Dynamic probability evaluation of safety levels of earth-rockfill dams using Bayesian approach

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.

Application of Bayesian Approach in the Parameter Estimation of Continuous Lumping Kinetic Model of Hydrocracking Process

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.

A Bayesian Approach with Prior Mixed Strategy Nash Equilibrium for Vehicle Intention Prediction

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.

Establishment and reliability evaluation of the design space for HPLC analysis of six alkaloids in Coptis chinensis(Huanglian) using Bayesian approach

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.

Frequentist and Bayesian Sample Size Determination for Single-Arm Clinical Trials Based on a Binary Response Variable: A Shiny App to Implement Exact Methods

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.

Robust adaptive beamforming algorithm based on Bayesian approach

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.

One-Sample Bayesian Predictive Analyses for a Nonhomogeneous Poisson Process with Delayed S-Shaped Intensity Function Using Non-Informative Priors

The delayed S-shaped software reliability growth model (SRGM) is one of the non-homogeneous Poisson process (NHPP) models which have been proposed for software reliability assessment. The model is distinctive because it has a mean value function that reflects the delay in failure reporting: there is a delay between failure detection and reporting time. The model captures error detection, isolation, and removal processes, thus is appropriate for software reliability analysis. Predictive analysis in software testing is useful in modifying, debugging, and determining when to terminate software development testing processes. However, Bayesian predictive analyses on the delayed S-shaped model have not been extensively explored. This paper uses the delayed S-shaped SRGM to address four issues in one-sample prediction associated with the software development testing process. Bayesian approach based on non-informative priors was used to derive explicit solutions for the four issues, and the developed methodologies were illustrated using real data.

Bayesian inference of the crust–core transition density via the neutron-star radius and neutron-skin thickness data

In this work,we perform a Bayesian inference of the crust-core transition density ρ_(t) of neutron stars based on the neutron-star radius and neutron-skin thickness data using a thermodynamical method.Uniform and Gaussian distributions for the ρ_(t) prior were adopted in the Bayesian approach.It has a larger probability of having values higher than 0.1 fm^(−3) for ρ_(t) as the uniform prior and neutron-star radius data were used.This was found to be controlled by the curvature K_(sym) of the nuclear symmetry energy.This phenomenon did not occur if K_(sym) was not extremely negative,namely,K_(sym)>−200 MeV.The value ofρ_(t) obtained was 0.075_(−0.01)^(+0.005) fm^(−3) at a confidence level of 68%when both the neutron-star radius and neutron-skin thickness data were considered.Strong anti-correlations were observed between ρ_(t),slope L,and curvature of the nuclear symmetry energy.The dependence of the three L-K_(sym) correlations predicted in the literature on crust-core density and pressure was quantitatively investigated.The most probable value of 0.08 fm^(−3) for ρ_(t) was obtained from the L-K_(sym) relationship proposed by Holt et al.while larger values were preferred for the other two relationships.

考虑需求响应及不确定性的综合能源优化调度

如何在区域综合能源系统中建立有效的需求侧模型,对于需求响应政策的实施至关重要。为提高用户参与需求响应积极性,引入实时定价机制,同时考虑系统的经济低碳性和电气热用户的用能满意度,构建兼顾系统和用户利益的综合需求响应主从博弈模型。针对用户参与需求响应的不确定性,引入贝叶斯方法更新负荷曲线。算例分析表明,所提博弈模型及贝叶斯方法能够有效平衡系统和用户之间的利益,提高了综合需求响应的可靠性。

Bayesian Set Estimation with Alternative Loss Functions: Optimality and Regret Analysis

Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses;2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example.

监测信息深度挖掘的供水管网污染源定位

为实现供水管网污染源及时准确地定位,针对配备在线水质监测设备的供水管网系统,提出一种充分挖掘水质传感器时序信息的贝叶斯方法,用于节点需水量随机波动条件下供水管网污染源定位。该方法采用蒙特卡洛模拟生成随机污染事件,构建各节点污染事件的观测信息概率分布,利用贝叶斯推断,根据传感器报警次序及时间观测信息,实时更新各候选污染节点的后验概率,并根据排序确定可疑污染源位置,同时对比不同传感器信息挖掘程度对定位结果的影响。结果表明,所提出的方法能在水质传感器报警信息累积时不断更新可疑候选节点的污染源后验概率,使候选节点个数降低,污染概率信息熵降低,能有效地识别出污染节点所在区域,且传感器信息挖掘程度越深,污染事件定位的准确率也越高。引入传感器首次报警时间作为辅助信息可以减少候选污染节点个数,降低候选节点污染源概率分布的不确定性,提高定位的准确性。

Bayesian反馈法估算体外循环术后患儿静注头孢拉定的药代动力学参数

目的 用Bayesian反馈法估算头孢拉定在体外循环术后患儿的药代动力学参数。方法 采用HPLC测定头孢拉定血药浓度。选择不同取样时间的 1个血药浓度作为反馈 ,用Bayesian法估算个体药代动力学参数 ,并与经典药代动力学方法估算的结果比较。结果 二步法估算个群体药代动力学参数为 :t1/ 2α(17.9± 6 .3)min ,t1/ 2 β(184.6± 10 0 .8)min ,Vc (0 .2 4± 0 .15 )L·kg-1,Vd(1.0 9± 0 .5 7)L·kg-1,CL(2 48.3± 5 5 .4)ml·h-1·kg-1。用 1个血药浓度反馈估算的药代动力学参数与经典药代动力学方法估算结果之间的差异无显著性。结论 用Bayesian反馈法估算个体药代动力学参数及预测血药浓度 ,可满足临床优化个体化给药方案的需要。

应用Bayesian反馈法预测阿替洛尔药物动力学参数及血药浓度

应用Ｂａｙｅｓｉａｎ反馈法预测２１例高血压病人，口服阿替洛尔的个体药动学参数及稳态血药浓度（Ｃｐｓｓ）并与经典药动学方法估算结果作比较，结果表明本法的Ｔ１／２为６．０±１．７ｈ，Ｖｄ为１．４３±０．１３Ｌ／ｋｇ，ＣＬ为１７２±３４ｍｌ／（ｈ·ｋｇ）；经典法的Ｔ１／２为６．８±２．４ｈ，Ｖｄ为１．４５±０．５６Ｌ／ｋｇ，ＣＬ为１６４±８５ｍｌ／（ｈ·ｋｇ）。两者无显著性差异（Ｐ＞０．０５）。两法所测得Ｃｐｓｓ有较好相关性（ｒ＝０．９９３）。

Bayesian反馈法估算体外循环术后患儿静注头孢拉定的药动学参数

目的：用Ｂａｙｅｓｉａｎ 反馈法估算头孢拉定在体外循环术后患儿的药动学参数，为临床应用提供依据。方法：采用ＨＰＬＣ法测定头孢拉定血药浓度。选择不同取样时间的１ 个血药浓度作为反馈，用Ｂａｙｅｓｉａｎ 法估算个体药动学参数，并与经典药动学方法估算的结果比较。结果：二步法估算的群体药动学参数为，Ｔ１／２α ０－３０ ±０－１０ｈ， Ｔ１／２β ３－０８ ±１－６８ｈ， Ｖｃ ０－２４ ±－１５Ｌ·ｋｇ－ １， Ｖｄ １－０９ ±０－５７Ｌ·ｋｇ－１ ， Ｃｌ２４８－３±５５－４ｍｌ·ｈ－１·ｋｇ－１ 。用１ 个血药浓度反馈估算的药动学参数与经典药动学方法估算结果之间的差异无显著性。结论：用Ｂａｙｅｓｉａｎ 反馈法估算个体药动学参数及预测血药浓度。

Small sample Bayesian analyses in assessment of weapon performance

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.

一种基于Bayesian方法的鲁棒自适应波束形成算法

由于在实际环境中,期望信号的阵列响应与实际阵列响应之间存在偏差,使得现存的一些自适应波束形成算法的性能下降.针对上述问题,基于Bayesian方法提出了鲁棒自适应波束形成算法,并且给出其递推形式.该算法利用接收到的采样信号对实际信号方向向量进行估计,降低了信号到来方向的不确定性,对信号方向向量的偏差具有较强的鲁棒性,从而可以保证输出阵列的信干噪比接近最优值.采用递推方法来计算逆矩阵,大大地降低了计算的复杂度,能够满足实时处理的要求.仿真实验表明,与传统自适应波束形成算法相比,所提鲁棒自适应波束形成算法具有更好的性能.

基于Bayesian方法的鲁棒约束LMS算法

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.

利用Bayesian-MC MC方法进行畜禽远交群多家系离散性状QTL连锁检测

利用Bayesian-MCMC方法对不同家系结构的畜禽远交群体的二级离散性状进行QTL连锁检测,在分析中,基于IBD方差组分的随机模型的定位策略,同时利用MCMC的3种不同抽样技术(Gibbs抽样、Metropolis抽样和ReversiblejumpMCMC抽样)产生相应QTL参数的后验样本,在此基础上进行目标参数的Bayesian统计推断。结果表明:Bayesian-MCMC方法能够对QTL数目进行准确估计,并且在不同家系结构下得到较为理想的参数估计结果。

Bayesian Reliability——Growth Analysis for Statistical of Diverse Population Based on Non-homogeneous Poisson Process

New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aiming at the test process which is high expense and small sample-size in the development of complex system, the specific methods are studied on how to process the statistical information of Bayesian reliability growth regarding diverse populations. Firstly, according to the characteristics of reliability growth during product development, the Bayesian method is used to integrate the testing information of multi-stage and the order relations of distribution parameters. And then a Gamma-Beta prior distribution is proposed based on non-homogeneous Poisson process（NHPP） corresponding to the reliability growth process. The posterior distribution of reliability parameters is obtained regarding different stages of product, and the reliability parameters are evaluated based on the posterior distribution. Finally, Bayesian approach proposed in this paper for multi-stage reliability growth test is applied to the test process which is small sample-size in the astronautics filed. The results of a numerical example show that the presented model can make use of the diverse information synthetically, and pave the way for the application of the Bayesian model for multi-stage reliability growth test evaluation with small sample-size. The method is useful for evaluating multi-stage system reliability and making reliability growth plan rationally.

指数分布可靠性增长分析的Bayesian整体推断方法

本文引入服从广义逆Gamma分布的折合因子,得到一种指数可靠性增长下失效率的Bayes整体推断技术,并采用Laguerre-Gauss积分方法得到了折合因子分布参数的精确数值解,通过典型示例与其它确定分布参数的方法进行比较,可知这种方法更加接近工程实际。