Flow characteristics and Shannon entropy analysis of dense-phase pneumatic conveying under high pressure

Experiments of dense-phase pneumatic conveying of pulverized coal using nitrogen are carded out in an experimental test facility with the conveying pressure up to 4. 0 MPa and the gas-solid ratio up to 450 kg/m^3. The influences of different conveying differential pressures, coal moisture contents, gas volume flow rates and superficial velocities on the solid-gas ratios are investigated. Shannon entropy analysis of pressure fluctuation time series is developed to reveal the flow characteristics. Through investigation of the distribution of the Shannon entropy under different conditions, the flow stability and the evolutional tendency of the Shannon entropy in different regimes and regime transition processes are discovered, and the relationship between the Shannon entropy and the flow regimes is also established. The results indicate that the solid-gas ratio and the Shannon entropy rise with the increase in conveying differential pressure. The solid-gas ratio and the Shannon entropy reveal preferable regularity with gas volume flow rates. The Shannon entropy is different for different flow regimes, and can be used to identify the flow regimes. Both mass flow rate and the Shannon entropy decrease with the increase in moisture contents. The Shannon entropy analysis is a feasible approach for researching the characteristics of flow regimes, flow stability and flow regime transitions in dense-phase pneumatic conveying under high pressure.

Effects of Shannon entropy and electric field on polaron in RbCl triangular quantum dot

In this paper, the time evolution of the quantum mechanical state of a polaron is examined using the Pekar type variational method on the condition of the electric-LO-phonon strong-coupling and polar angle in RbC1 triangular quantum dot. We obtain the eigenenergies, and the eigenfunctions of the ground state, and the first excited state respectively. This system in a quantum dot can be treated as a two-level quantum system qubit and the numerical calculations are performed. The effects of Shannon entropy and electric field on the polaron in the RbC1 triangular quantum dot are also studied.

Shannon Entropy as a Measurement of the Information in a Multiconfiguration Dirac-Fock Wavefunction

Discrete Shannon entropy is applied to describe the information in a multiconfiguration Dirac Fock wavefunction. The dependence of Shannon entropy is shown as enlarging the configuration space and it can reach saturation when there are enough configuration state wavefunctions to obtain the convergent energy levels; that is, the calculation procedure in multiconfiguration Dirae Fock method is an entropy saturation process. At the same accuracy level, the basis sets for the smallest entropy are best able to describe the energy state. Additionally, a connection between the sudden change of Shannon information entropies and energy level crossings along with isoelectronic sequence can be set up, which is helpful to find the energy level crossings of interest in interpreting and foreseeing the inversion scheme of energy levels for an x-ray laser.

Invariance and Noises of Shannon Entropy for Information on Oxidative Activity of DNA in All Living Cells for Medical Diagnostics

We analyze oxidative activity of DNA due to fluorescence of chromosomes inside cells, using flow cytometry method with nanometer spatial resolution. Statistics of fluorescence is presented in histogram as frequency distributions of flashes in the dependence on their intensity and in distributions of Shannon entropy, which was defined on the base of normalized distribution of information in original histogram for frequency of flashes. We show that overall sum of entropy, i.e. total entropy E , for any histogram is invariant and has identical trends of changes all values of E(r) = lnr at reduction of histogram’ rank r. This invariance reflects informational homeostasis of chromosomes activity in multi-scale networks of entropy inside all cells in various samples of blood for DNA inside neutrophils, lymphocytes, inside all leukocytes of human and inside chicken erythrocytes for various dyes, colors and various excitations of fluorescence. Informational homeostasis of oxidative activity of 3D DNA in the full set of chromosomes inside living cells exists for any Shannon-Weaver index of biodiversity of cells, at any state of health different beings. Regulation perturbations in information activity DNA provides informational adaptability and vitality of cells at homeostasis support. Noises of entropy, during regulation of informational homeostasis, depend on the states of health in real time. The main structural reconstructions of chromosomal correlations, corresponding to self-regulation of homeostasis, occur in the most large-scale networks of entropy, for rank r<32. We show that stability of homeostasis is supported by activity of all 46 chromosomes inside cells. Patterns, hidden switching and branching in sequences of averages of H?lder and central moments for noises in regulation of homeostasis define new opportunities in diagnostics of health and immunity. All people and all aerobic beings have one overall homeostatic level for countdown of information activity of DNA inside cells. We noted very bad and dangerous properties of artificial cells with other levels of informational homeostasis for all aerobic beings in foods, medical treatment and in biotechnologies.

An Improvement to Multiple Criteria ABC Inventory Classification Using Shannon Entropy

This paper extends the Ng-model [Ng, 2007] for multiple criteria ABC inventory classification based upon Shannon entropy. The proposed approach determines the common weights associated with all criteria importance rankings, and provides a comprehensive scoring scheme by aggregating all rankings of the criteria importance. A numerical illustration is presented to compare the model with previous studies.

Nonrelativistic Shannon information entropy for Kratzer potential

The Shannon information entropy is investigated within the nonrelativistic framework. The Kratzer potential is con- sidered as the interaction and the problem is solved in a quasi-exact analytical manner to discuss the ground and first excited states. Some interesting features of the information entropy densities as well as the probability densities are demonstrated. The Bialynicki-Birula-Mycielski inequality is also tested and found to hold for these cases.

Experimental study and Shannon entropy analysis of pressure fluctuations and flow mode transition in fluidized dense phase pneumatic conveying of fly ash

The objective of this study was to relate experimental pressure fluctuation behavior to the transition in mode of flow observed in fluidized dense phase pneumatic conveying of fly ash.Shannon entropy and wavelet analysis were utilized to extract features of the flow regimes.Daubechies db4 wavelet analysis of pulsating air pressure revealed that the flow mechanism of fly ash in a fluidized dense phase possessed non-steady characteristics associated with gradual aeration of dunes along the direction of flow.Variations of Shannon entropy values along the length of the pipeline were assessed to determine the location at which the flow converted from dense to dilute phase mode.The effects of conveying parameters and specific power consumption on Shannon entropy and variations of the local power consumption coefficient are discussed.

Experimental investigation into transient pressure pulses during pneumatic conveying of fine powders using Shannon entropy

This paper presents the results of an ongoing investigation into transient pressure pulses using Shan- non entropy. Pressure fluctuations （produced by gas-solid two-phase flow during fluidized dense-phase conveying） are recorded by pressure transducers installed at strategic locations along a pipeline. This work validates previous work on identifying the flow mode from pressure signals （Mittal, Mallick, ＆ Wypych, 2014）. Two different powders, namely fly ash （median particle diameter 45 μm, particle den- sity 1950 kg/m3. loosely poured bulk density 950 kg/m3） and cement （median particle diameter 15 p,m, particle density 3060 kg/m3, loosely poured bulk density 1070 kg/m3）, are conveyed through different pipelines （51 mm I.D. × 70 m length and 63 mm I.D. × 24 m length）. The transient nature of pressure fluc- tuations （instead of steady-state behavior） is considered in investigating flow characteristics. Shannon entropy is found to increase along straight pipe sections for both solids and both pipelines. However, Shannon entropy decreases after a bend. A comparison of Shannon entropy among different ranges of superficial air velocity reveals that high Shannon entropy corresponds to very low velocities （i.e. 3-5 m/s） and very high velocities （i.e. 11-14 m/s） while low Shannon entropy corresponds to mid-range velocities （i.e. 6-8 m/s）.

The Use of GIS, Remote Sensing and Shannon’s Entropy Statistical Techniques to Analyze and Monitor the Spatial and Temporal Patterns of Urbanization and Sprawl in Zarqa City, Jordan

The aim of this study is to understand and quantify the urban growth and trend in Zarqa city during the period 1990 to 2014 and to produce land use and cover map for the studied area through the use of the GIS and remote sensing techniques with Shannon’s Entropy statistical method. For this purpose, three Landsat images were used for land use classification by using supervised maximum likelihood classification techniques to extract and assess the changes of urban lands. The results indicated that the urban areas in Zarqa city increased by 22.15% in the period from 1990 to 2005 and 14.86% from 2005 to 2014, with a rate of expansion of 0.96 and by 1.31 km2/ year for the two time periods respectively. The entropy value increased from 1.20 in the first period to 1.38 in the second, while the entropy value for the NE, NW, SE and SW zones showed high values, which confirmed that urban expansion and sprawling had existed in the past twenty four years in the study area. Urban expansion and sprawl cause different impacts on the natural, economic, and aesthetic aspects of the city which lead and guide government officials and planners to understand and monitor current growth and visualize future growth.

Quantile-Based Shannon Entropy for Record Statistics

The quantile-based entropy measures possess some unique properties than their distribution function approach.The present communication deals with the study of the quantile-based Shannon entropy for record statistics.In this regard a generalized model is considered for which cumulative distribution function or probability density function does not exist and various examples are provided for illustration purpose.Further we consider the dynamic versions of the proposed entropy measure for record statistics and also give a characterization result for that.At the end,we study F^(α)-family of distributions for the proposed entropy measure.

Performance Evaluation of Public Bus Transportation by Using DEA Models and Shannon’s Entropy:An Example From a Company in a Large City of China

The purpose of this paper is to assess the operational efficiency of a public bus transportation via a case study from a company in a large city of China by using data envelopment analysis(DEA)model and Shannon’s entropy.This company operates 37 main routes on the backbone roads.Thus,it plays a significant role in public transportation in the city.According to bus industry norms,an efficiency evaluation index system is constructed from the perspective of both company operations and passenger demands.For passenger satisfaction,passenger waiting time and passenger-crowding degree are considered,and they are undesirable indicators.To describe such indicators,a superefficient DEA model is constructed.With this model,by using actual data,efficiency is evaluated for each bus route.Results show that the DEA model with Shannon’s entropy being combined achieves more reasonable results.Also,sensitivity analysis is presented.Therefore,the results are meaningful for the company to improve its operations and management.

On Clausius, Boltzmann and Shannon Notions of Entropy

Discrete dynamical systems are given by the pair (X,f) where X is a compact metric space and f: X→X is a continuous map. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. Among them, one of the most popular is that of topological entropy. In modern applications, other conditions on X and f have been considered. For example, X can be non-compact or f can be discontinuous (only in a finite number of points and with bounded jumps on the values of f or even non-bounded jumps). Such systems are interesting from theoretical point of view in Topological Dynamics and appear frequently in applied sciences such as Electronics and Control Theory. In this paper, we are reviewing the origins of the notion of entropy and studying some developing of it leading to modern notions of entropies. At the same time, we will incorporate some mathematical foundations of such old and new ideas until the appearance of Shannon entropy. To this end, we start with the introduction for the first time of the notion of entropy in thermodynamics by R. Clausius and its evolution by L. Boltzmann until the appearing in the twenty century of Shannon and Kolmogorov-Sinai entropies and the subsequent topological entropy. In turn, such notions have evolved to other recent situations where it is necessary to give some extended versions of them adapted to new problems. Of special interest is to appreciate the connexions of the notions of entropy from Boltzmann and Shannon. Since this history is long, we will not deal with the Kolmogorov-Sinai entropy or with topological entropy and modern approaches.

Entropy Bayesian Analysis for the Generalized Inverse Exponential Distribution Based on URRSS

This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.

Novel Approach for Fault Detection and Diagnosis of Sensors in Air Handling Units Using Wavelet Energy Entropy

A novel fault diagnosis method for sensors in air handling unit（AHU） using wavelet energy entropy was presented. Instead of directly comparing the numerous data under noise conditiom, the wavelet energy entropy residual was compared in the proposed method. Three.level wavelet analysis was used to decompose the measurement data under both fault-free and faulty operation conditions. The concept of Shannon entropy was referred to define wavelet energy entropy of the wavelet coefficients. The sensor faults were diagnosed by comparing the deviation of the wavelet energy entropy of the measured signal and the estimated one with the preset threshold. Testing results showed that the wavelet energy entropy was sensitive to diagnose the biased faults. The wavelet energy entropy residuals exceed the threshold significantly when faults occur. In addition, the severer the faults were, the larger the residuals would be. The results prove that the proposed method is feasible and effective for the fault detection and diagnosis of the sensors.

Quantile Version of Mathai-Haubold Entropy of Order Statistics

Many researchers measure the uncertainty of a random variable using quantile-based entropy techniques.These techniques are useful in engineering applications and have some exceptional characteristics than their distribution function method.Considering order statistics,the key focus of this article is to propose new quantile-based Mathai-Haubold entropy and investigate its characteristics.The divergence measure of theMathai-Haubold is also considered and some of its properties are established.Further,based on order statistics,we propose the residual entropy of the quantile-based Mathai-Haubold and some of its property results are proved.The performance of the proposed quantile-based Mathai-Haubold entropy is investigated by simulation studies.Finally,a real data application is used to compare our proposed quantile-based entropy to the existing quantile entropies.The results reveal the outperformance of our proposed entropy to the other entropies.

Characteristics Extraction of Vehicle State Information Based on Entropy Calculation

A method of extracting and detecting vehicle stability state characteristics based on entropy is proposed.The vehicle’s longitudinal and lateral dynamics models are established for complex driving and maneuver conditions.The corresponding state observer is designed by adopting the moving horizon estimation algorithm,which realizes the observation of the vehicle stability state considering the global state information.Meanwhile,the Shannon entropy is modified to approximate entropy,and the approximate entropy value of the observed vehicle state is calculated.Furthermore,the optimal controller is designed to further validate the reliability of the entropy value as the reference of control system.Simulation results demonstrate that this method can quickly detect the instability state of the system during the process of vehicle driving,which provides a reference for risk prediction and active control.

A STUDY OF WAVELET ENTROPY MEASURE DEFINITION AND ITS APPLICATION FOR FAULT FEATURE PICK-UP AND CLASSIFICATION

Shannon entropy in time domain is a measure of signal or system uncertainty.When based on spectrum entropy,Shannon entropy can be taken as a measure of signal or system complexity. Therefore,wavelet analysis based on wavelet entropy measure can signify the complexity of non-steady signal or system in both time and frequency domain.In this paper,in order to meet the requirements of post-analysis on abundant wavelet transform result data and the need of information mergence,the basic definition of wavelet entropy measure is proposed,corresponding algorithms of several wavelet entropies,such as wavelet average entropy,wavelet time-frequency entropy,wavelet distance entropy, etc.are put forward,and the physical meanings of these entropies are analyzed as well.The application principle of wavelet entropy measure in ElectroEncephaloGraphy (EEG) signal analysis,mechanical fault diagnosis,fault detection and classification in power system are analyzed.Finally,take the transmission line fault detection in power system for example,simulations in two different systems,a 10kV automatic blocking and continuous power transmission line and a 500kV Extra High Voltage (EHV) transmission line,are carried out,and the two methods,wavelet entropy and wavelet modulus maxima,are compared,the results show feasibility and application prospect of the six wavelet entro- pies.

Shannon information entropies for position-dependent mass Schrdinger problem with a hyperbolic well

The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ（x） for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs（x） and ρs（p） are demonstrated. The Bialynicki-Birula-Mycielski（BBM）inequality is also tested for these states and found to hold.

Shannon information entropies for rectangular multiple quantum well systems with constant total lengths

We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum（FWHM） of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki（BBM）inequality.

Exploring Motor Imagery EEG: Enhanced EEG Microstate Analysis with GMD-Driven Density Canopy Method

The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAHC),K-means clustering,Principal Component Analysis(PCA),and Independent Component Analysis(ICA)are limited by a fixed number of microstate maps and insufficient capability in cross-task feature extraction.Tackling these limitations,this study introduces a Global Map Dissimilarity(GMD)-driven density canopy K-means clustering algorithm.This innovative approach autonomously determines the optimal number of EEG microstate topographies and employs Gaussian kernel density estimation alongside the GMD index for dynamic modeling of EEG data.Utilizing this advanced algorithm,the study analyzes the Motor Imagery(MI)dataset from the GigaScience database,GigaDB.The findings reveal six distinct microstates during actual right-hand movement and five microstates across other task conditions,with microstate C showing superior performance in all task states.During imagined movement,microstate A was significantly enhanced.Comparison with existing algorithms indicates a significant improvement in clustering performance by the refined method,with an average Calinski-Harabasz Index(CHI)of 35517.29 and a Davis-Bouldin Index(DBI)average of 2.57.Furthermore,an information-theoretical analysis of the microstate sequences suggests that imagined movement exhibits higher complexity and disorder than actual movement.By utilizing the extracted microstate sequence parameters as features,the improved algorithm achieved a classification accuracy of 98.41%in EEG signal categorization for motor imagery.A performance of 78.183%accuracy was achieved in a four-class motor imagery task on the BCI-IV-2a dataset.These results demonstrate the potential of the advanced algorithm in microstate analysis,offering a more effective tool for a deeper understanding of the spatiotemporal features of EEG signals.