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Keywords = minimum Shannon entropy criterion

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29 pages, 2047 KiB  
Article
An Integrated Two-Step Optimization Model and Aggregative Multi-Criteria Approach for Establishing Sustainable Tram Transportation Plan
by Svetla Stoilova and Ivan Pulevski
Sustainability 2025, 17(2), 543; https://doi.org/10.3390/su17020543 - 12 Jan 2025
Cited by 1 | Viewed by 1055
Abstract
The choice of the most appropriate sustainable scheme for the organization of tram transportation in cities is of great importance for tram operators, for users of transportation services, and for the protection of the environment from harmful emissions. This study aims to propose [...] Read more.
The choice of the most appropriate sustainable scheme for the organization of tram transportation in cities is of great importance for tram operators, for users of transportation services, and for the protection of the environment from harmful emissions. This study aims to propose a methodology for formulating a tram transportation plan considering technological, environmental, economic, and social indicators. The variant schemes represent the routes of a tram in the tram network. The methodology includes four stages. The first stage involves the determination of variant schemes for a transportation plan of service with trams. In the second stage, a two-step optimization model is proposed to determine the number and trams by types for each tram route for each variant scheme, and also to establish the distribution of trams by depots. The third stage includes ranking the variant schemes by applying the sequential interactive model for urban systems (SIMUS) multi-criteria method. Eleven quantitative and qualitative criteria for evaluating the tram transportation plan were introduced. A verification of the results is performed in the fourth stage. For this purpose, a comparison of the preference ranking organization method for enrichment of evaluations (PROMETHEE) method and the technique for order of preference by similarity to ideal solution (TOPSIS) method is made. Both methods have different approaches for decision making and differ from the SIMUS method. Two strategies were proposed to determine the criteria weights. One is based on the Shannon entropy method and the other uses the objective weights obtained through the SIMUS method. Finally, in the fifth stage, the results obtained through the SIMUS, PROMEHEE and TOPSIS methods are combined using the expected value obtained by applying the program evaluation and review technique method (PERT). The proposed methodology was applied to study tram transportation in Sofia, Bulgaria. Five variant schemes were considered. The schemes are optimized through the criterion of minimum energy consumption. The number of trams by routes and by type was determined. An improved scheme for tram transportation in Sofia was proposed. The scheme makes it possible to increase the frequency of the trams by 13%, to reduce the zero mileage of rolling stock, and to reduce carbon dioxide pollution by 11%. Full article
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21 pages, 4656 KiB  
Technical Note
Spaceborne Synthetic Aperture Radar Aerial Moving Target Detection Based on Two-Dimensional Velocity Search
by Jialin Hao, He Yan, Hui Liu, Wenshuo Xu, Zhou Min and Daiyin Zhu
Remote Sens. 2024, 16(13), 2392; https://doi.org/10.3390/rs16132392 - 29 Jun 2024
Viewed by 1566
Abstract
Synthetic aperture radar (SAR) can detect moving targets on the ground/sea, and high-resolution imaging on the ground/sea has critical applications in both military and civilian fields. This paper attempts to use a spaceborne SAR system to detect and image moving targets in the [...] Read more.
Synthetic aperture radar (SAR) can detect moving targets on the ground/sea, and high-resolution imaging on the ground/sea has critical applications in both military and civilian fields. This paper attempts to use a spaceborne SAR system to detect and image moving targets in the air for the first time. Due to the high velocity of aerial targets, they usually appear as two-dimensional range and azimuth direction defocus in SAR images, and clutter will also have a profound impact on target detection. To solve the above problems, a method of detecting and focusing on a spaceborne SAR target based on a two-dimensional velocity search is proposed by combining the BP algorithm. According to the current environment of the aerial target and the number of system channels, the clutter suppression methods are set and combined with two-dimensional velocity search with different precision, the Shannon entropy under different search velocity groups is used to obtain the search velocity group closest to the actual velocity and realize the integrated processing of moving target detection–focused imaging parameter estimation. Combined with simulation data, the effectiveness of the proposed method is verified. Full article
(This article belongs to the Section Remote Sensing Image Processing)
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21 pages, 2010 KiB  
Article
Technique of Gene Expression Profiles Extraction Based on the Complex Use of Clustering and Classification Methods
by Sergii Babichev and Jiří Škvor
Diagnostics 2020, 10(8), 584; https://doi.org/10.3390/diagnostics10080584 - 12 Aug 2020
Cited by 29 | Viewed by 3658
Abstract
In this paper, we present the results of the research concerning extraction of informative gene expression profiles from high-dimensional array of gene expressions considering the state of patients’ health using clustering method, ML-based binary classifiers and fuzzy inference system. Applying of the proposed [...] Read more.
In this paper, we present the results of the research concerning extraction of informative gene expression profiles from high-dimensional array of gene expressions considering the state of patients’ health using clustering method, ML-based binary classifiers and fuzzy inference system. Applying of the proposed stepwise procedure can allow us to extract the most informative genes taking into account both the subtypes of disease or state of the patient’s health for further reconstruction of gene regulatory networks based on the allocated genes and following simulation of the reconstructed models. We used the publicly available gene expressions data as the experimental ones which were obtained using DNA microarray experiments and contained two types of patients’ gene expression profiles—the patients with lung cancer tumor and healthy patients. The stepwise procedure of the data processing assumes the following steps—in the beginning, we reduce the number of genes by removing non-informative genes in terms of statistical criteria and Shannon entropy; then, we perform the stepwise hierarchical clustering of gene expression profiles at hierarchical levels from 1 to 10 using the SOTA (Self-Organizing Tree Algorithm) clustering algorithm with correlation distance metric. The quality of the obtained clustering was evaluated using the complex clustering quality criterion which is considered both the gene expression profiles distribution relative to center of the clusters where these gene expression profiles are allocated and the centers of the clusters distribution. The result of this stage execution was a selection of the optimal cluster at each of the hierarchical levels which corresponded to the minimum value of the quality criterion. At the next step, we have implemented a classification procedure of the examined objects using four well known binary classifiers—logistic regression, support-vector machine, decision trees and random forest classifier. The effectiveness of the appropriate technique was evaluated based on the use of ROC (Receiver Operating Characteristic) analysis using criteria, included as the components, the errors of both the first and the second kinds. The final decision concerning the extraction of the most informative subset of gene expression profiles was taken based on the use of the fuzzy inference system, the inputs of which are the results of the appropriate single classifiers operation and the output is the final solution concerning state of the patient’s health. To our mind, the implementation of the proposed stepwise procedure of the informative gene expression profiles extraction create the conditions for the increasing effectiveness of the further procedure of gene regulatory networks reconstruction and the following simulation of the reconstructed models considering the subtypes of the disease and/or state of the patient’s health. Full article
(This article belongs to the Section Machine Learning and Artificial Intelligence in Diagnostics)
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18 pages, 2194 KiB  
Article
Optimization of Condition Monitoring Decision Making by the Criterion of Minimum Entropy
by Ahmed Raza and Vladimir Ulansky
Entropy 2019, 21(12), 1193; https://doi.org/10.3390/e21121193 - 4 Dec 2019
Cited by 13 | Viewed by 3272
Abstract
Condition-based maintenance (CBM) is a promising technique for a wide variety of deteriorating systems. Condition-based maintenance’s effectiveness largely depends on the quality of condition monitoring. The majority of CBM mathematical models consider perfect inspections, in which the system condition is assumed to be [...] Read more.
Condition-based maintenance (CBM) is a promising technique for a wide variety of deteriorating systems. Condition-based maintenance’s effectiveness largely depends on the quality of condition monitoring. The majority of CBM mathematical models consider perfect inspections, in which the system condition is assumed to be determined error-free. This article presents a mathematical model of CBM with imperfect condition monitoring conducted at discrete times. Mathematical expressions were derived for evaluating the probabilities of correct and incorrect decisions when monitoring the system condition at a scheduled time. Further, these probabilities were incorporated into the equation of the Shannon entropy. The problem of determining the optimal preventive maintenance threshold at each inspection time by the criterion of the minimum of Shannon entropy was formulated. For the first time, the article showed that Shannon’s entropy is a convex function of the preventive maintenance threshold for each moment of condition monitoring. It was also shown that the probabilities of correct and incorrect decisions depend on the time and parameters of the degradation model. Numerical calculations show that the proposed approach to determining the optimal preventive maintenance threshold can significantly reduce uncertainty when deciding on the condition of the monitoring object. Full article
(This article belongs to the Section Multidisciplinary Applications)
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22 pages, 4907 KiB  
Article
A Novel Interference Suppression Method for Interrupted Sampling Repeater Jamming Based on Singular Spectrum Entropy Function
by Muyao Yu, Shengbo Dong, Xiangyu Duan and Shangchao Liu
Sensors 2019, 19(1), 136; https://doi.org/10.3390/s19010136 - 2 Jan 2019
Cited by 26 | Viewed by 4258
Abstract
As a new type of jamming, the interrupted sampling repeater jamming (ISRJ) derived from the digital radio frequency memory (DRFM) technology, can generate coherent multiple false targets after pulse compression. At present, the traditional interference suppression method and its improved methods have insufficient [...] Read more.
As a new type of jamming, the interrupted sampling repeater jamming (ISRJ) derived from the digital radio frequency memory (DRFM) technology, can generate coherent multiple false targets after pulse compression. At present, the traditional interference suppression method and its improved methods have insufficient characteristics and poor detection performance under the condition of low signal-to-noise ratio (SNR). Aiming at addressing this defect, this paper proposes an interference suppression method for ISRJ based on singular spectrum entropy function (SSEF) from the aspects of singular value decomposition (SVD) and information entropy theories. In this method, firstly, considering the local fine characteristics and extraction efficiency, an adaptive multi-scale segmentation (AMS) method is proposed. The purpose of this processing is to extend the salient characteristics while to smooth the similar ones. In AMS, the segmentation criterion based on average energy of segments and the constraint of minimum segmentation is also proposed, then the improved delay embedded matrix is established from the improved trajectory matrix by AMS and delay embedded mapping. Secondly, the singular spectrum of the improved delay embedded matrix is extracted by SVD. Thirdly, because the recognition algorithms based on singular spectrum analysis (SSA), classical SSE and other characteristics fail at low SNR, this paper proposes a characteristic named as SSEF retrieved from the Shannon entropy model. The following proposed entropy-based threshold detection is carried out on the echo signal to realize the band-pass filtering and interference suppression. Finally, experiment results show that in comparison with other interference suppression approaches, SSEF can increase the probability of target detection and the peak-to-side-lobe ratio (PSR) after pulse compression, which validates its stability to noise and jamming especially in the condition of low SNRs. Full article
(This article belongs to the Section Remote Sensors)
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20 pages, 10850 KiB  
Article
An Optimal Image-Based Method for Identification of Acoustic Emission (AE) Sources in Plate-Like Structures Using a Lead Zirconium Titanate (PZT) Sensor Array
by Gang Yan and Li Zhou
Sensors 2018, 18(2), 631; https://doi.org/10.3390/s18020631 - 21 Feb 2018
Cited by 3 | Viewed by 3750
Abstract
This paper proposes an innovative method for identifying the locations of multiple simultaneous acoustic emission (AE) events in plate-like structures from the view of image processing. By using a linear lead zirconium titanate (PZT) sensor array to record the AE wave signals, a [...] Read more.
This paper proposes an innovative method for identifying the locations of multiple simultaneous acoustic emission (AE) events in plate-like structures from the view of image processing. By using a linear lead zirconium titanate (PZT) sensor array to record the AE wave signals, a reverse-time frequency-wavenumber (f-k) migration is employed to produce images displaying the locations of AE sources by back-propagating the AE waves. Lamb wave theory is included in the f-k migration to consider the dispersive property of the AE waves. Since the exact occurrence time of the AE events is usually unknown when recording the AE wave signals, a heuristic artificial bee colony (ABC) algorithm combined with an optimal criterion using minimum Shannon entropy is used to find the image with the identified AE source locations and occurrence time that mostly approximate the actual ones. Experimental studies on an aluminum plate with AE events simulated by PZT actuators are performed to validate the applicability and effectiveness of the proposed optimal image-based AE source identification method. Full article
(This article belongs to the Section Physical Sensors)
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11 pages, 338 KiB  
Article
An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion
by Badong Chen, Guangmin Wang, Nanning Zheng and Jose C. Principe
Entropy 2014, 16(4), 2223-2233; https://doi.org/10.3390/e16042223 - 17 Apr 2014
Cited by 1 | Viewed by 5008
Abstract
The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are [...] Read more.
The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are imposed. A recent paper has proved that if the conditional density is conditionally symmetric and unimodal (CSUM), then the optimal MEE estimate (with Shannon entropy) equals the conditional median. In this study, we extend this result to the generalized MEE estimation where the optimality criterion is the Renyi entropy or equivalently, the α-order information potential (IP). Full article
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19 pages, 3104 KiB  
Article
Optimal Multi-Level Thresholding Based on Maximum Tsallis Entropy via an Artificial Bee Colony Approach
by Yudong Zhang and Lenan Wu
Entropy 2011, 13(4), 841-859; https://doi.org/10.3390/e13040841 - 13 Apr 2011
Cited by 231 | Viewed by 18373
Abstract
This paper proposes a global multi-level thresholding method for image segmentation. As a criterion for this, the traditional method uses the Shannon entropy, originated from information theory, considering the gray level image histogram as a probability distribution, while we applied the Tsallis entropy [...] Read more.
This paper proposes a global multi-level thresholding method for image segmentation. As a criterion for this, the traditional method uses the Shannon entropy, originated from information theory, considering the gray level image histogram as a probability distribution, while we applied the Tsallis entropy as a general information theory entropy formalism. For the algorithm, we used the artificial bee colony approach since execution of an exhaustive algorithm would be too time-consuming. The experiments demonstrate that: 1) the Tsallis entropy is superior to traditional maximum entropy thresholding, maximum between class variance thresholding, and minimum cross entropy thresholding; 2) the artificial bee colony is more rapid than either genetic algorithm or particle swarm optimization. Therefore, our approach is effective and rapid. Full article
(This article belongs to the Special Issue Tsallis Entropy)
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