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.

Download Full-text

Optimal Parameter Selection of Multistage Time-Delay Systems

Springer Optimization and Its Applications - Optimal Control of Switched Systems Arising in Fermentation Processes ◽

10.1007/978-3-662-43793-3_9 ◽

2014 ◽

pp. 123-142

Author(s):

Chongyang Liu ◽

Zhaohua Gong

Keyword(s):

Time Delay ◽

Optimal Parameter ◽

Parameter Selection ◽

Delay Systems ◽

Time Delay Systems ◽

Selection Of ◽

Optimal Parameter Selection

Download Full-text

The Winter Habitat Selection of Red Deer (Cervus elaphus) Based on a Multi-Scale Model

Animals ◽

10.3390/ani10122454 ◽

2020 ◽

Vol 10 (12) ◽

pp. 2454

Author(s):

Yue Sun ◽

Yanze Yu ◽

Jinhao Guo ◽

Minghai Zhang

Keyword(s):

Habitat Selection ◽

Environmental Factors ◽

Cervus Elaphus ◽

Red Deer ◽

Scale Model ◽

Winter Habitat ◽

Multi Scale ◽

Optimal Scale ◽

Scale Models ◽

Selection Of

Single-scale frameworks are often used to analyze the habitat selections of species. Research on habitat selection can be significantly improved using multi-scale models that enable greater in-depth analyses of the scale dependence between species and specific environmental factors. In this study, the winter habitat selection of red deer in the Gogostaihanwula Nature Reserve, Inner Mongolia, was studied using a multi-scale model. Each selected covariate was included in multi-scale models at their “characteristic scale”, and we used an all subsets approach and model selection framework to assess habitat selection. The results showed that: (1) Univariate logistic regression analysis showed that the response scale of red deer to environmental factors was different among different covariate. The optimal scale of the single covariate was 800–3200 m, slope (SLP), altitude (ELE), and ratio of deciduous broad-leaved forests were 800 m in large scale, except that the farmland ratio was 200 m in fine scale. The optimal scale of road density and grassland ratio is both 1600 m, and the optimal scale of net forest production capacity is 3200 m; (2) distance to forest edges, distance to cement roads, distance to villages, altitude, distance to all road, and slope of the region were the most important factors affecting winter habitat selection. The outcomes of this study indicate that future studies on the effectiveness of habitat selections will benefit from multi-scale models. In addition to increasing interpretive and predictive capabilities, multi-scale habitat selection models enhance our understanding of how species respond to their environments and contribute to the formulation of effective conservation and management strategies for ungulata.

Download Full-text

Principled approach to the selection of the embedding dimension of networks

Nature Communications ◽

10.1038/s41467-021-23795-5 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Weiwei Gu ◽

Aditya Tandon ◽

Yong-Yeol Ahn ◽

Filippo Radicchi

Keyword(s):

Real World ◽

Structural Information ◽

General Purpose ◽

Embedding Dimension ◽

Network Embedding ◽

Machine Learning Technique ◽

Learning Technique ◽

Low Dimensional ◽

Large Corpus ◽

Selection Of

AbstractNetwork embedding is a general-purpose machine learning technique that encodes network structure in vector spaces with tunable dimension. Choosing an appropriate embedding dimension – small enough to be efficient and large enough to be effective – is challenging but necessary to generate embeddings applicable to a multitude of tasks. Existing strategies for the selection of the embedding dimension rely on performance maximization in downstream tasks. Here, we propose a principled method such that all structural information of a network is parsimoniously encoded. The method is validated on various embedding algorithms and a large corpus of real-world networks. The embedding dimension selected by our method in real-world networks suggest that efficient encoding in low-dimensional spaces is usually possible.

Download Full-text

Chaotic Time-Delay Signature Suppression and Entropy Growth Enhancement Using Frequency-Band Extractor

Entropy ◽

10.3390/e23050516 ◽

2021 ◽

Vol 23 (5) ◽

pp. 516

Author(s):

Yanqiang Guo ◽

Tong Liu ◽

Tong Zhao ◽

Haojie Zhang ◽

Xiaomin Guo

Keyword(s):

Time Delay ◽

Frequency Band ◽

Secure Communication ◽

Optical Feedback ◽

Random Number Generation ◽

Permutation Entropy ◽

Growth Enhancement ◽

Dynamical Process ◽

Promising Tool ◽

Entropy Growth

By frequency-band extracting, we experimentally and theoretically investigate time-delay signature (TDS) suppression and entropy growth enhancement of a chaotic optical-feedback semiconductor laser under different injection currents and feedback strengths. The TDS and entropy growth are quantified by the peak value of autocorrelation function and the difference of permutation entropy at the feedback delay time. At the optimal extracting bandwidth, the measured TDS is suppressed up to 96% compared to the original chaos, and the entropy growth is higher than the noise-dominated threshold, indicating that the dynamical process is noisy. The effects of extracting bandwidth and radio frequencies on the TDS and entropy growth are also clarified experimentally and theoretically. The experimental results are in good agreements with the theoretical results. The skewness of the laser intensity distribution is effectively improved to 0.001 with the optimal extracting bandwidth. This technique provides a promising tool to extract randomness and prepare desired entropy sources for chaotic secure communication and random number generation.

Download Full-text

Biological weight selection of multi-scale retinex via artificial bee colony algorithm

Optik ◽

10.1016/j.ijleo.2013.09.019 ◽

2014 ◽

Vol 125 (3) ◽

pp. 1434-1438 ◽

Cited By ~ 8

Author(s):

Qifu Zhang ◽

Haibin Duan

Keyword(s):

Artificial Bee Colony Algorithm ◽

Artificial Bee Colony ◽

Multi Scale ◽

Bee Colony ◽

Selection Of

Download Full-text

Design of LQR based PI controller with optimum selection of weights for Time Delay Process

10.1109/ibssc53889.2021.9673343 ◽

2021 ◽

Author(s):

K Harshavardhana Reddy ◽

Sachin Sharma ◽

B. Madhuri ◽

K Shivarama Krishna

Keyword(s):

Time Delay ◽

Pi Controller ◽

Optimum Selection ◽

Selection Of

Download Full-text

A Study On Methods for Determining Phase Space Reconstruction Parameters

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4052721 ◽

2021 ◽

Author(s):

Shihui Lang ◽

Zhu Hua ◽

Guodong Sun ◽

Yu Jiang ◽

Chunling Wei

Keyword(s):

Time Delay ◽

Phase Space ◽

Correlation Dimension ◽

Nearest Neighbor ◽

Correlation Method ◽

Phase Space Reconstruction ◽

Lorenz Attractor ◽

Embedding Dimension ◽

Phase Trajectories ◽

Auto Correlation

Abstract Several pairs of algorithms were used to determine the phase space reconstruction parameters to analyze the dynamic characteristics of chaotic time series. The reconstructed phase trajectories were compared with the original phase trajectories of the Lorenz attractor, Rössler attractor, and Chens attractor to obtain the optimum method for determining the phase space reconstruction parameters with high precision and efficiency. The research results show that the false nearest neighbor method and the complex auto-correlation method provided the best results. The saturated embedding dimension method based on the saturated correlation dimension method is proposed to calculate the time delay. Different time delays are obtained by changing the embedding dimension parameters of the complex auto-correlation method. The optimum time delay occurs at the point where the time delay is stable. The validity of the method is verified through combing the application of correlation dimension, showing that the proposed method is suitable for the effective determination of the phase space reconstruction parameters.

Download Full-text

Patterns with Equal Values in Permutation Entropy: Do They Really Matter for Biosignal Classification?

Complexity ◽

10.1155/2018/1324696 ◽

2018 ◽

Vol 2018 ◽

pp. 1-15 ◽

Cited By ~ 11

Author(s):

David Cuesta–Frau ◽

Manuel Varela–Entrecanales ◽

Antonio Molina–Picó ◽

Borja Vargas

Keyword(s):

Body Temperature ◽

Sensitivity And Specificity ◽

Scientific Literature ◽

Statistical Significance ◽

Permutation Entropy ◽

Limiting Factor ◽

Embedding Dimension ◽

Class Segmentation ◽

Biosignal Classification

Two main weaknesses have been identified for permutation entropy (PE): the neglect of subsequence pattern differences in terms of amplitude and the possible ambiguities introduced by equal values in the subsequences. A number of variations or customizations to the original PE method to address these issues have been proposed in the scientific literature recently. Specifically for ties, methods have tried to remove the ambiguity by assigning different weighted or computed orders to equal values. Although these methods are able to circumvent such ambiguity, they can substantially increase the algorithm costs, and a general characterization of their practical effectiveness is still lacking. This paper analyses the performance of PE using several biomedical datasets (electroencephalogram, heartbeat interval, body temperature, and glucose records) in order to quantify the influence of ties on its signal class segmentation capability. This capability is assessed in terms of statistical significance of the PE differences between classes and classification sensitivity and specificity. Being obvious that ties modify the PE results, we hypothesize that equal values are intrinsic to the acquisition process, and therefore, they impact all the classes more or less equally. The experimental results confirm ties are often not the limiting factor for PE, even they can be beneficial as a sort of stochastic resonance, and it can be far more effective to focus on the embedding dimension instead.

Download Full-text