Soil-water characteristic curve (SWCC) is significant to estimate the site-specific unsaturated soil properties (such as unsaturated shear strength and coefficient of permeability) for geotechnical analyses involving ...Soil-water characteristic curve (SWCC) is significant to estimate the site-specific unsaturated soil properties (such as unsaturated shear strength and coefficient of permeability) for geotechnical analyses involving unsaturated soils. Determining SWCC can be achieved by fitting data points obtained according to the prescribed experimental scheme, which is specified by the number of measuring points and their corresponding values of the control variable. The number of measuring points is limited since direct measurement of SWCC is often costly and time-consuming. Based on the limited number of measuring points, the estimated SWCC is unavoidably associated with uncertainties, which depends on measurement data obtained from the prescribed experimental scheme. Therefore, it is essential to plan the experimental scheme so as to reduce the uncertainty in the estimated SWCC. This study presented a Bayesian approach, called OBEDO, for probabilistic experimental design optimization of measuring SWCC based on the prior knowledge and information of testing apparatus. The uncertainty in estimated SWCC is quantified and the optimal experimental scheme with the maximum expected utility is determined by Subset Simulation optimization (SSO) in candidate experimental scheme space. The proposed approach is illustrated using an experimental design example given prior knowledge and the information of testing apparatus and is verified based on a set of real loess SWCC data, which were used to generate random experimental schemes to mimic the arbitrary arrangement of measuring points during SWCC testing in practice. Results show that the arbitrary arrangement of measuring points of SWCC testing is hardly superior to the optimal scheme obtained from OBEDO in terms of the expected utility. The proposed OBEDO approach provides a rational tool to optimize the arrangement of measuring points of SWCC test so as to obtain SWCC measurement data with relatively high expected utility for uncertainty reduction.展开更多
Coptis chinensis(Huanglian) is a commonly used traditional Chinese medicine(TCM) herb and alkaloids are the most important chemical constituents in it. In the present study, an isocratic reverse phase high performance...Coptis chinensis(Huanglian) is a commonly used traditional Chinese medicine(TCM) herb and alkaloids are the most important chemical constituents in it. In the present study, an isocratic reverse phase high performance liquid chromatography(RP-HPLC) method allowing the separation of six alkaloids in Huanglian was for the first time developed under the quality by design(Qb D) principles. First, five chromatographic parameters were identified to construct a Plackett-Burman experimental design. The critical resolution, analysis time, and peak width were responses modeled by multivariate linear regression. The results showed that the percentage of acetonitrile, concentration of sodium dodecyl sulfate, and concentration of potassium phosphate monobasic were statistically significant parameters(P < 0.05). Then, the Box-Behnken experimental design was applied to further evaluate the interactions between the three parameters on selected responses. Full quadratic models were built and used to establish the analytical design space. Moreover, the reliability of design space was estimated by the Bayesian posterior predictive distribution. The optimal separation was predicted at 40% acetonitrile, 1.7 g·m L-1of sodium dodecyl sulfate and 0.03 mol·m L-1 of potassium phosphate monobasic. Finally, the accuracy profile methodology was used to validate the established HPLC method. The results demonstrated that the Qb D concept could be efficiently used to develop a robust RP-HPLC analytical method for Huanglian.展开更多
In order to accurately predict and control the aging process of dams, new information should be collected continuously to renew the quantitative evaluation of dam safety levels. Owing to the complex structural charact...In order to accurately predict and control the aging process of dams, new information should be collected continuously to renew the quantitative evaluation of dam safety levels. Owing to the complex structural characteristics of dams, it is quite difficult to predict the time-varying factors affecting their safety levels. It is not feasible to employ dynamic reliability indices to evaluate the actual safety levels of dams. Based on the relevant regulations for dam safety classification in China, a dynamic probability description of dam safety levels was developed. Using the Bayesian approach and effective information mining, as well as real-time information, this study achieved more rational evaluation and prediction of dam safety levels. With the Bayesian expression of discrete stochastic variables, the a priori probabilities of the dam safety levels determined by experts were combined wfth the likelihood probability of the real-time check information, and the probability information for the evaluation of dam safety levels was renewed. The probability index was then applied to dam rehabilitation decision-making. This method helps reduce the difficulty and uncertainty of the evaluation of dam safety levels and complies with the current safe decision-making regulations for dams in China. It also enhances the application of current risk analysis methods for dam safety levels.展开更多
Hydrocracking is a catalytic reaction process in the petroleum refineries for converting the higher boiling temperature residue of crude oil into a lighter fraction of hydrocarbons such as gasoline and diesel. In this...Hydrocracking is a catalytic reaction process in the petroleum refineries for converting the higher boiling temperature residue of crude oil into a lighter fraction of hydrocarbons such as gasoline and diesel. In this study, a modified continuous lumping kinetic approach is applied to model the hydro-cracking of vacuum gas oil. The model is modified to take into consideration the reactor temperature on the reaction yield distribution. The model is calibrated by maximizing the likelihood function between the modeled and measured data at four different reactor temperatures. Bayesian approach parameter estimation is also applied to obtain the confidence interval of model parameters by considering the uncertainty associated with the measured errors and the model structural errors. Then Monte Carlo simulation is applied to the posterior range of the model parameters to obtain the 95% confidence interval of the model outputs for each individual fraction of the hydrocracking products. A good agreement is observed between the output of the calibrated model and the measured data points. The Bayesian approach based on the Markov Chain Monte Carlo simulation is shown to be efficient to quantify the uncertainty associated with the parameter values of the continuous lumping model.展开更多
The state-of-the-art technology in the field of vehicle automation will lead to a mixed traffic environment in the coming years,where connected and automated vehicles have to interact with human-driven vehicles.In thi...The state-of-the-art technology in the field of vehicle automation will lead to a mixed traffic environment in the coming years,where connected and automated vehicles have to interact with human-driven vehicles.In this context,it is necessary to have intention prediction models with the capability of forecasting how the traffic scenario is going to evolve with respect to the physical state of vehicles,the possible maneuvers and the interactions between traffic participants within the seconds to come.This article presents a Bayesian approach for vehicle intention forecasting,utilizing a game-theoretic framework in the form of a Mixed Strategy Nash Equilibrium(MSNE)as a prior estimate to model the reciprocal influence between traffic participants.The likelihood is then computed based on the Kullback-Leibler divergence.The game is modeled as a static nonzero-sum polymatrix game with individual preferences,a well known strategic game.Finding the MSNE for these games is in the PPAD∩PLS complexity class,with polynomial-time tractability.The approach shows good results in simulations in the long term horizon(10s),with its computational complexity allowing for online applications.展开更多
The performance of adaptive array beamform-ing algorithms substantially degrades in practice because of a slight mismatch between actual and presumed array res-ponses to the desired signal.A novel robust adaptive beam...The performance of adaptive array beamform-ing algorithms substantially degrades in practice because of a slight mismatch between actual and presumed array res-ponses to the desired signal.A novel robust adaptive beam-forming algorithm based on Bayesian approach is therefore proposed.The algorithm responds to the current envi-ronment by estimating the direction of arrival(DOA)of the actual signal from observations.Computational com-plexity of the proposed algorithm can thus be reduced com-pared with other algorithms since the recursive method is used to obtain inverse matrix.In addition,it has strong robustness to the uncertainty of actual signal DOA and makes the mean output array signal-to-interference-plus-noise ratio(SINR)consistently approach the optimum.Simulation results show that the proposed algorithm is bet-ter in performance than conventional adaptive beamform-ing algorithms.展开更多
随着天文观测数据日益增多,通过数据驱动的方法推断中子星物质的状态方程成为一种可行的方案。本文采用贝叶斯推断和天体物理观测约束相对论平均场(Relativistic Mean Field,RMF)模型,并以此为基础,研究了核状态方程(Equation of State,...随着天文观测数据日益增多,通过数据驱动的方法推断中子星物质的状态方程成为一种可行的方案。本文采用贝叶斯推断和天体物理观测约束相对论平均场(Relativistic Mean Field,RMF)模型,并以此为基础,研究了核状态方程(Equation of State,EOS)和中子星结构。通过分析不同交点密度下与耦合常数密度依赖行为,发现较高的交点密度加强了天体物理观测数据对物态方程的约束,导致大质量中子星的中等密度行为变软,中心能量密度增加。特别地,我们发现包括在大质量中子星核中,声速平方超过共形极限(v_(s)^(2)>1/3)的概率很高。推断的最大中子星质量(M_(max)≥2.5 M⊙)与引力波事件(如GW190814)的解释一致,即其小质量伴星很可能对应于大质量中子星。此外,极端密度下的对称能和压强也表现出交点密度依赖性,符合多信使约束。展开更多
The constitutive model is essential for predicting the deformation and stability of rocksoil mass.The estimation of constitutive model parameters is a necessary and important task for the reliable characterization of ...The constitutive model is essential for predicting the deformation and stability of rocksoil mass.The estimation of constitutive model parameters is a necessary and important task for the reliable characterization of mechanical behaviors.However,constitutive model parameters cannot be evaluated accurately with a limited amount of test data,resulting in uncertainty in the prediction of stress-strain curves.This paper proposes a Bayesian analysis framework to address this issue.It combines the Bayesian updating with the structural reliability and adaptive conditional sampling methods to assess the equation parameter of constitutive models.Based on the triaxial and ring shear tests on shear zone soils from the Huangtupo landslide,a statistical damage constitutive model and a critical state hypoplastic constitutive model were used to demonstrate the effectiveness of the proposed framework.Moreover,the parameter uncertainty effects of the damage constitutive model on landslide stability were investigated.Results show that reasonable assessments of the constitutive model parameter can be well realized.The variability of stress-strain curves is strongly related to the model prediction performance.The estimation uncertainty of constitutive model parameters should not be ignored for the landslide stability calculation.Our study provides a reference for uncertainty analysis and parameter assessment of the constitutive model.展开更多
Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct ...Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct power functions to select the optimal sample size. We revise this approach when the focus is on testing a single binomial proportion. We consider exact methods and introduce a conservative criterion to account for the typical non-monotonic behavior of the power functions, when dealing with discrete data. The main purpose of this paper is to present a Shiny App providing a user-friendly, interactive tool to apply these criteria. The app also provides specific tools to elicit the analysis and the design prior distributions, which are the core of the two-priors approach.展开更多
Abundant test data are required in assessment of weapon performance. When weapon test data are insufficient, Bayesian analyses in small sample circumstance should be considered and the test data should be provided by ...Abundant test data are required in assessment of weapon performance. When weapon test data are insufficient, Bayesian analyses in small sample circumstance should be considered and the test data should be provided by simulations. The several Bayesian approaches are discussed and some limitations are founded. An improvement is put forward after limitations of Bayesian approaches available are analyzed and the improved approach is applied to assessment of some new weapon performance.展开更多
输入信号的方向向量出现偏差时,最小均方误差算法会出现收敛速度慢、输出性能下降、不稳定等问题.本文针对这些问题,对传统LMS(least mean squares)算法进行了改进,提出了基于Bayesian方法的鲁棒约束LMS算法.该算法利用信号的先验信息...输入信号的方向向量出现偏差时,最小均方误差算法会出现收敛速度慢、输出性能下降、不稳定等问题.本文针对这些问题,对传统LMS(least mean squares)算法进行了改进,提出了基于Bayesian方法的鲁棒约束LMS算法.该算法利用信号的先验信息对实际信号方向向量进行估计,有效地抑制了方向向量偏差的影响,并提高了系统的鲁棒性.阵列输出的信干噪比得到了改善,更加接近最优值.仿真实验验证了该算法的有效性和可行性.展开更多
文摘Soil-water characteristic curve (SWCC) is significant to estimate the site-specific unsaturated soil properties (such as unsaturated shear strength and coefficient of permeability) for geotechnical analyses involving unsaturated soils. Determining SWCC can be achieved by fitting data points obtained according to the prescribed experimental scheme, which is specified by the number of measuring points and their corresponding values of the control variable. The number of measuring points is limited since direct measurement of SWCC is often costly and time-consuming. Based on the limited number of measuring points, the estimated SWCC is unavoidably associated with uncertainties, which depends on measurement data obtained from the prescribed experimental scheme. Therefore, it is essential to plan the experimental scheme so as to reduce the uncertainty in the estimated SWCC. This study presented a Bayesian approach, called OBEDO, for probabilistic experimental design optimization of measuring SWCC based on the prior knowledge and information of testing apparatus. The uncertainty in estimated SWCC is quantified and the optimal experimental scheme with the maximum expected utility is determined by Subset Simulation optimization (SSO) in candidate experimental scheme space. The proposed approach is illustrated using an experimental design example given prior knowledge and the information of testing apparatus and is verified based on a set of real loess SWCC data, which were used to generate random experimental schemes to mimic the arbitrary arrangement of measuring points during SWCC testing in practice. Results show that the arbitrary arrangement of measuring points of SWCC testing is hardly superior to the optimal scheme obtained from OBEDO in terms of the expected utility. The proposed OBEDO approach provides a rational tool to optimize the arrangement of measuring points of SWCC test so as to obtain SWCC measurement data with relatively high expected utility for uncertainty reduction.
基金supported by National Natural Science Foundation of China(No.81403112)Beijing Natural Science Foundation(No.7154217)+1 种基金Scientific Research Program of Beijing University of Chinese Medicine(No.2015-JYB-XS104)Special Program for Beijing Key Laboratory of Chinese Medicine Manufacturing Process Control and Quality Evaluation(No.Z151100001615065)
文摘Coptis chinensis(Huanglian) is a commonly used traditional Chinese medicine(TCM) herb and alkaloids are the most important chemical constituents in it. In the present study, an isocratic reverse phase high performance liquid chromatography(RP-HPLC) method allowing the separation of six alkaloids in Huanglian was for the first time developed under the quality by design(Qb D) principles. First, five chromatographic parameters were identified to construct a Plackett-Burman experimental design. The critical resolution, analysis time, and peak width were responses modeled by multivariate linear regression. The results showed that the percentage of acetonitrile, concentration of sodium dodecyl sulfate, and concentration of potassium phosphate monobasic were statistically significant parameters(P < 0.05). Then, the Box-Behnken experimental design was applied to further evaluate the interactions between the three parameters on selected responses. Full quadratic models were built and used to establish the analytical design space. Moreover, the reliability of design space was estimated by the Bayesian posterior predictive distribution. The optimal separation was predicted at 40% acetonitrile, 1.7 g·m L-1of sodium dodecyl sulfate and 0.03 mol·m L-1 of potassium phosphate monobasic. Finally, the accuracy profile methodology was used to validate the established HPLC method. The results demonstrated that the Qb D concept could be efficiently used to develop a robust RP-HPLC analytical method for Huanglian.
基金supported by the National Science and Technology Support Program of China (Program for the Eleventh Five-Year Plan, Grant No. 2006BAC14B03 and 2006BAC05B03)the National Natural Science Foundation of China (Grant No. 50679043)
文摘In order to accurately predict and control the aging process of dams, new information should be collected continuously to renew the quantitative evaluation of dam safety levels. Owing to the complex structural characteristics of dams, it is quite difficult to predict the time-varying factors affecting their safety levels. It is not feasible to employ dynamic reliability indices to evaluate the actual safety levels of dams. Based on the relevant regulations for dam safety classification in China, a dynamic probability description of dam safety levels was developed. Using the Bayesian approach and effective information mining, as well as real-time information, this study achieved more rational evaluation and prediction of dam safety levels. With the Bayesian expression of discrete stochastic variables, the a priori probabilities of the dam safety levels determined by experts were combined wfth the likelihood probability of the real-time check information, and the probability information for the evaluation of dam safety levels was renewed. The probability index was then applied to dam rehabilitation decision-making. This method helps reduce the difficulty and uncertainty of the evaluation of dam safety levels and complies with the current safe decision-making regulations for dams in China. It also enhances the application of current risk analysis methods for dam safety levels.
文摘Hydrocracking is a catalytic reaction process in the petroleum refineries for converting the higher boiling temperature residue of crude oil into a lighter fraction of hydrocarbons such as gasoline and diesel. In this study, a modified continuous lumping kinetic approach is applied to model the hydro-cracking of vacuum gas oil. The model is modified to take into consideration the reactor temperature on the reaction yield distribution. The model is calibrated by maximizing the likelihood function between the modeled and measured data at four different reactor temperatures. Bayesian approach parameter estimation is also applied to obtain the confidence interval of model parameters by considering the uncertainty associated with the measured errors and the model structural errors. Then Monte Carlo simulation is applied to the posterior range of the model parameters to obtain the 95% confidence interval of the model outputs for each individual fraction of the hydrocracking products. A good agreement is observed between the output of the calibrated model and the measured data points. The Bayesian approach based on the Markov Chain Monte Carlo simulation is shown to be efficient to quantify the uncertainty associated with the parameter values of the continuous lumping model.
文摘The state-of-the-art technology in the field of vehicle automation will lead to a mixed traffic environment in the coming years,where connected and automated vehicles have to interact with human-driven vehicles.In this context,it is necessary to have intention prediction models with the capability of forecasting how the traffic scenario is going to evolve with respect to the physical state of vehicles,the possible maneuvers and the interactions between traffic participants within the seconds to come.This article presents a Bayesian approach for vehicle intention forecasting,utilizing a game-theoretic framework in the form of a Mixed Strategy Nash Equilibrium(MSNE)as a prior estimate to model the reciprocal influence between traffic participants.The likelihood is then computed based on the Kullback-Leibler divergence.The game is modeled as a static nonzero-sum polymatrix game with individual preferences,a well known strategic game.Finding the MSNE for these games is in the PPAD∩PLS complexity class,with polynomial-time tractability.The approach shows good results in simulations in the long term horizon(10s),with its computational complexity allowing for online applications.
基金was supported by the Specialized Research Fund for the Doctoral Program of Higher Education(No.20050145019)Directive Plan of Science Research from the Bureau of Education of Hebei Province(No.Z 2004103).
文摘The performance of adaptive array beamform-ing algorithms substantially degrades in practice because of a slight mismatch between actual and presumed array res-ponses to the desired signal.A novel robust adaptive beam-forming algorithm based on Bayesian approach is therefore proposed.The algorithm responds to the current envi-ronment by estimating the direction of arrival(DOA)of the actual signal from observations.Computational com-plexity of the proposed algorithm can thus be reduced com-pared with other algorithms since the recursive method is used to obtain inverse matrix.In addition,it has strong robustness to the uncertainty of actual signal DOA and makes the mean output array signal-to-interference-plus-noise ratio(SINR)consistently approach the optimum.Simulation results show that the proposed algorithm is bet-ter in performance than conventional adaptive beamform-ing algorithms.
文摘随着天文观测数据日益增多,通过数据驱动的方法推断中子星物质的状态方程成为一种可行的方案。本文采用贝叶斯推断和天体物理观测约束相对论平均场(Relativistic Mean Field,RMF)模型,并以此为基础,研究了核状态方程(Equation of State,EOS)和中子星结构。通过分析不同交点密度下与耦合常数密度依赖行为,发现较高的交点密度加强了天体物理观测数据对物态方程的约束,导致大质量中子星的中等密度行为变软,中心能量密度增加。特别地,我们发现包括在大质量中子星核中,声速平方超过共形极限(v_(s)^(2)>1/3)的概率很高。推断的最大中子星质量(M_(max)≥2.5 M⊙)与引力波事件(如GW190814)的解释一致,即其小质量伴星很可能对应于大质量中子星。此外,极端密度下的对称能和压强也表现出交点密度依赖性,符合多信使约束。
基金supported by the Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education(No.GLAB 2024ZR03)the National Natural Science Foundation of China(No.42407248)+2 种基金the Guizhou Provincial Basic Research Program(Natural Science)(No.QKHJC-[2023]-YB066)the Key Laboratory of Smart Earth(No.KF2023YB04-02)the Fundamental Research Funds for the Central Universities。
文摘The constitutive model is essential for predicting the deformation and stability of rocksoil mass.The estimation of constitutive model parameters is a necessary and important task for the reliable characterization of mechanical behaviors.However,constitutive model parameters cannot be evaluated accurately with a limited amount of test data,resulting in uncertainty in the prediction of stress-strain curves.This paper proposes a Bayesian analysis framework to address this issue.It combines the Bayesian updating with the structural reliability and adaptive conditional sampling methods to assess the equation parameter of constitutive models.Based on the triaxial and ring shear tests on shear zone soils from the Huangtupo landslide,a statistical damage constitutive model and a critical state hypoplastic constitutive model were used to demonstrate the effectiveness of the proposed framework.Moreover,the parameter uncertainty effects of the damage constitutive model on landslide stability were investigated.Results show that reasonable assessments of the constitutive model parameter can be well realized.The variability of stress-strain curves is strongly related to the model prediction performance.The estimation uncertainty of constitutive model parameters should not be ignored for the landslide stability calculation.Our study provides a reference for uncertainty analysis and parameter assessment of the constitutive model.
文摘Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct power functions to select the optimal sample size. We revise this approach when the focus is on testing a single binomial proportion. We consider exact methods and introduce a conservative criterion to account for the typical non-monotonic behavior of the power functions, when dealing with discrete data. The main purpose of this paper is to present a Shiny App providing a user-friendly, interactive tool to apply these criteria. The app also provides specific tools to elicit the analysis and the design prior distributions, which are the core of the two-priors approach.
文摘Abundant test data are required in assessment of weapon performance. When weapon test data are insufficient, Bayesian analyses in small sample circumstance should be considered and the test data should be provided by simulations. The several Bayesian approaches are discussed and some limitations are founded. An improvement is put forward after limitations of Bayesian approaches available are analyzed and the improved approach is applied to assessment of some new weapon performance.
文摘输入信号的方向向量出现偏差时,最小均方误差算法会出现收敛速度慢、输出性能下降、不稳定等问题.本文针对这些问题,对传统LMS(least mean squares)算法进行了改进,提出了基于Bayesian方法的鲁棒约束LMS算法.该算法利用信号的先验信息对实际信号方向向量进行估计,有效地抑制了方向向量偏差的影响,并提高了系统的鲁棒性.阵列输出的信干噪比得到了改善,更加接近最优值.仿真实验验证了该算法的有效性和可行性.
