针对一般模糊规则模型对含有重尾噪声的数据集鲁棒性较差的问题,提出了面向重尾噪声的模糊规则(Rule-based Fuzzy Model for Heavy-tailed Noisy Data,HtRbF)模型.该模型使用了两种新的聚类方法,学生t分布均值聚类算法(Student’s t-dis...针对一般模糊规则模型对含有重尾噪声的数据集鲁棒性较差的问题,提出了面向重尾噪声的模糊规则(Rule-based Fuzzy Model for Heavy-tailed Noisy Data,HtRbF)模型.该模型使用了两种新的聚类方法,学生t分布均值聚类算法(Student’s t-distribution C-Means,StCM)和学生t分布下的背景模糊聚类方法(Student’s t-distribution Context Fuzzy C-Means,StCFCM),并将其应用在初始规则和新规则的生成中,使模型在重尾噪声场景下生成更为准确的规则,有效减少了模型的输出误差,使其更接近真实输出.HtRbF模型具有良好的抗噪能力,通过对数据集添加不同类型的重尾噪声进行系统性实验,实验结果证明了HtRbF模型的有效性.展开更多
Amplitude variation with offset and azimuth(AVOA)inversion is a mainstream method for predicting and evaluating fracture parameters of conventional oil and gas reservoirs.However,its application to coal seams is limit...Amplitude variation with offset and azimuth(AVOA)inversion is a mainstream method for predicting and evaluating fracture parameters of conventional oil and gas reservoirs.However,its application to coal seams is limited because of the specificity of the equivalent media model for coal—also,the traditional seismic acquisition system employed in coal fields falls within a narrow azimuth.In this study,we initially derived a P‒P wave reflection coefficient approximation formula for coal seams,which is directly expressed in terms of fracture parameters using the Schoenberg linear-slide model and Hudson model.We analyzed the P‒P wave reflection coefficient’s response to the fracture parameters using a two-layer forward model.Accordingly,we designed a twostep inversion workflow for AVOA inversion of the fracture parameters.Thereafter,high-density wide-azimuth pre-stack 3D seismic data were utilized for inverting the fracture density and strike of the target coal seam.The inversion accuracy was constrained by Student’s tdistribution testing.The analysis and validation of the inversion results revealed that the relative fracture density corresponds to fault locations,with the strike of the fractures and faults mainly at 0°.Therefore,the AVOA inversion method and technical workflow proposed here can be used to efficiently predict and evaluate fracture parameters of coal seams.展开更多
A Student’s t-distribution is obtained from a weighted average over the standard deviation of a normal distribution, σ, when 1/σ is distributed as chi. Left truncation at q of the chi distribution in the mixing int...A Student’s t-distribution is obtained from a weighted average over the standard deviation of a normal distribution, σ, when 1/σ is distributed as chi. Left truncation at q of the chi distribution in the mixing integral leads to an effectively truncated Student’s t-distribution with tails that decay as exp (-q2t2). The effect of truncation of the chi distribution in a chi-normal mixture is investigated and expressions for the pdf, the variance, and the kurtosis of the t-like distribution that arises from the mixture of a left-truncated chi and a normal distribution are given for selected degrees of freedom 5. This work has value in pricing financial assets, in understanding the Student’s t--distribution, in statistical inference, and in analysis of data.展开更多
Some moments and limiting properties of independent Student’s t increments are studied. Inde-pendent Student’s t increments are independent draws from not-truncated, truncated, and effectively truncated Student’s t...Some moments and limiting properties of independent Student’s t increments are studied. Inde-pendent Student’s t increments are independent draws from not-truncated, truncated, and effectively truncated Student’s t-distributions with shape parameters and can be used to create random walks. It is found that sample paths created from truncated and effectively truncated Student’s t-distributions are continuous. Sample paths for Student’s t-distributions are also continuous. Student’s t increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.展开更多
Three Bayesian related approaches,namely,variational Bayesian(VB),minimum message length(MML)and Bayesian Ying-Yang(BYY)harmony learning,have been applied to automatically determining an appropriate number of componen...Three Bayesian related approaches,namely,variational Bayesian(VB),minimum message length(MML)and Bayesian Ying-Yang(BYY)harmony learning,have been applied to automatically determining an appropriate number of components during learning Gaussian mixture model(GMM).This paper aims to provide a comparative investigation on these approaches with not only a Jeffreys prior but also a conjugate Dirichlet-Normal-Wishart(DNW)prior on GMM.In addition to adopting the existing algorithms either directly or with some modifications,the algorithm for VB with Jeffreys prior and the algorithm for BYY with DNW prior are developed in this paper to fill the missing gap.The performances of automatic model selection are evaluated through extensive experiments,with several empirical findings:1)Considering priors merely on the mixing weights,each of three approaches makes biased mistakes,while considering priors on all the parameters of GMM makes each approach reduce its bias and also improve its performance.2)As Jeffreys prior is replaced by the DNW prior,all the three approaches improve their performances.Moreover,Jeffreys prior makes MML slightly better than VB,while the DNW prior makes VB better than MML.3)As the hyperparameters of DNW prior are further optimized by each of its own learning principle,BYY improves its performances while VB and MML deteriorate their performances when there are too many free hyper-parameters.Actually,VB and MML lack a good guide for optimizing the hyper-parameters of DNW prior.4)BYY considerably outperforms both VB and MML for any type of priors and whether hyper-parameters are optimized.Being different from VB and MML that rely on appropriate priors to perform model selection,BYY does not highly depend on the type of priors.It has model selection ability even without priors and performs already very well with Jeffreys prior,and incrementally improves as Jeffreys prior is replaced by the DNW prior.Finally,all algorithms are applied on the Berkeley segmentation database of real world images.Again,BYY co展开更多
基金supported by the University Synergy Innovation Program of Anhui Province(Nos.GXXT-2021-016 and GXXT-2019-029)the National Natural Science Foundation of China(Grant No.41902167)the Institute of Energy,Hefei Comprehensive National Science Center(No.21KZS215).
文摘Amplitude variation with offset and azimuth(AVOA)inversion is a mainstream method for predicting and evaluating fracture parameters of conventional oil and gas reservoirs.However,its application to coal seams is limited because of the specificity of the equivalent media model for coal—also,the traditional seismic acquisition system employed in coal fields falls within a narrow azimuth.In this study,we initially derived a P‒P wave reflection coefficient approximation formula for coal seams,which is directly expressed in terms of fracture parameters using the Schoenberg linear-slide model and Hudson model.We analyzed the P‒P wave reflection coefficient’s response to the fracture parameters using a two-layer forward model.Accordingly,we designed a twostep inversion workflow for AVOA inversion of the fracture parameters.Thereafter,high-density wide-azimuth pre-stack 3D seismic data were utilized for inverting the fracture density and strike of the target coal seam.The inversion accuracy was constrained by Student’s tdistribution testing.The analysis and validation of the inversion results revealed that the relative fracture density corresponds to fault locations,with the strike of the fractures and faults mainly at 0°.Therefore,the AVOA inversion method and technical workflow proposed here can be used to efficiently predict and evaluate fracture parameters of coal seams.
文摘A Student’s t-distribution is obtained from a weighted average over the standard deviation of a normal distribution, σ, when 1/σ is distributed as chi. Left truncation at q of the chi distribution in the mixing integral leads to an effectively truncated Student’s t-distribution with tails that decay as exp (-q2t2). The effect of truncation of the chi distribution in a chi-normal mixture is investigated and expressions for the pdf, the variance, and the kurtosis of the t-like distribution that arises from the mixture of a left-truncated chi and a normal distribution are given for selected degrees of freedom 5. This work has value in pricing financial assets, in understanding the Student’s t--distribution, in statistical inference, and in analysis of data.
文摘Some moments and limiting properties of independent Student’s t increments are studied. Inde-pendent Student’s t increments are independent draws from not-truncated, truncated, and effectively truncated Student’s t-distributions with shape parameters and can be used to create random walks. It is found that sample paths created from truncated and effectively truncated Student’s t-distributions are continuous. Sample paths for Student’s t-distributions are also continuous. Student’s t increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.
基金The work described in this paper was supported by a grant of the General Research Fund(GRF)from the Research Grant Council of Hong Kong SAR(Project No.CUHK418011E).
文摘Three Bayesian related approaches,namely,variational Bayesian(VB),minimum message length(MML)and Bayesian Ying-Yang(BYY)harmony learning,have been applied to automatically determining an appropriate number of components during learning Gaussian mixture model(GMM).This paper aims to provide a comparative investigation on these approaches with not only a Jeffreys prior but also a conjugate Dirichlet-Normal-Wishart(DNW)prior on GMM.In addition to adopting the existing algorithms either directly or with some modifications,the algorithm for VB with Jeffreys prior and the algorithm for BYY with DNW prior are developed in this paper to fill the missing gap.The performances of automatic model selection are evaluated through extensive experiments,with several empirical findings:1)Considering priors merely on the mixing weights,each of three approaches makes biased mistakes,while considering priors on all the parameters of GMM makes each approach reduce its bias and also improve its performance.2)As Jeffreys prior is replaced by the DNW prior,all the three approaches improve their performances.Moreover,Jeffreys prior makes MML slightly better than VB,while the DNW prior makes VB better than MML.3)As the hyperparameters of DNW prior are further optimized by each of its own learning principle,BYY improves its performances while VB and MML deteriorate their performances when there are too many free hyper-parameters.Actually,VB and MML lack a good guide for optimizing the hyper-parameters of DNW prior.4)BYY considerably outperforms both VB and MML for any type of priors and whether hyper-parameters are optimized.Being different from VB and MML that rely on appropriate priors to perform model selection,BYY does not highly depend on the type of priors.It has model selection ability even without priors and performs already very well with Jeffreys prior,and incrementally improves as Jeffreys prior is replaced by the DNW prior.Finally,all algorithms are applied on the Berkeley segmentation database of real world images.Again,BYY co
