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Entropy
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Multiscale Entropy Approaches and Their Applications III
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Multiscale Entropy Approaches and Their Applications III

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 8227

Special Issue Editor

Dr. Anne Humeau-Heurtier

E-Mail Website
Guest Editor
Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), GEII Department, University of Angers, IUT, 4 Boulevard Lavoisier, BP 42018, 49016 Angers CEDEX, France
Interests: signal and image processing for the biomedical field; multiscale and entropy-based analysis; image texture analysis; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Multiscale entropy measures have been proposed from the beginning of the 2000s to evaluate the complexity of time series, by taking into account the multiple time scales in physical systems. Since then, these approaches have received a great deal of attention and have been used in a large range of applications. Multivariate approaches have also been developed.

The algorithms for a multiscale entropy approach are composed of two main steps: (i) a coarse-graining procedure to represent the system’s dynamics on different scales and (ii) the entropy computation for the original signal and for the coarse-grained time series to evaluate the irregularity for each scale. Moreover, different entropy measures have been associated with the coarse-graining approach, each one having its advantages and drawbacks: approximate entropy, sample entropy, permutation entropy, fuzzy entropy, distribution entropy, dispersion entropy, etc.

Furthermore, recently entropy measures for multidimensional data (images, volumes) have been proposed.

In this Special Issue, we would like to collect papers focusing on both the theory and applications of multiscale entropy approaches. Any kind of entropy measure is considered (see above).

The main topics of this Special Issue include (but are not limited to):

  • Improvement of the coarse-graining concept;
  • Improvement in the entropy measure itself;
  • Applications of the multiscale approach on univariate or multivariate time series.

One-dimensional and multidimensional data are welcome. Applications can include biomedical engineering, chemical engineering, hydrology, pharmaceutical sciences, financial analyses, neurosciences, industrial engineering, geosciences, information sciences, etc.

Volume I: Multiscale Entropy Approaches and Their Applications

Volume II: Multiscale Entropy Approaches and Their Applications II

Dr. Anne Humeau-Heurtier
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (4 papers)

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12 pages, 2900 KiB  
Article
Application of Multiscale Sample Entropy in Assessing Effects of Exercise Training on Skin Blood Flow Oscillations in People with Spinal Cord Injury
by Fuyuan Liao, Hengyang Zhao, Cheng-Feng Lin, Panpan Chen, Philbert Chen, Kingsley Onyemere and Yih-Kuen Jan
Entropy 2023, 25(4), 690; https://doi.org/10.3390/e25040690 - 19 Apr 2023
Cited by 1 | Viewed by 1753
Abstract
Spinal cord injury (SCI) causes a disruption of autonomic nervous regulation to the cardiovascular system, leading to various cardiovascular and microvascular diseases. Exercise training is an effective intervention for reducing risk for microvascular diseases in healthy people. However, the effectiveness of exercise training [...] Read more.
Spinal cord injury (SCI) causes a disruption of autonomic nervous regulation to the cardiovascular system, leading to various cardiovascular and microvascular diseases. Exercise training is an effective intervention for reducing risk for microvascular diseases in healthy people. However, the effectiveness of exercise training on improving microvascular function in people with SCI is largely unknown. The purpose of this study was to compare blood flow oscillations in people with spinal cord injury and different physical activity levels to determine if such a lifestyle might influence skin blood flow. A total of 37 participants were recruited for this study, including 12 athletes with SCI (ASCI), 9 participants with SCI and a sedentary lifestyle (SSCI), and 16 healthy able-bodied controls (AB). Sacral skin blood flow (SBF) in response to local heating at 42 °C for 50 min was measured using laser Doppler flowmetry. The degree of the regularity of blood flow oscillations (BFOs) was quantified using a multiscale entropy approach. The results showed that BFO was significantly more irregular in ASCI and AB compared to SSCI during the maximal vasodilation period. Our results also demonstrate that the difference in the regularity of BFOs between original SBF signal and phase-randomized surrogate time series was larger in ASCI and AB compared to SSCI. Our findings indicate that SCI causes a loss of complexity of BFOs and exercise training may improve complexity in people with SCI. This study demonstrates that multiscale entropy is a sensitive method for detecting differences between different categories of people with SCI and might be able to detect effects of exercise training related to skin blood flow. Full article
(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications III)
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20 pages, 9362 KiB  
Article
Damage Detection of Regular Civil Buildings Using Modified Multi-Scale Symbolic Dynamic Entropy
by Tzu-Kang Lin, Dong-You Lee, Yu-Chung Hsu and Kai-Wei Kuo
Entropy 2022, 24(7), 987; https://doi.org/10.3390/e24070987 - 17 Jul 2022
Cited by 1 | Viewed by 1474
Abstract
Based on the examination of the fundamental characteristics of structures, structural health monitoring (SHM) has received increased attention in recent years. Studies have shown that the SHM method using entropy analysis can precisely identify the damaged location of the structure, which is very [...] Read more.
Based on the examination of the fundamental characteristics of structures, structural health monitoring (SHM) has received increased attention in recent years. Studies have shown that the SHM method using entropy analysis can precisely identify the damaged location of the structure, which is very helpful for the daily inspection or maintenance of civil structures. Although entropy analysis has shown excellent accuracy, it still consumes too much time and too many resources in terms of data processing. To improve the dilemma, in this study, modified multi-scale symbolic dynamic entropy (MMSDE) is adopted to identify the damaged location of the civil structure. A damage index (DI) based on the entropy diagram is also proposed to clearly indicate the damage location. A seven-story numerical model was created to verify the efficiency of the proposed SHM system. The results of the analysis of each case of damage show that the MMSDE curve for the damaged floor is lower than that for the healthy floor, and the structural damage can be correctly diagnosed by the damage index. Subsequently, a scaled-down steel benchmark experiment, including 15 damage cases, was conducted to verify the practical performance of the SHM system. The confusion matrix was used to further evaluate the SHM system. The results demonstrated that the MMSD-based system can quickly diagnose structural safety with reliability and accuracy. It can be used in the field of long-term structural health monitoring in the near future. Full article
(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications III)
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33 pages, 15040 KiB  
Article
Remaining Useful Life Prediction Model for Rolling Bearings Based on MFPE–MACNN
by Yaping Wang, Jinbao Wang, Sheng Zhang, Di Xu and Jianghua Ge
Entropy 2022, 24(7), 905; https://doi.org/10.3390/e24070905 - 30 Jun 2022
Cited by 6 | Viewed by 1724
Abstract
Aiming to resolve the problem of redundant information concerning rolling bearing degradation characteristics and to tackle the difficulty faced by convolutional deep learning models in learning feature information in complex time series, a prediction model for remaining useful life based on multiscale fusion [...] Read more.
Aiming to resolve the problem of redundant information concerning rolling bearing degradation characteristics and to tackle the difficulty faced by convolutional deep learning models in learning feature information in complex time series, a prediction model for remaining useful life based on multiscale fusion permutation entropy (MFPE) and a multiscale convolutional attention neural network (MACNN) is proposed. The original signal of the rolling bearing was extracted and decomposed by resonance sparse decomposition to obtain the high-resonance and low-resonance components. The multiscale permutation entropy of the low-resonance component was calculated. Moreover, the locally linear-embedding algorithm was used for dimensionality reduction to remove redundant information. The multiscale convolution module was constructed to learn the feature information at different time scales. The attention module was used to fuse the feature information and input it into the remaining useful life prediction module for evaluation. The appropriate network structure and parameter configuration were determined, and a multiscale convolutional attention neural network was designed to determine the remaining useful life prediction model. The results show that the method demonstrates effectiveness and superiority in degrading the feature information representation and improving the remaining useful life prediction accuracy compared with other models. Full article
(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications III)
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15 pages, 1891 KiB  
Article
Novel Application of Multiscale Cross-Approximate Entropy for Assessing Early Changes in the Complexity between Systolic Blood Pressure and ECG R-R Intervals in Diabetic Rats
by Wei-Min Liu, Hsin-Ru Liu, Po-Wei Chen, Huai-Ren Chang, Chen-Mao Liao and An-Bang Liu
Entropy 2022, 24(4), 473; https://doi.org/10.3390/e24040473 - 29 Mar 2022
Cited by 5 | Viewed by 2222
Abstract
Cardiac autonomic neuropathy (CAN) is a common complication of diabetes mellitus, and can be assessed using heart rate variability (HRV) and the correlations between systolic blood pressure (SBP) and ECG R-R intervals (RRIs), namely baroreflex sensitivity (BRS). In this study, we propose a [...] Read more.
Cardiac autonomic neuropathy (CAN) is a common complication of diabetes mellitus, and can be assessed using heart rate variability (HRV) and the correlations between systolic blood pressure (SBP) and ECG R-R intervals (RRIs), namely baroreflex sensitivity (BRS). In this study, we propose a novel parameter for the nonlinear association between SBP and RRIs based on multiscale cross-approximate entropy (MS-CXApEn). Sixteen male adult Wistar Kyoto rats were equally divided into two groups: streptozotocin-induced diabetes and age-matched controls. RRIs and SBP were acquired in control rats and the diabetic rats at the onset of hyperglycemia and insulin-treated euglycemia to determine HRV by the ratio of low-frequency to high-frequency power (LF/HF) and Poincaré plot as SSR (SD1/SD2), BRS, and MS-CXApEn. SSR and BRS were not significantly different among the three groups. The LF/HF was significantly higher in the hyperglycemic diabetics than those in the controls and euglycemic diabetic rats. MS-CXApEn was higher in the diabetic hyperglycemic rats than the control rats from scales 2 to 10, and approached the values of controls in diabetic euglycemic rats at scales 9 and 10. Conclusions: We propose MS-CXApEn as a novel parameter to quantify the dynamic nonlinear interactions between SBP and RRIs that reveals more apparent changes in early diabetic rats. Furthermore, changes in this parameter were related to correction of hyperglycemia and could be useful for detecting and assessing CAN in early diabetes. Full article
(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications III)
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