiscale permutation entropy analysis of oil-in-water type two-phase flow pattern

We investigate the dynamic characteristics of vertical upward water-dominant oil-water two-phase flow by multiscale permutation entropy algorithm. We first measure the two-phase flow conductance fluctuation signals in a 20 mm inner-diameter pipe. Then we calculate the multiscale permutation entropies for different water-dominant flow patterns. The results indicate that multiscale permutation entropy rate and average of mutiscale permutation entropy can be used as quantitative parameters for measuring complexity of water dominant oil-water two-phase flow. In addition, we propose a new approach to identify different water-dominant flow patterns by using the joint distribution of multiscale permutation entropy rate and cumulant of increment series.