基于贝叶斯理论的钢筋混凝土柱受剪承载力计算

现行混凝土结构设计规范中钢筋混凝土柱的受剪承载力公式为半经验半理论计算公式,由于试验数据的有限性和钢筋混凝土材料离散性较大的本质特性,规范建议公式缺乏明确的理论模型。该文以贝叶斯动态信息更新思路,根据主观经验信息选定现行规范中钢筋混凝土柱受剪承载力计算公式作为贝叶斯先验模型,通过已完成试验研究的柱受剪承载力数据,应用贝叶斯方法综合这两类信息进行推断,建立钢筋混凝土柱在反复荷载作用下受剪承载力的概率模型,对未知参数进行估计,修正先验模型并建立后验模型,以达到对先验模型的更新。通过先验模型计算值、后验模型计算值及试验值相互间的对比分析可知：贝叶斯方法继承了先验信息的完备性和大量试验数据的准确性,能够更准确地预测钢筋混凝土柱的受剪承载力。     

Discrete uniform mixtures via posterior means

In this paper, we are concerned with identification of a discrete uniform mixture by the posterior mean. An exact formula for a prior distribution is given. Also some examples featuring negative binomial, negative hypergeometric and beta-Pascal distributions are provided.     

基于贝叶斯信息融合的测量不确定度评定与实时更新

基于贝叶斯信息融合与统计推断原理,建立不确定度动态评定模型,对测量不确定度进行实时更新。引入最大熵原理和爬山搜索优化算法,确定先验分布概率密度函数及样本信息似然函数,结合贝叶斯公式求出后验分布概率密度函数,实现不确定度的优化估计。仿真及实例分析表明,基于贝叶斯和最大熵方法评定及更新的测量不确定度更加接近理论值。     

多元先验信息的融合问题

在多元先验信息条件下，运用Bayes理论讨论问题时，必然会遇到先验信息融合问题，文中提出了几种简化形式，并针对产品失效率的多个先验信息情形，结合实例与熵度量的拟合优度说明了该方法的合理性。     

Information tradeoff

Summary A prior may be noninformative for one parameter at the cost of being informative for another parameter. This leads to the idea of tradeoff priors: priors that give up noninformativity for some parameters to achieve noninformativity for others. We propose a general framework where priors are selected by optimizing a functional with two components. The first component formalizes the requirement that the optimal prior be noninformative for the parameter of interest. The second component is a penalty term that forces the optimizing prior to be close to some target prior. Optimizing such a functional results in a parameterized family of priors from which a specific prior may be selected as the tradeoff prior. An important particular example of such functionals is provided by choosing the first term to be the marginal missing information for the parameter of interest (generalizing Bernardo’s notion of missing information) and the second term to be the relative entropy between the unknown prior and the Jeffreys prior. In this case we find a closed form expression for the tradeoff prior and we make explicit connections with the Berger-Bernardo prior. In particular, we show that under certain conditions, the Berger-Bernardo prior and the Jeffreys prior are special cases of the tradeoff prior. We consider several examples.     

评估ATAM计算效率提高程度的新算法

在《与荷载同步变化的时间步自动调整方法》中提出的时间步自动调整方法(apriori time adaptive method,ATAM)是先验式误差评估研究领域的一次有益尝试。在ATAM使用过程中,由于一般情况下难以获得解析解,所以对数值计算程序应用ATAM自动调整时间步长后,相比时间步调整前,无法评估计算效率具体提高了多少。为了解决这个问题,提出了解决方法并对其进行了验证。在此基础上,进一步提出了一种简易评估算法,并推导出评估计算效率提高程度的计算公式。根据此计算公式,不需要采用最小时间步长代入到原数值程序中进行计算,可直接获得计算效率的提高程度,节省了大量计算成本。同时,对简易评估算法进行了验证,结果证实所提算法实用有效。     

MI-Pack: Increased confidence of metabolite identification in mass spectra by integrating accurate masses and metabolic pathways

Metabolite identification is of central importance to metabolomics as it provides the route to new knowledge. Automated identification of the thousands of peaks detected by high resolution mass spectrometry is currently not possible, largely due to the finite mass accuracy of the spectrometer and the complexity that one peak can be assigned to one or more empirical formula(e) and each formula maps to one or more metabolites. Biological samples are not, however, composed of random metabolite mixtures, but instead comprise of thousands of compounds related through specific chemical transformations. Here we evaluate if prior biological knowledge of these transformations can improve metabolite identification accuracy.Our identification algorithm - which uses metabolite interconnectivity from the KEGG database to putatively identify metabolites by name - is based on mapping an experimentally-derived empirical formula difference for a pair of peaks to a known empirical formula difference between substrate-product pairs derived from KEGG, termed transformation mapping (TM). To maximize identification accuracy, we also developed a novel semi-automated method to calculate a mass error surface associated with experimental peak-pair differences. The TM algorithm with mass error surface has been extensively validated using simulated and experimental datasets by calculating false positive and false negative rates of metabolite identification. Compared to the traditional identification method of database searching accurate masses on a single-peak-by-peak basis, the TM algorithm reduces the false positive rate of identification by > 4-fold, while maintaining a minimal false negative rate. The mass error surface, putative identification of metabolite names, and calculation of false positive and false negative rates collectively advance and improve upon related previous research on this topic [1, 2]. We conclude that inclusion of prior biological knowledge in the form of metabolic pathways provides one route to more accurate metabolite identification.     

Implicit and explicit prior information in near-infrared spectral imaging: accuracy, quantification and diagnostic value

Near-infrared spectroscopy (NIRS) of tissue provides quantification of absorbers, scattering and luminescent agents in bulk tissue through the use of measurement data and assumptions. Prior knowledge can be critical about things such as (i) the tissue shape and/or structure, (ii) spectral constituents, (iii) limits on parameters, (iv) demographic or biomarker data, and (v) biophysical models of the temporal signal shapes. A general framework of NIRS imaging with prior information is presented, showing that prior information datasets could be incorporated at any step in the NIRS process, with the general workflow being: (i) data acquisition, (ii) pre-processing, (iii) forward model, (iv)?inversion/reconstruction, (v) post-processing, and (vi) interpretation/diagnosis. Most of the development in NIRS has used ad hoc or empirical implementations of prior information such as pre-measured absorber or fluorophore spectra, or tissue shapes as estimated by additional imaging tools. A comprehensive analysis would examine what prior information maximizes the accuracy in recovery and value for medical diagnosis, when implemented at separate stages of the NIRS sequence. Individual applications of prior information can show increases in accuracy or improved ability to estimate biochemical features of tissue, while other approaches may not. Most beneficial inclusion of prior information has been in the inversion/reconstruction process, because it solves the mathematical intractability. However, it is not clear that this is always the most beneficial stage.     

改进的模糊阈值图像分割方法

提出了一种自适应的模糊阈值图像分割方法,通过预分割和直方图信息相结合的方法,解决了传统的模糊闽值图像分割法难以自动获取窗宽的困难;并针对模糊闽值图像分割方法不能适用于直方图呈单峰分布的图像的缺陷,提出了一个新的平滑迭代公式。该平滑迭代公式利用像素点的邻域信息使图像增强,再使用自适应的模糊阈值图像分割方法进行分割,可以拓宽模糊阈值图像分割方法的适用范围。实验结果表明,使用该方法的目标分割正确率达97.3％,显示了较高的分割精度和较强的鲁棒性。     

结构施工过程中节段参数的连续识别

通过考虑施工因素的相关性,将随机结构分析的概念引入结构施工过程的节段参数识别中。再考虑施工过程中结构体系不断变化的特点,进行系统重构,将节段参数的相关信息引入识别过程。最后根据最大后验概率的参数估计准则,推导得到了对多个节段参数的均值和方差进行连续识别的递进估计算法。数值算例的结果显示,通过考虑实际施工中的相关信息,本文方法对结构施工过程中的节段参数不仅能进行有效的识别,还具有良好的预测功能,可对施工过程控制进行指导。     

Perspective projection of non-convex polyhedra

An algorithm is presented for removing hidden lines for isometric and perspective projections of three-dimensional objects. An object can be regarded as being made up of a number of planes, and the whole picture can therefore be visualized as only a collection of planes. Considering planes as the basic element of a picture, non-convex polyhedra can be displayed directly without prior subdivisions into convex ones. Lines connecting nodal points are first retrieved from the model to be plotted by a simple but efficient technique. On the picture planes, each unique line is examined in turn to see if it is totally or partially hidden. The intersections between a unique line and a projected plane (with or without openings) are determined by a new method which, even in the presence of numerical errors, will always give correct intersection information. Unlike many classical algorithms, intersections are determined by a single formula without tedious case subdivisions. With little additional calculations, object penetrations can also be tackled.     

Shannon optimal priors on independent identically distributed statistical experiments converge weakly to Jeffreys' prior

In 1979, J.M. Bernardo argued heuristically that in the case of regular product experiments his information theoretic reference prior is equal to Jeffreys' prior. In this context, B.S. Clarke and A.R. Barron showed in 1994, that in the same class of experiments Jeffreys' prior is asymptotically optimal in the sense of Shannon, or, in Bayesian terms, Jeffreys' prior is asymptotically least favorable under Kullback Leibler risk. In the present paper, we prove, based on Clarke and Barron's results, that every sequence of Shannon optimal priors on a sequence of regular iid product experiments converges weakly to Jeffreys' prior. This means that for increasing sample size Kullback Leibler least favorable priors tend to Jeffreys' prior.     

The bayesian approach to the combination of forecasts: Some extensions into a Skewed environment

Where a decision-maker has to rely on expert opinions a need for a normative model to combine these forecasts appears. This can be done using Bayes' formula and by making some assumptions on the prior distribution and the distribution of the expert assessments. We extend the case to skewed distributions of these assessments. By using an Edgeworth expansion of the density function including the skewness parameter, we are able to obtain the formula to combine the forecasts in a Bayesian way.      

近程毫米波合成孔径辐射计被动测距原理

毫米波合成孔径技术利用了物体自身辐射电磁波的相位信息,采用很少阵元就能实现实时成像,但目前合成孔径技术只是限于亮温成像,缺少了目标的距离信息,这对于目标探测与识别很不利。提出在近程条件下合成孔径被动测距原理和相应的双正交傅立叶变换算法,并给出了近程距离分辨率公式,近程成像的特点是成像公式中存在二次相位因子,而且距离分辨率和距离的平方成反比。毫米波合成孔径被动成像可以同时得到物体辐射的亮温分布和距离分布,能够有效克服离焦引起的图像模糊,对图像的反降晰和目标识别具有重要意义。     

基于超拉普拉斯先验与核谱特性噪声图像盲去模糊

现有大部分盲图像去模糊方法对噪声敏感,即使少量的噪声可大大降低恢复图像的质量．考虑到模糊图像中同时隐含有清晰图像信息和模糊核信息,我们同时利用卷积核谱特性先验和清晰图像梯度域超拉普拉斯先验联合建立含噪图像盲去模糊模型,较单独使用卷积核先验与清晰图像先验建模更合理,也能获得更精确的估计图像．本文借助于Hessian矩阵,利用模糊图像及卷积核联合生成先验子,而非单独的估计图像先验子,建立优化模型．求解模型时,通过迭代策略交替细化模糊核和清晰图像．在清晰图像恢复阶段,因存在超拉普拉斯先验项,提出用变量分离法计算清晰图像．清晰图像采用快速傅里叶变换及封闭阈值公式求解,以提高优化速度．实验结果表明：与其他方法相比,本文方法能获得更鲁棒的模糊核和更精确的清晰图像,且收敛速度更快．     

一种自动提取IVUS图像血管包络的新方法

提取血管内超声(IVUS)图像的血管包络对冠状动脉疾病的诊断有一定的积极意义。本文综合考虑IVUS图像的灰度特征、序列时间特性、先验知识等三类信息,提出一种自动提取血管包络的方法。先由序列时间特性和先验知识减少噪声和伪像干扰,提取出第一帧图像的初始包络;然后用结合梯度、灰度方差、灰度均值信息的B样条GVFsnake对初始包络进行变形得到第一帧的最终包络;最后利用序列图像的时间特性提取后续帧的包络。通过实验表明:综合三类信息的包络自动提取方法在精度和鲁棒性等方面优于以往的方法。     

系统识别过程中参数协差阵的先验估计

系统识别的损伤检测和估计是建立在参数估计上的。当考虑参数的随机特性时,必须对参数的方差和参数之间的相关系数作出估计。本文提出了参数协差阵的先验估计方法,对于同一单元内不同类型的参数,通过将参数分解为一系列统计独立的要素,利用函数协差阵与变量协差阵之间的关系求得参数的协差阵。不同单元的同一类型参数的相关系数通过对检测数据的数理统计或利用工程师的经验得到估计。     

Effects of a priori parameter selection in minimum relative entropy method on inverse electrocardiography problem

The goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface measurements and a mathematical model of torso–heart geometry that relates the sources to the measurements. This problem is ill-posed due to attenuation and smoothing that occur inside the thorax, and small errors in the measurements yield large reconstruction errors. To overcome this, ill-posedness, traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition and statistical approaches such as Bayesian Maximum A Posteriori estimation and Kalman filter have been applied. Statistical methods have yielded accurate inverse solutions; however, they require knowledge of a good a priori probability density function, or state transition definition. Minimum relative entropy (MRE) is an approach for inferring probability density function from a set of constraints and prior information, and may be an alternative to those statistical methods since it operates with more simple prior information definitions. However, success of the MRE method also depends on good choice of prior parameters in the form of upper and lower bound values, expected uncertainty in the model and the prior mean. In this paper, we explore the effects of each of these parameters on the solution of inverse ECG problem and discuss the limitations of the method. Our results show that the prior expected value is the most influential of the three MRE parameters.     

Prediction of compressive strength of concrete with fly ash as sand replacement material

Fly ash (FA) acts as a partial replacement material for both Portland cement and fine aggregate. The published information on FA as sand (fine aggregate) replacement material (SRM) is limited and rational guidelines to estimate the compressive strength of concrete are not available. This aspect was investigated and a formula to predict the compressive strength of concrete at 28 day is suggested in this paper. This formula, containing cementing efficiency factor, k, of FA, is useful also when the quantity of FA used is more than that of sand replaced. Application of the formula to the test data in published literature, indicate that it can estimate the compressive strength of concrete containing different levels of sand replacement by fly ash.     

斜投影显微图像分析法测量片状颗粒厚度的研究

与传统正投影显微图像分析方法不同,本文应用斜投影法,通过变换观测颗粒群的角度,依据获得的光学显微镜下颗粒群的信息,推导出了颗粒群厚度的计算公式,并讨论了厚度分辨能力与倾斜角、放大倍数之间的关系,同时应用实例证明了该方法的可行性。