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"Entropy method"
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A Comprehensive Weight-Based Severity Evaluation Method of Voltage Sag in Distribution Networks
With the increasing use of sensitive loads in frequency converters and in relays in distribution networks, voltage sag has become a major power quality issue that urgently needs to be solved. For the purpose of improving the understanding of voltage sag severity in distribution networks, a comprehensive weight-based severity evaluation method of voltage sag is presented in this paper. First, a multi-side index system that takes into account the combined influence of the source, network, and the load is established. A comprehensive weight method, which combines the improved analytic hierarchy process (IAHP) and the entropy method, is then adopted to determine the index weight. The weight of each index and the degree of superiority are linearly weighted to obtain the severity of voltage sag at different observation points. Finally, the effectiveness of the proposed method is verified using a distribution network model established in DIgSILENT PowerFactory (15.1.7, Gomaringen, Germany).
Journal Article
Ni-doped SnS2: an investigation into its optical, magnetic, and electronic structures
The electronic and local structure of dilute magnetic materials with 2.5%, 5%, and 7.5% Ni-doped SnS
2
was characterized using X-ray diffraction (XRD) data. These magnetic semiconductors can be used in spintronics, half-metals, and valleytronics. This research utilizes XRD data to elucidate the electron density mapping (electronic structure) of 3D and 2D MEM (maximum entropy method), focusing on bonding behavior and the accumulation of interstitial charges in regions outside the regular lattice. Pure tin disulfide (SnS
2
) is diamagnetic, but nickel (Ni) doping converts it to mild ferromagnetism, with a maximum magnetization of 0.4726 emu/g and 0.4659 emu/g and a coercivity of 78 Oe and 93 Oe at 2.5% and 7.5% Ni concentrations, respectively. Using MEM electron density analysis, magnetic saturation and coercivity are also highly connected. The 5% Ni-doped SnS
2
composition has the highest interstitial charge, resulting in a more covalent character responsible for excellent electrical conduction and reduced magnetism. Optical absorption and energy gap engineering are discussed based on cation deficiency analysis employing XRD data. Photoluminescence (PL) emission reveals that Ni doping has no direct influence on SnS
2
systems. However, Ni doping in SnS
2
increases the vacancy/interstitial charge, which indirectly corresponds with PL emission. Electron spin resonance (ESR) analysis reveals the presence of interstitial Ni
2+
and substitutional Ni
3+
ions. This study found a correlation between charge buildup at substitutional and interstitial sites, type, and strength of bonding, and physical properties like magnetism and optical properties.
Journal Article
Entropy Theory and its Application in Environmental and Water Engineering
Entropy Theory and its Application in Environmental and Water Engineering responds to the need for a book that deals with basic concepts of entropy theory from a hydrologic and water engineering perspective and then for a book that deals with applications of these concepts to a range of water engineering problems. The range of applications of entropy is constantly expanding and new areas finding a use for the theory are continually emerging. The applications of concepts and techniques vary across different subject areas and this book aims to relate them directly to practical problems of environmental and water engineering. The book presents and explains the Principle of Maximum Entropy (POME) and the Principle of Minimum Cross Entropy (POMCE) and their applications to different types of probability distributions. Spatial and inverse spatial entropy are important for urban planning and are presented with clarity. Maximum entropy spectral analysis and minimum cross entropy spectral analysis are powerful techniques for addressing a variety of problems faced by environmental and water scientists and engineers and are described here with illustrative examples. Giving a thorough introduction to the use of entropy to measure the unpredictability in environmental and water systems this book will add an essential statistical method to the toolkit of postgraduates, researchers and academic hydrologists, water resource managers, environmental scientists and engineers. It will also offer a valuable resource for professionals in the same areas, governmental organizations, private companies as well as students in earth sciences, civil and agricultural engineering, and agricultural and rangeland sciences. This book: * Provides a thorough introduction to entropy for beginners and more experienced users * Uses numerous examples to illustrate the applications of the theoretical principles * Allows the reader to apply entropy theory to the solution of practical problems * Assumes minimal existing mathematical knowledge * Discusses the theory and its various aspects in both univariate and bivariate cases * Covers newly expanding areas including neural networks from an entropy perspective and future developments.
eBook
Measurement and spatiotemporal characteristics of China’s green finance
To study the extent of green finance development in China, this article constructs a green finance index system and employs the entropy value method to measure China’s green finance by using a yearly provincial panel data from 2001 to 2020. The Thiel and Moran indices are then used to systematically analyze the temporal and spatial distribution of China’s regional green finance. The findings are summarized as follows. Firstly, the overall green finance index in China experiences an upward trend. The development of green finance in the eastern region is superior to that in other regions in terms of absolute value and growth rate. Moreover, the differences in China’s green finance index have shown an increasing trend over the last two decades, which is mostly contributed by the intra-regional differences. Finally, the inter-regional distribution of green finance index demonstrates that green finance development has a spatial spillover effect.
Journal Article
Structural global reliability assessment considering nonlinear correlation effects by enhanced high-order moment method
The global reliability analysis of complex engineering structures considering the correlations between basic random variables remains a challenge, especially for nonlinear correlation problems. In this work, to take into account the influence of nonlinear correlation between random variables, an enhanced high-order moment method is proposed for structural global reliability analysis. Firstly, the traditional Nataf transformation is reviewed, and the generalized Nataf transformation is presented by introducing the Copula theory. Secondly, the corresponding performance functions of global reliability problems are described uniformly by the state variable description method, and the GL
2
-discrepancy point set is developed for the high-order moments estimation and sensitivity analysis of the state variable. Thirdly, the global reliability of the structures is accurately determined by using the improved maximum entropy method (IMEM). Finally, two examples, including one static and one dynamic, are investigated to demonstrate the accuracy and efficiency of the proposed method and the influence of nonlinear correlation between random variables on the global reliability of the structures, in which the results obtained from the proposed method are compared with Monte Carlo simulation (MCS) method. The results of the examples show the nonlinear correlation between random variables has a significant impact on the global reliability of structures, and the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and global reliability analysis.
Journal Article
Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking
Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N2 atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.Graphical Abstract
Journal Article
Parameter Estimation of the Dirichlet Distribution Based on Entropy
The Dirichlet distribution as a multivariate generalization of the beta distribution is especially important for modeling categorical distributions. Hence, its applications vary within a wide range from modeling cell probabilities of contingency tables to modeling income inequalities. Thus, it is commonly used as the conjugate prior of the multinomial distribution in Bayesian statistics. In this study, the parameters of a bivariate Dirichlet distribution are estimated by entropy formalism. As an alternative to maximum likelihood and the method of moments, two methods based on the principle of maximum entropy are used, namely the ordinary entropy method and the parameter space expansion method. It is shown that in estimating the parameters of the bivariate Dirichlet distribution, the ordinary entropy method and the parameter space expansion method give the same results as the method of maximum likelihood. Thus, we emphasize that these two methods can be used alternatively in modeling bivariate and multinomial Dirichlet distributions.
Journal Article
Location of Cu2+ in CHA zeolite investigated by X-ray diffraction using the Rietveld/maximum entropy method
Accurate structural models of reaction centres in zeolite catalysts are a prerequisite for mechanistic studies and further improvements to the catalytic performance. The Rietveld/maximum entropy method is applied to synchrotron powder X-ray diffraction data on fully dehydrated CHA-type zeolites with and without loading of catalytically active Cu2+ for the selective catalytic reduction of NOx with NH3 . The method identifies the known Cu2+ sites in the six-membered ring and a not previously observed site in the eight-membered ring. The sum of the refined Cu occupancies for these two sites matches the chemical analysis and thus all the Cu is accounted for. It is furthermore shown that approximately 80% of the Cu2+ is located in the new 8-ring site for an industrially relevant CHA zeolite with Si/Al = 15.5 and Cu/Al = 0.45. Density functional theory calculations are used to corroborate the positions and identity of the two Cu sites, leading to the most complete structural description of dehydrated silicoaluminate CHA loaded with catalytically active Cu2+ cations.
Journal Article
A Fast and Robust Range Alignment Method for ISAR Imaging Based on a Deep Learning Network and Regional Multi-Scale Minimum Entropy Method
In inverse synthetic aperture radar (ISAR) imaging, range alignment (RA) is crucial for translational compensation. To address the need for rapidity and accuracy in the RA process, a fast and robust range alignment method is proposed based on a deep learning network and minimum entropy (ME) method. The proposed method consists primarily of two components: the CNN-RNN attention mechanism network (CRAN) architecture and the regional multi-scale minimum entropy (RMSME) method. The main distinction of this method from existing approaches lies in its utilization of a deep learning network for rapid coarse alignment, followed by the search for minimum entropy within local regions at multiple scales. The integration strategy effectively addresses the current challenges of poor generalization in deep learning networks and low efficiency in the traditional ME method. The experimental results of simulation data indicate that the proposed method achieves the best range alignment performance compared to RNN, CRAN, and the traditional ME method. The experimental results of the measured data further validate the practicality of the proposed method. This research provides reference significance for the joint application of deep learning and traditional methods in the RA process.
Journal Article