Bayesian compressive sensing for cluster structured sparse signals

In traditional framework of compressive sensing (CS), only sparse prior on the property of signals in time or frequency domain is adopted to guarantee the exact inverse recovery. Other than sparse prior, structures on the sparse pattern of the signal have also been used as an additional prior, called model-based compressive sensing, such as clustered structure and tree structure on wavelet coefficients. In this paper, the cluster structured sparse signals are investigated. Under the framework of Bayesian compressive sensing, a hierarchical Bayesian model is employed to model both the sparse prior and cluster prior, then Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms which are also taking into account the cluster prior, the proposed algorithm solves the inverse problem automatically—prior information on the number of clusters and the size of each cluster is unknown. The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms.     

Support vector regression via MCMC within evidence framework

This paper proposes a novel approach, Markov Chain Monte Carlo (MCMC) sampling approximation, to deal with intractable high-dimension integral in the evidence framework applied to Support Vector Regression (SVR). Unlike traditional variational or mean field method, the proposed approach follows the idea of MCMC, firstly draws some samples from the posterior distribution on SVR??s weight vector, and then approximates the expected output integrals by finite sums. Experimental results show the proposed approach is feasible and robust to noise. It also shows the performance of proposed approach and Relevance Vector Machine (RVM) is comparable under the noise circumstances. They give better robustness compared to standard SVR.     

一种改进的MCMC移动步骤的U粒子滤波算法

粒子退化是标准粒子滤波算法的主要缺陷。针对这一缺陷,提出了一种改进算法,在提出的具有MCMC移动步骤的U粒子滤波算法上进行性能分析,从样本产生和对MCMC移动步骤的使用两个方面对算法进行改进,减小了算法的计算量,提高算法的运算速度。仿真结果表明,改进后的算法大大减少了运算量,从一定程度上提高了运行效率。     

Comparison of different uncertainty techniques in urban stormwater quantity and quality modelling

Urban drainage models are important tools used by both practitioners and scientists in the field of stormwater management. These models are often conceptual and usually require calibration using local datasets. The quantification of the uncertainty associated with the models is a must, although it is rarely practiced. The International Working Group on Data and Models, which works under the IWA/IAHR Joint Committee on Urban Drainage, has been working on the development of a framework for defining and assessing uncertainties in the field of urban drainage modelling. A part of that work is the assessment and comparison of different techniques generally used in the uncertainty assessment of the parameters of water models. This paper compares a number of these techniques: the Generalized Likelihood Uncertainty Estimation (GLUE), the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), an approach based on a multi-objective auto-calibration (a multialgorithm, genetically adaptive multi-objective method, AMALGAM) and a Bayesian approach based on a simplified Markov Chain Monte Carlo method (implemented in the software MICA). To allow a meaningful comparison among the different uncertainty techniques, common criteria have been set for the likelihood formulation, defining the number of simulations, and the measure of uncertainty bounds. Moreover, all the uncertainty techniques were implemented for the same case study, in which the same stormwater quantity and quality model was used alongside the same dataset. The comparison results for a well-posed rainfall/runoff model showed that the four methods provide similar probability distributions of model parameters, and model prediction intervals. For ill-posed water quality model the differences between the results were much wider; and the paper provides the specific advantages and disadvantages of each method. In relation to computational efficiency (i.e. number of iterations required to generate the probability distribution of parameters), it was found that SCEM-UA and AMALGAM produce results quicker than GLUE in terms of required number of simulations. However, GLUE requires the lowest modelling skills and is easy to implement. All non-Bayesian methods have problems with the way they accept behavioural parameter sets, e.g. GLUE, SCEM-UA and AMALGAM have subjective acceptance thresholds, while MICA has usually problem with its hypothesis on normality of residuals. It is concluded that modellers should select the method which is most suitable for the system they are modelling (e.g. complexity of the model’s structure including the number of parameters), their skill/knowledge level, the available information, and the purpose of their study.     

基于滑窗MCMC的弹道导弹分导团目标数据关联研究

弹道导弹在再入过程中为了提高自身突防能力往往伴随着分导现象。由于分导弹头数目未知,距离目标近且再入速度非常相近,使其以团状形态运动,在未知导弹任何先验信息前提下如何对分导弹头进行快速关联已成为亟待解决的难题。该文提出了一种改进的实时滑窗马尔可夫链-蒙特卡洛(Markov Chain Monte Carlo,MCMC)次优数据关联算法,它应用蒙特卡洛采样方法对监控区域的测量集合进行组合优化,获得最大的后验概率密度进而逼近马氏链的平稳分布。该算法结合弹头分导实际情况,重新分配关联假设权值并优化了继承性,极大地减小了关联时间。仿真结果表明该算法与经典的多假设算法相比,关联概率随着目标密集程度增加而显著提高,并且计算量远小于多假设算法。     

一种基于阵列单通道的DOA估计新方法

为克服阵列多通道系统硬件量大,造价高及通道间存在不一致时性能恶化等不足,提出了一种新的基于阵列单通道的DOA估计方法。首先,通过射频开关控制接收通道轮流对各阵元进行采样建立新的阵列单通道窄带信号空间谱估计模型,接着基于该模型推导了来波方向的后验概率密度函数,然后结合马尔科夫链蒙特卡洛方法(MCMC),实现了DOA的估计。仿真实验结果表明,该方法参数估计性能好,分辨率高,能够处理相干信号。     

重力影响条件下拱的振动分析

利用哈密尔顿原理推导了均匀分布重力作用下圆弧拱振动控制方程,用Galerkin方法计算了考虑重力影响条件下拱结构的振动频率,分析了均匀分布重力的大小对拱结构振动频率的影响。     

考虑地基及楼板变形时框剪结构协同分析

采用沿高度方向连续化方法,对考虑地基及楼板变形的框架-剪力墙结构进行协同分析.把每榀抗侧力单元看作竖放的铁摩辛柯梁,通过弹性楼板协同工作,并考虑地基变形的影响,导出框架-剪力墙结构协同分析的哈密顿正则方程.通过Matlab编程,用精细积分法求出问题的高精度数值解.     

Calibrating and validating bacterial water quality models: A Bayesian approach

Water resource management decisions often depend on mechanistic or empirical models to predict water quality conditions under future pollutant loading scenarios. These decisions, such as whether or not to restrict public access to a water resource area, may therefore vary depending on how models reflect process, observation, and analytical uncertainty and variability. Nonetheless, few probabilistic modeling tools have been developed which explicitly propagate fecal indicator bacteria (FIB) analysis uncertainty into predictive bacterial water quality model parameters and response variables. Here, we compare three approaches to modeling variability in two different FIB water quality models. We first calibrate a well-known first-order bacterial decay model using approaches ranging from ordinary least squares (OLS) linear regression to Bayesian Markov chain Monte Carlo (MCMC) procedures. We then calibrate a less frequently used empirical bacterial die-off model using the same range of procedures (and the same data). Finally, we propose an innovative approach to evaluating the predictive performance of each calibrated model using a leave-one-out cross-validation procedure and assessing the probability distributions of the resulting Bayesian posterior predictive p-values. Our results suggest that different approaches to acknowledging uncertainty can lead to discrepancies between parameter mean and variance estimates and predictive performance for the same FIB water quality model. Our results also suggest that models without a bacterial kinetics parameter related to the rate of decay may more appropriately reflect FIB fate and transport processes, regardless of how variability and uncertainty are acknowledged.     

MCMC粒子滤波算法研究及应用

粒子滤波算法是一种基于贝叶斯估计的蒙特卡罗方法,适用于非线性非高斯系统的分析,被广泛应用于跟踪、定位等问题的研究中。为了解决粒子滤波算法在重采样后,丧失粒子多样性的问题,本文在粒子滤波算法的重采样步骤后,加入了马尔可夫链蒙特卡罗（Markov Chain Monte Carlo,简称MCMC）移动步骤,增加粒子的多样性。利用粒子滤波算法和MCMC粒子滤波算法对目标跟踪问题进行了仿真,并且通过分析仿真实验结果,比较了两种算法的性能,结果说明加入MCMC粒子滤波算法的性能优于粒子滤波算法。