Based on the Aki-Richards approximate equations for reflection coefficients and Bayes theorem, we developed an inversion method to estimate P- and S-wave velocity contrasts and density contrast from combined PP and PS...Based on the Aki-Richards approximate equations for reflection coefficients and Bayes theorem, we developed an inversion method to estimate P- and S-wave velocity contrasts and density contrast from combined PP and PS data. This method assumes that the parameters satisfy a normal distribution and introduces the covariance matrix to describe the degree of correlation between the parameters and thus to improve the inversion stability. Then, we suppose that the parameter sequence is subject to the Cauchy distribution and employs another matrix Q to describe the parameter sequence sparseness to improve the inversion result resolution. Tests on both synthetic and real multi-component data prove that this method is valid, efficient, more stable, and more accurate compared to methods using PP data only.展开更多
Coupling Bayes’Theorem with a two-dimensional(2D)groundwater solute advection-diffusion transport equation allows an inverse model to be established to identify a set of contamination source parameters including sour...Coupling Bayes’Theorem with a two-dimensional(2D)groundwater solute advection-diffusion transport equation allows an inverse model to be established to identify a set of contamination source parameters including source intensity(M),release location(0 X,0 Y)and release time(0 T),based on monitoring well data.To address the issues of insufficient monitoring wells or weak correlation between monitoring data and model parameters,a monitoring well design optimization approach was developed based on the Bayesian formula and information entropy.To demonstrate how the model works,an exemplar problem with an instantaneous release of a contaminant in a confined groundwater aquifer was employed.The information entropy of the model parameters posterior distribution was used as a criterion to evaluate the monitoring data quantity index.The optimal monitoring well position and monitoring frequency were solved by the two-step Monte Carlo method and differential evolution algorithm given a known well monitoring locations and monitoring events.Based on the optimized monitoring well position and sampling frequency,the contamination source was identified by an improved Metropolis algorithm using the Latin hypercube sampling approach.The case study results show that the following parameters were obtained:1)the optimal monitoring well position(D)is at(445,200);and 2)the optimal monitoring frequency(Δt)is 7,providing that the monitoring events is set as 5 times.Employing the optimized monitoring well position and frequency,the mean errors of inverse modeling results in source parameters(M,X0,Y0,T0)were 9.20%,0.25%,0.0061%,and 0.33%,respectively.The optimized monitoring well position and sampling frequency canIt was also learnt that the improved Metropolis-Hastings algorithm(a Markov chain Monte Carlo method)can make the inverse modeling result independent of the initial sampling points and achieves an overall optimization,which significantly improved the accuracy and numerical stability of the inverse modeling results.展开更多
This paper proposes one method of feature selection by using Bayes＇ theorem. The purpose of the proposed method is to reduce the computational complexity and increase the classification accuracy of the selected featu...This paper proposes one method of feature selection by using Bayes＇ theorem. The purpose of the proposed method is to reduce the computational complexity and increase the classification accuracy of the selected feature subsets. The dependence between two attributes （binary） is determined based on the probabilities of their joint values that contribute to positive and negative classification decisions. If opposing sets of attribute values do not lead to opposing classification decisions （zero probability）, then the two attributes are considered independent of each other, otherwise dependent, and one of them can be removed and thus the number of attributes is reduced. The process must be repeated on all combinations of attributes. The paper also evaluates the approach by comparing it with existing feature selection algorithms over 8 datasets from University of California, Irvine （UCI） machine learning databases. The proposed method shows better results in terms of number of selected features, classification accuracy, and running time than most existing algorithms.展开更多
基金supported by the China Important National Science & Technology Specific Projects (Grant No. 2011ZX05019-008)the National Natural Science Foundation of China (Grant No. 40839901)
文摘Based on the Aki-Richards approximate equations for reflection coefficients and Bayes theorem, we developed an inversion method to estimate P- and S-wave velocity contrasts and density contrast from combined PP and PS data. This method assumes that the parameters satisfy a normal distribution and introduces the covariance matrix to describe the degree of correlation between the parameters and thus to improve the inversion stability. Then, we suppose that the parameter sequence is subject to the Cauchy distribution and employs another matrix Q to describe the parameter sequence sparseness to improve the inversion result resolution. Tests on both synthetic and real multi-component data prove that this method is valid, efficient, more stable, and more accurate compared to methods using PP data only.
基金This work was supported by Major Science and Technology Program for Water Pollution Control and Treatment(No.2015ZX07406005)Also thanks to the National Natural Science Foundation of China(No.41430643 and No.51774270)the National Key Research&Development Plan(No.2016YFC0501109).
文摘Coupling Bayes’Theorem with a two-dimensional(2D)groundwater solute advection-diffusion transport equation allows an inverse model to be established to identify a set of contamination source parameters including source intensity(M),release location(0 X,0 Y)and release time(0 T),based on monitoring well data.To address the issues of insufficient monitoring wells or weak correlation between monitoring data and model parameters,a monitoring well design optimization approach was developed based on the Bayesian formula and information entropy.To demonstrate how the model works,an exemplar problem with an instantaneous release of a contaminant in a confined groundwater aquifer was employed.The information entropy of the model parameters posterior distribution was used as a criterion to evaluate the monitoring data quantity index.The optimal monitoring well position and monitoring frequency were solved by the two-step Monte Carlo method and differential evolution algorithm given a known well monitoring locations and monitoring events.Based on the optimized monitoring well position and sampling frequency,the contamination source was identified by an improved Metropolis algorithm using the Latin hypercube sampling approach.The case study results show that the following parameters were obtained:1)the optimal monitoring well position(D)is at(445,200);and 2)the optimal monitoring frequency(Δt)is 7,providing that the monitoring events is set as 5 times.Employing the optimized monitoring well position and frequency,the mean errors of inverse modeling results in source parameters(M,X0,Y0,T0)were 9.20%,0.25%,0.0061%,and 0.33%,respectively.The optimized monitoring well position and sampling frequency canIt was also learnt that the improved Metropolis-Hastings algorithm(a Markov chain Monte Carlo method)can make the inverse modeling result independent of the initial sampling points and achieves an overall optimization,which significantly improved the accuracy and numerical stability of the inverse modeling results.
文摘This paper proposes one method of feature selection by using Bayes＇ theorem. The purpose of the proposed method is to reduce the computational complexity and increase the classification accuracy of the selected feature subsets. The dependence between two attributes （binary） is determined based on the probabilities of their joint values that contribute to positive and negative classification decisions. If opposing sets of attribute values do not lead to opposing classification decisions （zero probability）, then the two attributes are considered independent of each other, otherwise dependent, and one of them can be removed and thus the number of attributes is reduced. The process must be repeated on all combinations of attributes. The paper also evaluates the approach by comparing it with existing feature selection algorithms over 8 datasets from University of California, Irvine （UCI） machine learning databases. The proposed method shows better results in terms of number of selected features, classification accuracy, and running time than most existing algorithms.
