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
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
Laser-induced fluorescence(LIF)spectroscopy is employed for plasma diagnosis,necessitating the utilization of deconvolution algorithms to isolate the Doppler effect from the raw spectral signal.However,direct deconvol...Laser-induced fluorescence(LIF)spectroscopy is employed for plasma diagnosis,necessitating the utilization of deconvolution algorithms to isolate the Doppler effect from the raw spectral signal.However,direct deconvolution becomes invalid in the presence of noise as it leads to infinite amplification of high-frequency noise components.To address this issue,we propose a deconvolution algorithm based on the maximum entropy principle.We validate the effectiveness of the proposed algorithm by utilizing simulated LIF spectra at various noise levels(signal-to-noise ratio,SNR=20–80 d B)and measured LIF spectra with Xe as the working fluid.In the typical measured spectrum(SNR=26.23 d B)experiment,compared with the Gaussian filter and the Richardson–Lucy(R-L)algorithm,the proposed algorithm demonstrates an increase in SNR of 1.39 d B and 4.66 d B,respectively,along with a reduction in the root-meansquare error(RMSE)of 35%and 64%,respectively.Additionally,there is a decrease in the spectral angle(SA)of 0.05 and 0.11,respectively.In the high-quality spectrum(SNR=43.96 d B)experiment,the results show that the running time of the proposed algorithm is reduced by about98%compared with the R-L iterative algorithm.Moreover,the maximum entropy algorithm avoids parameter optimization settings and is more suitable for automatic implementation.In conclusion,the proposed algorithm can accurately resolve Doppler spectrum details while effectively suppressing noise,thus highlighting its advantage in LIF spectral deconvolution applications.展开更多
In view of the problem of fine characterization of narrow and thin channels,the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution.On the basis of effectively improv...In view of the problem of fine characterization of narrow and thin channels,the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution.On the basis of effectively improving the time-frequency resolution of seismic signal,a new method of microscopic ancient river channel identification is established.Based on the principle of the equivalence between the maximum entropy power spectrum and the AR model power spectrum,the prediction error and the autoregression coefficient of AR model are obtained using the Burg algorithm and Levinson-Durbin recurrence rule.Under the condition of the first derivative of autocorrelation function being 0,the Wigner-Ville Distribution of seismic signal is calculated,and the Wigner-Ville Distribution time-frequency power spectrum(MEWVD)is obtained under the maxi-mum entropy criterion of the microscopic ancient river channel.Through analysis of emulational seismic signal and forward numerical simulation signal of narrow thin model,it is found that MEWVD can effectively avoid the interference of cross term of Wigner-Ville Distribution,and obtain more accurate spectral characteristics than STFT and CWT signal analysis methods.It is also proved that the narrow and thin river channels of different scales can be identified effectively by MEWVD of different frequencies.The method is applied to the third member of Jurassic Shaximiao Formation(J2s33-2)gas reservoir of the Zhongji-ang gas field in Sichuan Basin.The spatial information of width and direction of narrow and thin river channels with width less than 500 m and sandstone thickness less than 35 m is accurately identified,providing bases for well deployment and horizontal well fracturing section selection.展开更多
A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distributio...A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability, Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions, In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.展开更多
A method of applying maximum entropy probability density estimation approachto constituting diagnostic criterions of oil monitoring data is presented. The method promotes theprecision of diagnostic criterions for eval...A method of applying maximum entropy probability density estimation approachto constituting diagnostic criterions of oil monitoring data is presented. The method promotes theprecision of diagnostic criterions for evaluating the wear state of mechanical facilities, andjudging abnormal data. According to the critical boundary points defined, a new measure onmonitoring wear state and identifying probable wear faults can be got. The method can be applied tospectrometric analysis and direct reading ferrographic analysis. On the basis of the analysis anddiscussion of two examples of 8NVD48A-2U diesel engines, the practicality is proved to be aneffective method in oil monitoring.展开更多
This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic...This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic theories are discussed from the viewpoint of Maximum Entropy Production (MEP). According to the MEP principle, open systems existing in the state far from equilibrium are stabilized when entropy production is maximized, creating dissipative structures with low entropy such as the tree-shaped network. We prepare two simulation models: one is the Poisson equation model that simulates the state far from equilibrium, and the other is the Laplace equation model that simulates the isolated state or the state near thermodynamic equilibrium. The output of these equations is considered to be positively correlated to entropy production of the system. Setting the Poisson equation model so that entropy production is maximized, tree network formation is advanced. We suppose that this is due to the invocation of the MEP principle, that is, entropy of the system is lowered by emitting maximal entropy out of the system. On the other hand, tree network formation is not observed in the Laplace equation model. Our simulation results will offer the persuasive evidence that certifies the effect of the MEP principle.展开更多
Complete prior statistical information is currently required in the majority of statistical evaluations of complex models. The principle of maximum entropy is often utilized in this context to fill in the missing piec...Complete prior statistical information is currently required in the majority of statistical evaluations of complex models. The principle of maximum entropy is often utilized in this context to fill in the missing pieces of available information and is normally claimed to be fair and objective. A rarely discussed aspect is that it relies upon testable information, which is never known but estimated, i.e. results from processing of raw data. The subjective choice of this processing strongly affects the result. Less conventional posterior completion of information is equally accurate but is computationally superior to prior, as much less information enters the analysis. Our recently proposed methods of lean deterministic sampling are examples of very few approaches that actively promote the use of minimal incomplete prior information. The inherited subjective character of maximum entropy distributions and the often critical implications of prior and posterior completion of information are here discussed and illustrated, from a novel perspective of consistency, rationality, computational efficiency and realism.展开更多
The structural, electronic and elastic properties of common intermetallic compounds in FeTiCoNiVCrMnCuAI system high entropy alloy were investigated by the first principles calculation. The calculation results of form...The structural, electronic and elastic properties of common intermetallic compounds in FeTiCoNiVCrMnCuAI system high entropy alloy were investigated by the first principles calculation. The calculation results of formation enthalpy and cohesive energy show that FeTi, Fe2Ti, AlCrFe2, Co2Ti, AlMn2V and Mn2Ti phases may form in the formation process of the alloy. Further studies show that FeTi, FezTi, AlCrFe2, Co2Ti and AlMn2V phases with higher shear modulus and elastic modulus would be excellent strengthening phases in high entropy alloy and would improve the hardness of the alloy. In addition, the partial density of states was investigated for revealing the bonding mode, and the analyses on the strength of p-d hybridization also reveal the underlying mechanism for the elastic properties of these compounds.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
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
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
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 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
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
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
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.
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.
文摘Laser-induced fluorescence(LIF)spectroscopy is employed for plasma diagnosis,necessitating the utilization of deconvolution algorithms to isolate the Doppler effect from the raw spectral signal.However,direct deconvolution becomes invalid in the presence of noise as it leads to infinite amplification of high-frequency noise components.To address this issue,we propose a deconvolution algorithm based on the maximum entropy principle.We validate the effectiveness of the proposed algorithm by utilizing simulated LIF spectra at various noise levels(signal-to-noise ratio,SNR=20–80 d B)and measured LIF spectra with Xe as the working fluid.In the typical measured spectrum(SNR=26.23 d B)experiment,compared with the Gaussian filter and the Richardson–Lucy(R-L)algorithm,the proposed algorithm demonstrates an increase in SNR of 1.39 d B and 4.66 d B,respectively,along with a reduction in the root-meansquare error(RMSE)of 35%and 64%,respectively.Additionally,there is a decrease in the spectral angle(SA)of 0.05 and 0.11,respectively.In the high-quality spectrum(SNR=43.96 d B)experiment,the results show that the running time of the proposed algorithm is reduced by about98%compared with the R-L iterative algorithm.Moreover,the maximum entropy algorithm avoids parameter optimization settings and is more suitable for automatic implementation.In conclusion,the proposed algorithm can accurately resolve Doppler spectrum details while effectively suppressing noise,thus highlighting its advantage in LIF spectral deconvolution applications.
基金Supported by the General Project of National Natural Science Foundation(4207416041574099)the Sichuan Science and Tech-nology Plan Project(2020JDRC0013)。
文摘In view of the problem of fine characterization of narrow and thin channels,the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution.On the basis of effectively improving the time-frequency resolution of seismic signal,a new method of microscopic ancient river channel identification is established.Based on the principle of the equivalence between the maximum entropy power spectrum and the AR model power spectrum,the prediction error and the autoregression coefficient of AR model are obtained using the Burg algorithm and Levinson-Durbin recurrence rule.Under the condition of the first derivative of autocorrelation function being 0,the Wigner-Ville Distribution of seismic signal is calculated,and the Wigner-Ville Distribution time-frequency power spectrum(MEWVD)is obtained under the maxi-mum entropy criterion of the microscopic ancient river channel.Through analysis of emulational seismic signal and forward numerical simulation signal of narrow thin model,it is found that MEWVD can effectively avoid the interference of cross term of Wigner-Ville Distribution,and obtain more accurate spectral characteristics than STFT and CWT signal analysis methods.It is also proved that the narrow and thin river channels of different scales can be identified effectively by MEWVD of different frequencies.The method is applied to the third member of Jurassic Shaximiao Formation(J2s33-2)gas reservoir of the Zhongji-ang gas field in Sichuan Basin.The spatial information of width and direction of narrow and thin river channels with width less than 500 m and sandstone thickness less than 35 m is accurately identified,providing bases for well deployment and horizontal well fracturing section selection.
基金This project was financially supported by the National Natural Science Foundation of China(Grant No.49876012,49976003)
文摘A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability, Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions, In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.
基金This project is supported by Foundation of Shanghai Automobile Industry Corporation Group, China (No.0204).
文摘A method of applying maximum entropy probability density estimation approachto constituting diagnostic criterions of oil monitoring data is presented. The method promotes theprecision of diagnostic criterions for evaluating the wear state of mechanical facilities, andjudging abnormal data. According to the critical boundary points defined, a new measure onmonitoring wear state and identifying probable wear faults can be got. The method can be applied tospectrometric analysis and direct reading ferrographic analysis. On the basis of the analysis anddiscussion of two examples of 8NVD48A-2U diesel engines, the practicality is proved to be aneffective method in oil monitoring.
文摘This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic theories are discussed from the viewpoint of Maximum Entropy Production (MEP). According to the MEP principle, open systems existing in the state far from equilibrium are stabilized when entropy production is maximized, creating dissipative structures with low entropy such as the tree-shaped network. We prepare two simulation models: one is the Poisson equation model that simulates the state far from equilibrium, and the other is the Laplace equation model that simulates the isolated state or the state near thermodynamic equilibrium. The output of these equations is considered to be positively correlated to entropy production of the system. Setting the Poisson equation model so that entropy production is maximized, tree network formation is advanced. We suppose that this is due to the invocation of the MEP principle, that is, entropy of the system is lowered by emitting maximal entropy out of the system. On the other hand, tree network formation is not observed in the Laplace equation model. Our simulation results will offer the persuasive evidence that certifies the effect of the MEP principle.
文摘Complete prior statistical information is currently required in the majority of statistical evaluations of complex models. The principle of maximum entropy is often utilized in this context to fill in the missing pieces of available information and is normally claimed to be fair and objective. A rarely discussed aspect is that it relies upon testable information, which is never known but estimated, i.e. results from processing of raw data. The subjective choice of this processing strongly affects the result. Less conventional posterior completion of information is equally accurate but is computationally superior to prior, as much less information enters the analysis. Our recently proposed methods of lean deterministic sampling are examples of very few approaches that actively promote the use of minimal incomplete prior information. The inherited subjective character of maximum entropy distributions and the often critical implications of prior and posterior completion of information are here discussed and illustrated, from a novel perspective of consistency, rationality, computational efficiency and realism.
基金Project supported by the National Key Laboratory Opening Funding of Advanced Composites in Special Environments in Harbin Institute of Technology,China
文摘The structural, electronic and elastic properties of common intermetallic compounds in FeTiCoNiVCrMnCuAI system high entropy alloy were investigated by the first principles calculation. The calculation results of formation enthalpy and cohesive energy show that FeTi, Fe2Ti, AlCrFe2, Co2Ti, AlMn2V and Mn2Ti phases may form in the formation process of the alloy. Further studies show that FeTi, FezTi, AlCrFe2, Co2Ti and AlMn2V phases with higher shear modulus and elastic modulus would be excellent strengthening phases in high entropy alloy and would improve the hardness of the alloy. In addition, the partial density of states was investigated for revealing the bonding mode, and the analyses on the strength of p-d hybridization also reveal the underlying mechanism for the elastic properties of these compounds.
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.
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.
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）.
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.
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.
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.
