Let Ф（u ×v, k, Aa, Ac） be the largest possible number of codewords among all two- dimensional （u ×v, k, λa, λc） optical orthogonal codes. A 2-D （u× v, k, λa, λ）-OOC with Ф（u× v, k, λ...Let Ф（u ×v, k, Aa, Ac） be the largest possible number of codewords among all two- dimensional （u ×v, k, λa, λc） optical orthogonal codes. A 2-D （u× v, k, λa, λ）-OOC with Ф（u× v, k, λa, λc） codewords is said to be maximum. In this paper, the number of codewords of a maximum 2-D （u × v, 4, 1, 3）-OOC has been determined.展开更多
In order to improve the global search ability of biogeography-based optimization(BBO)algorithm in multi-threshold image segmentation,a multi-threshold image segmentation based on improved BBO algorithm is proposed.Whe...In order to improve the global search ability of biogeography-based optimization(BBO)algorithm in multi-threshold image segmentation,a multi-threshold image segmentation based on improved BBO algorithm is proposed.When using BBO algorithm to optimize threshold,firstly,the elitist selection operator is used to retain the optimal set of solutions.Secondly,a migration strategy based on fusion of good solution and pending solution is introduced to reduce premature convergence and invalid migration of traditional migration operations.Thirdly,to reduce the blindness of traditional mutation operations,a mutation operation through binary computation is created.Then,it is applied to the multi-threshold image segmentation of two-dimensional cross entropy.Finally,this method is used to segment the typical image and compared with two-dimensional multi-threshold segmentation based on particle swarm optimization algorithm and the two-dimensional multi-threshold image segmentation based on standard BBO algorithm.The experimental results show that the method has good convergence stability,it can effectively shorten the time of iteration,and the optimization performance is better than the standard BBO algorithm.展开更多
The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The e...The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.展开更多
We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics...We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.展开更多
In the multilevel thresholding segmentation of the image, the classification number is always given by the supervisor. To solve this problem, a fast multilevel thresholding algorithm considering both the threshold val...In the multilevel thresholding segmentation of the image, the classification number is always given by the supervisor. To solve this problem, a fast multilevel thresholding algorithm considering both the threshold value and the classification number is proposed based on the maximum entropy, and the self-adaptive criterion of the classification number is given. The algorithm can obtain thresholds and automatically decide the classification number. Experimental results show that the algorithm is effective.展开更多
Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a var...Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.展开更多
A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main p...A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main points of the method are as follows: (1) based on the Hamiltonian principle, a maximum entropy probability density function for the extreme waveheight H, f(H)=αHγ e -βH4 is derived from a Lagrangian function subject to some necessary and rational constraints; (2) the parameters α, β, and γ in the function are expressed in terms of the mean , variance V= (H-)2 and bias B= (H-)3 ; and (3) with , V and B estimated from observed data, the n -year return-period wave height H n is computed in accordance with the formula 11-F(H n)=n , where F(H n) is defined as F(H n)=∫ H n 0f(H) d H. Examples of estimating the 50 and 100-year return period waveheights by the present method and by some currently used method from observed data acquired from two hydrographic stations are given. A comparison of the estimated results shows that the present method is superior to the others.展开更多
Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh f...Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.展开更多
Marine environmental design parameter extrapolation has important applications in marine engineering and coastal disaster prevention.The distribution models used for environmental design parameter usually pass the hyp...Marine environmental design parameter extrapolation has important applications in marine engineering and coastal disaster prevention.The distribution models used for environmental design parameter usually pass the hypothesis tests in statistical analysis,but the calculation results of different distribution models often vary largely.In this paper,based on the information entropy,the overall uncertainty test criteria were studied for commonly used distributions including Gumbel,Weibull,and Pearson-III distribution.An improved method for parameter estimation of the maximum entropy distribution model is proposed on the basis of moment estimation.The study in this paper shows that the number of sample data and the degree of dispersion are proportional to the information entropy,and the overall uncertainty of the maximum entropy distribution model is minimal compared with other models.展开更多
Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the...Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method （LSMEQFM） and that with constraint condition （LSMEQFMCC） are proposed. To improve the confidence level of quantile function estimation, scatter factor method is combined with maximum entropy method to estimate the confidence interval of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quantile function accurately on the small samples but inaccurately on the very small samples （10 samples）; LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples; with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples （10 samples）.展开更多
A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a conti...A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.展开更多
This paper investigates the maximum entropy restoration of blurred binary image.In concerning with the binary property of image,a new maximum entropy restoration methodwith binary constraint is proposed.The properties...This paper investigates the maximum entropy restoration of blurred binary image.In concerning with the binary property of image,a new maximum entropy restoration methodwith binary constraint is proposed.The properties of existence and uniqueness of solution arediscussed.The problem of maximum of entropy with two constraints is solved and the corre-sponding algorithm is given.In this paper,the maximum bounded entropy principle is employedconcerning the prior knowledge of binary image,and the maximum bounded entropy restora-tion method with binary constraint is put forward.The proposes methods,Wiener filter(WF)restoration method and maximum entropy restoration method are compared.The experimen-tal results show that the maximum entropy restoration method and maximum bounded entropyrestoration method with binary constraint can improve the quality of restored image.展开更多
Tibetan spruce (Picea smithiana) is an endemic species of the Himalayas,and it distributes only in a re-stricted area with very low number.To address the lack of detailed distributional information,we used maximum en-...Tibetan spruce (Picea smithiana) is an endemic species of the Himalayas,and it distributes only in a re-stricted area with very low number.To address the lack of detailed distributional information,we used maximum en-tropy (Maxent) niche-based model to predict the species' potential distribution from limited occurrence-only records.The location data of P.smithiana,relative bioclimatic variables,vegetation data,digital elevation model (DEM),and the derived data were analyzed in Maxent.The receiver operating characteristic (ROC) curve was applied to assess the prediction accuracy.The Maxent jackknife test was performed to quantify the training gains from data layers and the response of P.smithiana distribution to four typical environmental variables was analyzed.Results show that the model performs well at the regional scale.There is a potential for continued expansion of P.smithiana population numbers and distribution in China.P.smithiana potentially distributes in the lower reaches of Gyirong Zangbo and Poiqu rivers in Gyirong and Nyalam counties in Qomolangma (Mount Everest) National Nature Preserve (QNNP),China.The species prefers warm temperate climate in mountain area and mainly distributes in needle-leaved evergreen closed to open forest and mixed forest along the river valley at relatively low altitudes of about 2000-3000 m.Model simulations suggest that distribution patterns of rare species with few species numbers can be well predicted by Max-ent.展开更多
A crowdsourcing experiment in which viewers (the “crowd”) of a British Broadcasting Corporation (BBC) television show submitted estimates of the number of coins in a tumbler was shown in an antecedent paper (Part 1)...A crowdsourcing experiment in which viewers (the “crowd”) of a British Broadcasting Corporation (BBC) television show submitted estimates of the number of coins in a tumbler was shown in an antecedent paper (Part 1) to follow a log-normal distribution ∧(m,s2). The coin-estimation experiment is an archetype of a broad class of image analysis and object counting problems suitable for solution by crowdsourcing. The objective of the current paper (Part 2) is to determine the location and scale parameters (m,s) of ∧(m,s2) by both Bayesian and maximum likelihood (ML) methods and to compare the results. One outcome of the analysis is the resolution, by means of Jeffreys’ rule, of questions regarding the appropriate Bayesian prior. It is shown that Bayesian and ML analyses lead to the same expression for the location parameter, but different expressions for the scale parameter, which become identical in the limit of an infinite sample size. A second outcome of the analysis concerns use of the sample mean as the measure of information of the crowd in applications where the distribution of responses is not sought or known. In the coin-estimation experiment, the sample mean was found to differ widely from the mean number of coins calculated from ∧(m,s2). This discordance raises critical questions concerning whether, and under what conditions, the sample mean provides a reliable measure of the information of the crowd. This paper resolves that problem by use of the principle of maximum entropy (PME). The PME yields a set of equations for finding the most probable distribution consistent with given prior information and only that information. If there is no solution to the PME equations for a specified sample mean and sample variance, then the sample mean is an unreliable statistic, since no measure can be assigned to its uncertainty. Parts 1 and 2 together demonstrate that the information content of crowdsourcing resides in the distribution of responses (very often log-normal in form), which can be obtained empirically or by appropriate modeling.展开更多
The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limi...The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.展开更多
The maximum entropy spectral characteristics of seismicity in the seismic enhanced region of 11 great earthquakes is analysed in this paper to seek the difference of seismic period spectral structure between the norm...The maximum entropy spectral characteristics of seismicity in the seismic enhanced region of 11 great earthquakes is analysed in this paper to seek the difference of seismic period spectral structure between the normal and the abnormal stage of seismic activity in this paper. The results show that, during decades or even one hundred years before great earthquakes, only short periods with 6.5～24.3 years appear, and long ones disappear. Otherwise, long periods with 18.5～38.5 years exist chiefly within the normal stages. Decades years after great earthquakes, the period spectra of seismicity are generally about several or ten years. Then the characteristics of great earthquakes is explained physically by applying the strong body seismogenic model, so a method of studying and predicting great earthquakes is offered.展开更多
This paper presents an analytical, numerical, and experimental study on atomization characteristics and droplet distribution of a twin-fluid two-phase internal mixing atomizer to develop a Maximum Entropy Method(MEM)....This paper presents an analytical, numerical, and experimental study on atomization characteristics and droplet distribution of a twin-fluid two-phase internal mixing atomizer to develop a Maximum Entropy Method(MEM). A two-phase Eulerian-Lagrangian method is utilized for atomization modeling of the inside and outside atomizer. In order to modify energy and momentum sources in the MEM, parametric studies are performed, and experimental tests are carried out to verify the results by applying the shadowgraph method. An advanced test stand is developed to prepare a wide range of changes in atomization characteristics and mixing ratios. A high degree of consistency is found between numerical results from the developed MEM and experimental tests with different gas-phase pressures and liquid flow rates. The droplet diameter and velocity distribution are reviewed based on various Weber numbers, sources of energy, and momentum. Turbulence modeling assists to estimate the breakup length and time scale precisely in the developed MEM, and distribution ranges with mean values are achieved. With reference to a strong correlation between upstream turbulence flow and the developed MEM verified by experimental tests, an ideal droplet size and velocity distribution prediction is observed.展开更多
In machine-vision-based systems for detecting foreign fibers, due to the background of the cotton layer has the absolute advantage in the whole image, while the foreign fiber only account for a very small part, and w...In machine-vision-based systems for detecting foreign fibers, due to the background of the cotton layer has the absolute advantage in the whole image, while the foreign fiber only account for a very small part, and what’s more, the brightness and contrast of the image are all poor. Using the traditional image segmentation method, the segmentation results are very poor. By adopting the maximum entropy and genetic algorithm, the maximum entropy function was used as the fitness function of genetic algorithm. Through continuous optimization, the optimal segmentation threshold is determined. Experimental results prove that the image segmentation of this paper not only fast and accurate, but also has strong adaptability.展开更多
The spatial interaction model is an effective way to explore the geographical disparities inherent in the Belt and Road Initiative(BRI) by simulating spatial flows. The traditional gravity model implies the hypothesis...The spatial interaction model is an effective way to explore the geographical disparities inherent in the Belt and Road Initiative(BRI) by simulating spatial flows. The traditional gravity model implies the hypothesis of equilibrium points without any reference to when or how to achieve it. In this paper, a dynamic gravity model was established based on the Maximum Entropy(MaxEnt) theory to estimate and monitor the interconnection intensity and dynamic characters of bilateral relations. In order to detect the determinants of interconnection intensity, a Geodetector method was applied to identify and evaluate the determinants of spatial networks in five dimensions. The empirical study clearly demonstrates a heterogeneous and non-circular spatial structure. The main driving forces of spatial-temporal evolution are foreign direct investment, tourism and railway infrastructure construction, while determinants in different sub-regions show obvious spatial differentiation. Southeast Asian countries are typically multi-island area where aviation infrastructure plays a more important role. North and Central Asian countries regard oil as a pillar industry where power and port facilities have a greater impact on the interconnection. While Western Asian countries are mostly influenced by the railway infrastructure, Eastern European countries already have relatively robust infrastructure where tariff policies provide a greater impetus.展开更多
Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability ...Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.展开更多
基金Supported by the National Natural Science Foundation of China(61071221,10831002)
文摘Let Ф（u ×v, k, Aa, Ac） be the largest possible number of codewords among all two- dimensional （u ×v, k, λa, λc） optical orthogonal codes. A 2-D （u× v, k, λa, λ）-OOC with Ф（u× v, k, λa, λc） codewords is said to be maximum. In this paper, the number of codewords of a maximum 2-D （u × v, 4, 1, 3）-OOC has been determined.
基金Science and Technology Plan of Gansu Province(No.144NKCA040)
文摘In order to improve the global search ability of biogeography-based optimization(BBO)algorithm in multi-threshold image segmentation,a multi-threshold image segmentation based on improved BBO algorithm is proposed.When using BBO algorithm to optimize threshold,firstly,the elitist selection operator is used to retain the optimal set of solutions.Secondly,a migration strategy based on fusion of good solution and pending solution is introduced to reduce premature convergence and invalid migration of traditional migration operations.Thirdly,to reduce the blindness of traditional mutation operations,a mutation operation through binary computation is created.Then,it is applied to the multi-threshold image segmentation of two-dimensional cross entropy.Finally,this method is used to segment the typical image and compared with two-dimensional multi-threshold segmentation based on particle swarm optimization algorithm and the two-dimensional multi-threshold image segmentation based on standard BBO algorithm.The experimental results show that the method has good convergence stability,it can effectively shorten the time of iteration,and the optimization performance is better than the standard BBO algorithm.
基金supported by National Natural Science Foundation of China under Grant No.60872065Open Foundation of State Key Laboratory for Novel Software Technology at Nanjing University under Grant No.KFKT2010B17
文摘The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.
基金Gui-Qiang CHEN was supported in part by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE(EP/E035027/1)the NSFC under a joint project Grant 10728101+4 种基金the Royal Society-Wolfson Research Merit Award(UK)Changguo XIAO was supported in part by the NSFC under a joint project Grant 10728101Yongqian ZHANG was supported in part by NSFC Project 11031001NSFC Project 11121101the 111 Project B08018(China)
文摘We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.
文摘In the multilevel thresholding segmentation of the image, the classification number is always given by the supervisor. To solve this problem, a fast multilevel thresholding algorithm considering both the threshold value and the classification number is proposed based on the maximum entropy, and the self-adaptive criterion of the classification number is given. The algorithm can obtain thresholds and automatically decide the classification number. Experimental results show that the algorithm is effective.
基金This workis financially supported by the National Natural Science Foundation of China (Grant No.40490263 andNo.40276006)
文摘Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.
基金ThisworkisfinanciallysupportedbythePh.D.FoundationoftheMinistryoftheEducationofChina (No .2 0 0 0 4 2 30 8)
文摘A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main points of the method are as follows: (1) based on the Hamiltonian principle, a maximum entropy probability density function for the extreme waveheight H, f(H)=αHγ e -βH4 is derived from a Lagrangian function subject to some necessary and rational constraints; (2) the parameters α, β, and γ in the function are expressed in terms of the mean , variance V= (H-)2 and bias B= (H-)3 ; and (3) with , V and B estimated from observed data, the n -year return-period wave height H n is computed in accordance with the formula 11-F(H n)=n , where F(H n) is defined as F(H n)=∫ H n 0f(H) d H. Examples of estimating the 50 and 100-year return period waveheights by the present method and by some currently used method from observed data acquired from two hydrographic stations are given. A comparison of the estimated results shows that the present method is superior to the others.
文摘Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.
基金This research was financially supported by the National Natural Science Foundation of China(Grant Nos.52071306 and 51379195)the Natural Science Foundation of Shandong Province(Grant No.ZR2019MEE050).
文摘Marine environmental design parameter extrapolation has important applications in marine engineering and coastal disaster prevention.The distribution models used for environmental design parameter usually pass the hypothesis tests in statistical analysis,but the calculation results of different distribution models often vary largely.In this paper,based on the information entropy,the overall uncertainty test criteria were studied for commonly used distributions including Gumbel,Weibull,and Pearson-III distribution.An improved method for parameter estimation of the maximum entropy distribution model is proposed on the basis of moment estimation.The study in this paper shows that the number of sample data and the degree of dispersion are proportional to the information entropy,and the overall uncertainty of the maximum entropy distribution model is minimal compared with other models.
文摘Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method （LSMEQFM） and that with constraint condition （LSMEQFMCC） are proposed. To improve the confidence level of quantile function estimation, scatter factor method is combined with maximum entropy method to estimate the confidence interval of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quantile function accurately on the small samples but inaccurately on the very small samples （10 samples）; LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples; with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples （10 samples）.
基金supported by the Open Fund of the Key Laboratory of Research on Marine Hazards Forecasting (Grant No.LOMF1101)the Shanghai Typhoon Research Fund (Grant No. 2009ST05)the National Natural Science Foundation of China(Grant No. 40776006)
文摘A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.
文摘This paper investigates the maximum entropy restoration of blurred binary image.In concerning with the binary property of image,a new maximum entropy restoration methodwith binary constraint is proposed.The properties of existence and uniqueness of solution arediscussed.The problem of maximum of entropy with two constraints is solved and the corre-sponding algorithm is given.In this paper,the maximum bounded entropy principle is employedconcerning the prior knowledge of binary image,and the maximum bounded entropy restora-tion method with binary constraint is put forward.The proposes methods,Wiener filter(WF)restoration method and maximum entropy restoration method are compared.The experimen-tal results show that the maximum entropy restoration method and maximum bounded entropyrestoration method with binary constraint can improve the quality of restored image.
基金Under the auspices of National Basic Research Program of China (No.2010CB951704)Institutional Consolidation for Coordinated and Integrated Monitoring of Natural Resources towards Sustainable Development and Environmental Conservation in the Hindu Kush-Karakoram-Himalaya Mountain Complex (No.76444-000)External Cooperation Program of Chinese Academy of Sciences (No.GJHZ0954)
文摘Tibetan spruce (Picea smithiana) is an endemic species of the Himalayas,and it distributes only in a re-stricted area with very low number.To address the lack of detailed distributional information,we used maximum en-tropy (Maxent) niche-based model to predict the species' potential distribution from limited occurrence-only records.The location data of P.smithiana,relative bioclimatic variables,vegetation data,digital elevation model (DEM),and the derived data were analyzed in Maxent.The receiver operating characteristic (ROC) curve was applied to assess the prediction accuracy.The Maxent jackknife test was performed to quantify the training gains from data layers and the response of P.smithiana distribution to four typical environmental variables was analyzed.Results show that the model performs well at the regional scale.There is a potential for continued expansion of P.smithiana population numbers and distribution in China.P.smithiana potentially distributes in the lower reaches of Gyirong Zangbo and Poiqu rivers in Gyirong and Nyalam counties in Qomolangma (Mount Everest) National Nature Preserve (QNNP),China.The species prefers warm temperate climate in mountain area and mainly distributes in needle-leaved evergreen closed to open forest and mixed forest along the river valley at relatively low altitudes of about 2000-3000 m.Model simulations suggest that distribution patterns of rare species with few species numbers can be well predicted by Max-ent.
文摘A crowdsourcing experiment in which viewers (the “crowd”) of a British Broadcasting Corporation (BBC) television show submitted estimates of the number of coins in a tumbler was shown in an antecedent paper (Part 1) to follow a log-normal distribution ∧(m,s2). The coin-estimation experiment is an archetype of a broad class of image analysis and object counting problems suitable for solution by crowdsourcing. The objective of the current paper (Part 2) is to determine the location and scale parameters (m,s) of ∧(m,s2) by both Bayesian and maximum likelihood (ML) methods and to compare the results. One outcome of the analysis is the resolution, by means of Jeffreys’ rule, of questions regarding the appropriate Bayesian prior. It is shown that Bayesian and ML analyses lead to the same expression for the location parameter, but different expressions for the scale parameter, which become identical in the limit of an infinite sample size. A second outcome of the analysis concerns use of the sample mean as the measure of information of the crowd in applications where the distribution of responses is not sought or known. In the coin-estimation experiment, the sample mean was found to differ widely from the mean number of coins calculated from ∧(m,s2). This discordance raises critical questions concerning whether, and under what conditions, the sample mean provides a reliable measure of the information of the crowd. This paper resolves that problem by use of the principle of maximum entropy (PME). The PME yields a set of equations for finding the most probable distribution consistent with given prior information and only that information. If there is no solution to the PME equations for a specified sample mean and sample variance, then the sample mean is an unreliable statistic, since no measure can be assigned to its uncertainty. Parts 1 and 2 together demonstrate that the information content of crowdsourcing resides in the distribution of responses (very often log-normal in form), which can be obtained empirically or by appropriate modeling.
基金This work was financially supported by the National Natural Science Foundation of China (Grant No50479028)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No20060423009)
文摘The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.
文摘The maximum entropy spectral characteristics of seismicity in the seismic enhanced region of 11 great earthquakes is analysed in this paper to seek the difference of seismic period spectral structure between the normal and the abnormal stage of seismic activity in this paper. The results show that, during decades or even one hundred years before great earthquakes, only short periods with 6.5～24.3 years appear, and long ones disappear. Otherwise, long periods with 18.5～38.5 years exist chiefly within the normal stages. Decades years after great earthquakes, the period spectra of seismicity are generally about several or ten years. Then the characteristics of great earthquakes is explained physically by applying the strong body seismogenic model, so a method of studying and predicting great earthquakes is offered.
文摘This paper presents an analytical, numerical, and experimental study on atomization characteristics and droplet distribution of a twin-fluid two-phase internal mixing atomizer to develop a Maximum Entropy Method(MEM). A two-phase Eulerian-Lagrangian method is utilized for atomization modeling of the inside and outside atomizer. In order to modify energy and momentum sources in the MEM, parametric studies are performed, and experimental tests are carried out to verify the results by applying the shadowgraph method. An advanced test stand is developed to prepare a wide range of changes in atomization characteristics and mixing ratios. A high degree of consistency is found between numerical results from the developed MEM and experimental tests with different gas-phase pressures and liquid flow rates. The droplet diameter and velocity distribution are reviewed based on various Weber numbers, sources of energy, and momentum. Turbulence modeling assists to estimate the breakup length and time scale precisely in the developed MEM, and distribution ranges with mean values are achieved. With reference to a strong correlation between upstream turbulence flow and the developed MEM verified by experimental tests, an ideal droplet size and velocity distribution prediction is observed.
文摘In machine-vision-based systems for detecting foreign fibers, due to the background of the cotton layer has the absolute advantage in the whole image, while the foreign fiber only account for a very small part, and what’s more, the brightness and contrast of the image are all poor. Using the traditional image segmentation method, the segmentation results are very poor. By adopting the maximum entropy and genetic algorithm, the maximum entropy function was used as the fitness function of genetic algorithm. Through continuous optimization, the optimal segmentation threshold is determined. Experimental results prove that the image segmentation of this paper not only fast and accurate, but also has strong adaptability.
基金the auspices of A Category of Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA20010101)。
文摘The spatial interaction model is an effective way to explore the geographical disparities inherent in the Belt and Road Initiative(BRI) by simulating spatial flows. The traditional gravity model implies the hypothesis of equilibrium points without any reference to when or how to achieve it. In this paper, a dynamic gravity model was established based on the Maximum Entropy(MaxEnt) theory to estimate and monitor the interconnection intensity and dynamic characters of bilateral relations. In order to detect the determinants of interconnection intensity, a Geodetector method was applied to identify and evaluate the determinants of spatial networks in five dimensions. The empirical study clearly demonstrates a heterogeneous and non-circular spatial structure. The main driving forces of spatial-temporal evolution are foreign direct investment, tourism and railway infrastructure construction, while determinants in different sub-regions show obvious spatial differentiation. Southeast Asian countries are typically multi-island area where aviation infrastructure plays a more important role. North and Central Asian countries regard oil as a pillar industry where power and port facilities have a greater impact on the interconnection. While Western Asian countries are mostly influenced by the railway infrastructure, Eastern European countries already have relatively robust infrastructure where tariff policies provide a greater impetus.
基金Project(50978112) supported by the National Natural Science Foundation of China
文摘Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.
