混响背景下GTM回波检测算法研究

为改善混响背景下传统匹配滤波算法效果不佳问题,在分析其非平稳性、有色性和非高斯性的基础上,提出了混合高斯时变自回归模型(Gaussian mixture Tvar Model,GTM),推导了模型公式及其参数求解方法,形成了GTM回波检测算法。为对混响特性及滤波效果进行定量描述进而验证算法性能,给出了一种定量衡量混响非平稳性、有色性、非高斯特性的滤波效果评价方法。通过实测混响分析表明,GTM模型能够较好地拟合实测混响的概率密度曲线和功率谱密度曲线,实现了混响背景下回波的有效检测并改善混响特性。     

混合高斯概率密度模型动态簇算法参数估计

混合高斯概率密度模型可以很好地拟合样本的概率密度。在各高斯分量概率密度互不重叠的条件下，使用动态簇算法可以快速而精确地估计出混合高斯概率密度模型参数。这是一种基于最小均方差原则的递推算法，在正向推导出各种可能簇边界后，再根据确定的最末边界值逆向推定各前导簇边界，从而得到混合高斯概率密度模型参数估计值。算法介绍之后，给出了两个拥有不同概率密度分布的仿真建模实例．最后总结分析了该算法的优劣，并简介了算法的推广．     

混合高斯参数估计的动态簇算法

混合高斯概率密度模型可以很好地拟合非高斯样本的概率密度。在各高斯分量概率密度互不重叠的条件下,使用动态簇算法可以快速而精确地估计出混合高斯概率密度模型参数。这是一种基于最小均方差原则的递推算法,在正向推导出各种可能的簇边界后,再根据确定的最末边界值逆向推定各前导簇边界,从而得到混合高斯概率密度模型参数估计值。描述模型及参数估计问题之后,动态簇算法被推导出来。然后深入探讨了该算法的实质及适用条件。最后结合数值仿真实例,分析了动态簇算法的估计性能。     

混合高斯概率密度模型参数的期望最大化估计

混合高斯模型是对非高斯数据进行概率密度拟合典型模型,其参数估计可以通过期望最大化(EM)迭代算法获得。多维混合高斯模型参数的EM估计因结构庞杂而难以求解,而对主动检测背景的统计特性拟合来说,一维的混合高斯模型一般即已足够。描述了该情形下的混合高斯模型及其参数估计问题之后,导出了一种工程实用的、简化的EM迭代算法,并给出了可计算机编程实现的算法流程图。然后详细探讨了对EM估计精度与速度有着重要影响的参数初始化问题,给出了三种可选择的初值设置方案:高速度方案、高精度方案和二者的折衷方案,并分析了它们各自的适用场合。最后,结合一组数值仿真实例,演示了EM迭代算法的良好的混合高斯模型参数估计性能。     

Alpha稳定分布序列的数值仿真方法

Alpha稳定分布是对水声混响数据进行非高斯概率密度拟合的最优模型之一,而仿真产生服从标准参数系下的Alpha稳定分布序列是展开相应研究的基础。论述了三种参数系下服从Alpha稳定分布随机变量的变换关系及各种参数系表述的优缺点,实现了标准参数系下任意参数组合Alpha稳定分布序列的数值仿真;同时还利用直接数值积分法完成了无显性概率密度表达式的Alpha稳定分布序列概率密度值计算,以之作为理论值与统计值进行了分析比较,验证了数值仿真方法的正确性。     

偏斜非高斯随机振动信号幅值概率密度函数研究

偏斜非高斯振动信号幅值概率密度没有明确、简洁的解析表达式。研究概率密度的解析表达式,对于非高斯振动理论研究具有重要意义。针对以上需求,提出了一种基于高斯混合模型的概率密度函数表示方法。首先,通过时间样本序列得到偏斜非高斯振动信号前五阶矩的估计值。其次,根据平稳高斯随机过程各阶矩之间的定量关系,结合二阶高斯混合模型的数学表达式建立方程组,求解得到混合模型中每个高斯分量的均值、标准差和权重系数。然后,将每个高斯分量的参数代入高斯混合模型,得到偏斜非高斯振动信号的幅值概率密度的解析表达式。最后,将所提出的方法应用于仿真非高斯加速度信号和实测非高斯振动应力信号,充分验证了该方法的有效性和适用性。     

高斯流场中单自由度线性体系非高斯振动响应试验研究

对于风湍流等高斯分布流速场中的线性结构体系,当考虑荷载中脉动流速二次项的影响时,理论上其振动响应将呈现非高斯分布特性。基于调试得到的不同粗糙工况高斯流场,开展了单自由度线性体系顺流向振动响应测试,研究了单自由度线性体系加速度响应的非高斯分布特性,分析了粗糙度对响应非高斯成分的影响,讨论了三种常见非高斯概率密度逼近方法对响应的拟合效果。试验结果表明:试验高斯流场中单自由度线性体系的顺流向加速度响应主要呈现出尖峰非高斯分布特征,且随着紊流度的提高,响应非高斯性有增强的趋势;响应的非高斯概率密度宜采用高斯混合模型方法进行拟合。     

MMCE算法在FAGMM中的应用

提高说话人模型的识别性能一直是语音识别领域的一个重要课题。因子分析高斯混合模型（FAGMM）是因子分析方法与高斯混合模型（GMM）结合而成的多维概率统计模型,能更好地表征语音特征矢量的相关性,然而模型参数过多导致不能实现很好的分类。把改进的最小分类错误（MMCE）算法应用于该模型,形成一种新的FAGMM＋MMCE模型,能解决前述问题,而且克服了传统的最小分类错误（MCE）算法在系统训练时不灵活、训练速度慢的缺点。实验结果表明,在30个说话人的识别应用中,本模型的识别率随着高斯混合数的增加而提高,较传统的MCE算法,识别率平均提高了3%,训练时间也平均节省了20%,说明该方法是有效的。     

混合高斯参数估计的两种EM算法比较

混合高斯模型是一种典型的非高斯概率密度模型,获得广泛应用。其参数的优效估计可以通过最大似然方法获得,但最大似然估计往往因其非线性而难以实现,故期望最大化(Expectation-Maximization,EM)迭代算法成为一种常用的替代方法。常规EM算法性能受迭代初值设置影响大,且不能对模型阶数做出估计。一种名为贪婪EM的改进算法可以克服这两个缺点,获得更为准确的模型参数估计,但其运算量一般会远大于前者。本文对这两种EM算法进行综合研究,深入挖掘两者之间的关系,并基于相同的数值仿真实例,直观地演示比较两者的性能差异。     

一种新的基于声信号的故障分类算法

提出采用相空间重构与高斯混合模型相结合的方法,利用声信号对设备进行故障分类．此方法首先将一维声信号时间序列进行相空间重构,在高维相空间展示各故障状态下的动力学特性,然后通过最大期望值算法建立相空间的高斯混合模型,最后采用贝叶斯分类算法进行故障的识别．从齿轮故障试验台上采集常见齿轮故障的声信号并进行分类实验,验证了该方法的有效性．     

Improved modelling of the loading spectra using a mixture model approach

In order to perform a fatigue-life analysis of structures the parameters of the structure loading spectra must be assessed. If the load time series are counted using a two-parametric rainflow counting method, the structure loading spectrum provides a probability for the occurrence of a load-cycle with certain amplitude and mean values. It is beneficial for the prediction of the fatigue life to describe the loading spectrum by a continuous function. We have previously discovered that mixtures of Gaussian probability density functions can be used to model the loading spectra. The main problems of this approach that have not been satisfactorily resolved before are related to the estimation of the number of components in the applied mixture models, and to the modelling of the load-cycle distributions with relatively fat tails. In this article, we describe a method for estimating the parameters of mixture models, which allows automatic determination of the number of components in a mixture model. The presented method is applied for modelling simulated and measured loading spectra using mixtures of the multivariate Gaussian or t probability density functions. In the article we also show that the mixture of t probability density functions sometimes better describes the loading spectra than the mixture of Gaussian probability density functions.     

Distribution system state estimation through Gaussian mixture model of the load as pseudo-measurement

This study presents an approach to utilise the loads as pseudo-measurements for the purpose of distribution system state estimation (DSSE). The load probability density function (pdf) in the distribution network shows a number of variations at different nodes and cannot be represented by any specific distribution. The approach presented in this study represents all the load pdfs through the Gaussian mixture model (GMM). The expectation maximisation (EM) algorithm is used to obtain the parameters of the mixture components. The standard weighted least squares (WLS) algorithm utilises these load models as pseudo-measurements. The effectiveness of WLS is assessed through some statistical measures such as bias, consistency and quality of the estimates in a 95-bus generic distribution network model.     

有限混合体模型上的自动模型选择:一种崭新的数据建模方式

在数据建模和分析中,有限混合体模型被广泛地使用着。然而,如何仅仅针对一组来自于某个有限混合体模型的数据选择出分量或聚类的个数则依然是一个非常困难的问题。由于分量个数是混合体模型的规模度量,其选择问题被称为有限混合体的模型选择问题。最近,针对有限混合体模型,特别是高斯混合模型,一种自动模型选择学习机制逐步发展成熟起来。这种新的机制能够在学习参数的过程中自动地完成模型选择,为数据的建模与分析提供了一种新的思路与途径。本文将对于高斯混合模型或一般有限混合体模型的自动模型选择学习算法及其典型应用进行综述与总结。首先,我们综述了基于贝叶斯阴阳机和谐学习原则的自动模型选择学习算法。然后,我们描述了另一种基于熵惩罚的自动模型选择学习算法。最后,我们给出了自动模型选择学习算法的一些典型的应用。     

Image analysis applications on assessing static stability and flowability of self-consolidating concrete

A digital image processing (DIP) method associated with a MATLAB algorithm is used to evaluate cross sectional images of self-consolidating concrete (SCC). Two new parameters, such as inter-particle spacing of coarse aggregate and average mortar-to-coarse aggregate ratio, defined as average mortar thickness index (MTI), were proposed to quantitatively evaluate the static stability of SCC. Statistical models were developed to predict flowability of SCC mixtures. Test results revealed that the proposed DIP method and MATLAB algorithm can be successfully used to derive inter-particle spacing and MTI and quantitatively evaluate the static stability on hardened SCC samples. A probability density of 60% from histogram analysis appears to be a reasonable threshold for indicating a uniformly distributed SCC mixture. For a given mortar yield stress, a critical mortar viscosity of 1.30 Pa s tends to significantly affect the trend of slump flow changing with MTI. The investigated relationship between parameters measured from DIP method and existing theoretical frames is well correlated. The outcome of this study can be of practical value for providing an efficient and useful tool in designing mixture proportions of SCC.     

Identification of probabilistic distribution parameters for the mesoscopic stochastic fracture model

As a kind of multiphase composite material, the basic mechanical behaviors of concrete are randomness and nonlinearity. The mesoscopic stochastic fracture model (MSFM) which can reflect the coupling effect of randomness and nonlinearity, has been widely used for the nonlinear analysis of concrete structures. In this paper, we proposed a new stochastic modeling principle to identify the probabilistic distribution parameters of MSFM. In order to reduce the modeling works, a dimension-reduced algorithm is proposed as well. In this paper, an overview of MSFM is firstly presented to introduce the background of the research. Then the stochastic harmonic function (SHF) representation is introduced to express the random field mentioned in the MSFM, and the probability density evolution method (PDEM) is applied to obtain the theoretical probability density function (PDF) of the stress–strain relationships. Furthermore, a stochastic modeling principle is proposed, in which minimizing the Kullback–Leibler divergence (KLD) is taken as the optimization object. Based on the framework of genetic algorithm, a dimension-reduced algorithm is proposed to identify the parameters with reference to the data from tested complete curves of uniaxial compressive and uniaxial tensile stress–strain relationship of concrete. The results indicate that the proposed principle and algorithm can be used to identify the parameters of MSFM accurately and efficiently.     

基于高斯混合模型的非高斯随机振动幅值概率密度函数

针对非高斯振动信号的幅值概率密度函数难以用数学模型表述的问题,提出了基于高斯混合模型的非高斯概率密度函数表示方法。首先,基于时域样本信号得到非高斯振动信号的高阶矩估计值。其次,基于高斯随机过程偶次高阶矩之间的定量关系,结合二阶高斯混合模型建立方程组,求解得到混合模型中每个高斯分量的方差和权值。然后,将各高斯分量的权值和方差代入高斯混合模型,得到适用于对称非高斯振动信号的幅值概率密度函数。最后,通过仿真信号和实测振动信号,验证了该方法的有效性和适用性。     

Optimal Bayesian Experimental Design for Priors of Compact Support with Application to Shock‐Tube Experiments for Combustion Kinetics

The analysis of reactive systems in combustion science and technology relies on detailed models comprising many chemical reactions that describe the conversion of fuel and oxidizer into products and the formation of pollutants. Shock‐tube experiments are a convenient setting for measuring the rate parameters of individual reactions. The temperature, pressure, and concentration of reactants are chosen to maximize the sensitivity of the measured quantities to the rate parameter of the target reaction. In this study, we optimize the experimental setup computationally by optimal experimental design in a Bayesian framework. We approximate the posterior probability density functions (pdf) using truncated Gaussian distributions in order to account for the bounded domain of the uniform prior pdf of the parameters. The underlying Gaussian distribution is obtained in the spirit of the Laplace method, more precisely, the mode is chosen as the maximum a posteriori (MAP) estimate, and the covariance is chosen as the negative inverse of the Hessian of the misfit function at the MAP estimate. The model related entities are obtained from a polynomial surrogate. The optimality, quantified by the information gain measures, can be estimated efficiently by a rejection sampling algorithm against the underlying Gaussian probability distribution, rather than against the true posterior. This approach offers a significant error reduction when the magnitude of the invariants of the posterior covariance are comparable with the size of the bounded domain of the prior. We demonstrate the accuracy and superior computational efficiency of our method for shock‐tube experiments aiming to measure the model parameters of a key reaction, which is part of the complex kinetic network describing the hydrocarbon oxidation. In the experiments, the initial temperature and fuel concentration are optimized with respect to the expected information gain in the estimation of the parameters of the target reaction rate. We show that the expected information gain surface can change its “shape” dramatically according to the level of noise introduced into the synthetic data. The information that can be extracted from the data saturates as a logarithmic function of the number of experiments, and few experiments are needed when they are conducted at the optimal experimental design conditions. Furthermore, inversion of the legacy data indicates the validity and robustness of our designs. Copyright © 2016 John Wiley & Sons, Ltd.