A Bimaximum Entropy Method for Solving Nonlinear Constrained Continuous Minimax Problem

2012 ◽  
Vol 532-533 ◽  
pp. 1011-1015 ◽  
Author(s):  
Qiu Hong Huang ◽  
De Xin Cao
Keyword(s):  
Objective Function ◽  
Maximum Entropy ◽  
Penalty Function ◽  
Minimax Problem ◽  
Entropy Method ◽  
Entropy Function ◽  
Basic Algorithm ◽  
Decision Variables ◽  
Maximum Entropy Function ◽  
Continuous Minimax

A numerical method is proposed for solving a sort of constrained continuous minimax problem, in which both the objective function and the constraint functions are continuously differentiable about superior decision variables and are continuous about lower decision variables .Besides,the constraint functions include only superior or lower decision variables．The problem is transformed into unconstrained differentiable problem with the idea of the discrete maximum entropy function and the continuous maximum entropy function and the penalty function method．The basic algorithm is established．The convergence is proofed．Numerical examples are given and show the efficiency and the reliability of the algorithm.

Inversion of nuclear magnetic resonance echo data based on maximum entropy

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. D1-D8 ◽  
Author(s):  
Youlong Zou ◽  
Ranhong Xie ◽  
Yejiao Ding ◽  
Alon Arad
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Objective Function ◽  
Maximum Entropy ◽  
Shannon Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Entropy Function ◽  
S Curve ◽  
Nuclear Magnetic

Nuclear magnetic resonance (NMR) [Formula: see text] inversion is an ill-posed problem in which regularization techniques are usually adopted to suppress the oscillations caused by noise in the solutions. The maximum entropy concept provides an unbiased way to obtain information from incomplete data, and it implicitly imposes a positive constraint on probability distribution, so we used the maximum entropy method to invert NMR echo data. We have developed a simple and effective method for solving the objective function of the maximum entropy method. First, the solution was replaced by a positive function to achieve the positive constraint of the solution, the objective function was converted to an unconstrained one, and then the Levenberg-Marquardt method was used to solve the newly obtained unconstrained objective function. To suppress the highly tilted tail at the short relaxation time of the [Formula: see text] distribution, a modified or normalized Shannon entropy function was used to replace the standard Shannon entropy function as the penalty term. Furthermore, the S-curve method was used to select the regularization parameter and the formula of the slope of the S-curve was developed. We have determined that the maximum entropy method was better able to separate the peaks of short and long relaxation times in the [Formula: see text] distribution in comparison with the truncated singular value decomposition method. This was true for low signal-to-noise ratio data derived from numerical simulation and the NMR log. In addition, the short relaxation peak caused by the norm smoothing method can also be reduced.

scholarly journals Modified Entropy Estimator Using a Haar Matrix to Fit the Weibull Growth Model

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Basim Shlaibah Msallam ◽  
Saifaldin Hashim Kamar
Keyword(s):  
Maximum Entropy ◽  
Growth Model ◽  
Oil Production ◽  
Real Data ◽  
Entropy Method ◽  
Model Parameters ◽  
Linear Regression Models ◽  
Generalized Maximum Entropy ◽  
Entropy Estimator ◽  
Maximum Entropy Function

It is well known that the Generalized Maximum Entropy method can be used to fit linear regression models, especially as they are not restricted by the conditions to be verified as are other classical methods. Therefore, in this paper, a new method for estimating the parameters of the four-parameter Weibull growth model was proposed using the Generalized Maximum Entropy function by fitting data based on the Haar matrix which was used in the wavelet method. The suggested and classical entropy estimators for Weibull growth model parameters were compared using simulation and the preference for the suggested method estimator was shown. The Modified Generalized Maximum Entropy estimator was applied to the real data representing annual Iraqi oil production for the period 2010–2017. Iraqi crude oil production for the year 2022 was predicted and appeared as 4.4 million bb/day.

Enhanced Information Recovery in 2D On-and Off-Resonance Nutation NQR using the Maximum Entropy Method

1996 ◽  
Vol 51 (5-6) ◽  
pp. 337-347 ◽  
Author(s):  
Mariusz Maćkowiak ◽  
Piotr Kątowski
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Theoretical Description ◽  
Entropy Method ◽  
Zero Field ◽  
Resonance Effects ◽  
Information Recovery ◽  
Truncation Errors ◽  
Enhanced Resolution ◽  
2D Data

Abstract Two-dimensional zero-field nutation NQR spectroscopy has been used to determine the full quadrupolar tensor of spin - 3/2 nuclei in serveral molecular crystals containing the 3 5 Cl and 7 5 As nuclei. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. It is shown that the replacement of conventional Fourier transform by an alternative data processing by MEM in 2D NQR spectroscopy leads to sensitivity improvement, reduction of instrumental artefacts and truncation errors, shortened data acquisition times and suppression of noise, while at the same time increasing the resolution. The effects of off-resonance irradiation in nutation experiments are demonstrated both experimentally and theoretically. It is shown that off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments, thus facilitating the determination of asymmetry parameters in multiple spectrum. The theoretical description of the off-resonance effects in 2D nutation NQR spectroscopy is given, and general exact formulas for the asymmetry parameter are obtained. In off-resonance conditions, the resolution of the nutation NQR spectrum decreases with the spectrometer offset. However, an enhanced resolution can be achieved by using the maximum entropy method in 2D-data reconstruction.

Estimating the distribution of primary reflection coefficients

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1417-1422 ◽  
Author(s):  
Danilo R. Velis
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Reflection Coefficients ◽  
Log Data ◽  
Neuquen Basin ◽  
Neuquén Basin ◽  
Skewness And Kurtosis

The distribution of primary reflection coefficients can be estimated by means of the maximum entropy method, giving rise to smooth nonparametric functions which are consistent with the data. Instead of using classical moments (e.g. skewness and kurtosis) to constraint the maximization, nonconventional sample statistics help to improve the quality of the estimates. Results using real log data from various wells located in the Neuquen Basin (Argentina) show the effectiveness of the method to estimate both robust and consistent distributions that may be used to simulate realistic sequences.

Maximum entropy method in phase-encoding NMR imaging

1987 ◽  
Vol 4 (1) ◽  
pp. 78-82 ◽  
Author(s):  
B. C. De Simone ◽  
F. De Luca ◽  
B. Maraviglia
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Nmr Imaging ◽  
Phase Encoding
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