基于熵的语音音质评价方法

研究一种基于熵的语音音质客观评价方法,解决语音编、解码,通信设备研制以及通信干扰性能判定过程中长期使用主观评价的不便性。首先详细分析了信息的统计特性,在此基础上引入了马尔可夫信源并论证了语音信号的马尔可夫特性,介绍了一种用马尔可夫熵来表征语音音质变化的方法,试验数据验证了该方法具有一定的可靠性、可行性和应用前景。     

Maximum entropy principle and non-stationary distributions of stochastic systems

The principle of maximum entropy (in its classical form), successfully applied in many fields (e.g. statistics, reliability, estimation), has recently been extended to analyze the systems governed by stochastic differential equations and especially to determining the stationary probability distribution of the solution process. In this paper we develop the maximum entropy approach to characterize non-stationary probability distributions of the solutions of stochastic systems. The variational problem for the entropy functional includes time-dependent constraints in the form of differential equations for moments. The general scheme of the method is given along with the effective treatment of a number of first and second order stochastic systems. The maximum entropy probability distributions are compared with the exact solutions and with the simulation results.     

基于近似熵的语音端点检测

提高语音信号端点检测的正确率一直是语音识别领域的一个重要课题,特别是提高在各种实际噪声环境下语音端点检测的正确率更为重要,而传统的基于能量与过零率的方法在噪声环境下不能有效地工作。近似熵是一种新的度量序列复杂性的方法,它具有较强的抗干扰能力。从信号复杂性的角度提出了一种基于近似熵的带噪语音端点检测方法,证明了通过给定一个合理的阈值可以有效地进行语音端点检测。在不同类型噪声及不同信噪比环境下进行实验,结果表明,对语音信号起点和终点的检测性能均要比传统基于能量的方法要好,即使是在较低的信噪比下,该方法仍能够比较准确地检测出语音的起止端点。     

前视成像声呐最大熵超分辨算法及验证

声呐方位向上的接收信息可以看作是目标散射信息和波束方向图卷积的结果,通过解卷积的方法可以恢复出目标的散射信息,但是反问题的求解存在着固有的"病态性"问题.为了使解卷积的"病态性"问题转换成"良性"问题求解,文章采用最大熵作为正则化约束项,不局限于原始场景中的目标分布,利用Frieden熵作为衡量最终解的标准,引入图像熵...     

Uncertainty-based sensitivity indices for imprecise probability distributions

An uncertainty-based sensitivity index represents the contribution that uncertainty in model input X_i makes to the uncertainty in model output Y. This paper addresses the situation where the uncertainties in the model inputs are expressed as closed convex sets of probability measures, a situation that exists when inputs are expressed as intervals or sets of intervals with no particular distribution specified over the intervals, or as probability distributions with interval-valued parameters. Three different approaches to measuring uncertainty, and hence uncertainty-based sensitivity, are explored. Variance-based sensitivity analysis (VBSA) estimates the contribution that each uncertain input, acting individually or in combination, makes to variance in the model output. The partial expected value of perfect information (partial EVPI), quantifies the (financial) value of learning the true numeric value of an input. For both of these sensitivity indices the generalization to closed convex sets of probability measures yields lower and upper sensitivity indices. Finally, the use of relative entropy as an uncertainty-based sensitivity index is introduced and extended to the imprecise setting, drawing upon recent work on entropy measures for imprecise information.     

A maximum entropy characterization of symmetric Kotz type and Burr multivariate distributions

In this paper a maximum entropy characterization is presented for Kotz type symmetric multivariate distributions as well as for multivariate Burr and Pareto type III distributions. Analytical formulae for the Shannon entropy of these multivariate distributions are also derived.     

Lancaster bivariate probability distributions with Poisson, negative binomial and gamma margins

The so-called Lancaster probabilities on R² are a class of distributions satisfying an orthogonality condition involving orthogonal polynomials with respect to their marginal laws. They are characterized in the cases where the two identical margins are Gaussian, gamma (the latter are known results, but a new treatment is given), Poisson or negative binomial distributions. Some partial results are obtained in the cases of two different Poisson or negative binomial margins, and also in the case where one margin is gamma and the other margin is negative binomial.     

Maximum entropy pdfs and the moment problem under near-Gaussian conditions

This paper focuses on a class of continuous probability density functions (pdfs) that are generated by the maximum entropy method (mem), which are of potential interest in fluid dynamics. It discusses their properties and presents a method for obtaining approximate solutions to the moment problem that is associated with this class of pdfs. The method allows one to express pdf parameters in terms of constrained moments, alone. The results thus obtained hold for pdfs that represent small perturbations from a known pdf within this class. On combining these results with exact moment equations, one obtains successful approximations to the closure relations that are associated with these pdfs. The Gaussian pdf belongs in this class, and the method can be used to explore the near-Gaussian region.     

Local estimation of failure probability function and its confidence interval with maximum entropy principle

An approach is developed to locally estimate the failure probability of a system under various design values. Although it seems to require numerous reliability analysis runs to locally estimate the failure probability function, which is a function of the design variables, the approach only requires a single reliability analysis run. The approach can be regarded as an extension of that proposed by Au [Au SK. Reliability-based design sensitivity by efficient simulation. Computers and Structures 2005;83(14):1048–61], but it proposes a better framework in estimating the failure probability function. The key idea is to implement the maximum entropy principle in estimating the failure probability function. The resulting local failure probability function estimate is more robust; moreover, it is possible to find the confidence interval of the failure probability function as well as estimate the gradient of the logarithm of that function with respect to the design variables. The use of the new approach is demonstrated with several simulated examples. The results show that the new approach can effectively locally estimate the failure probability function and the confidence interval with one single Subset Simulation run. Moreover, the new approach is applicable when the dimension of the uncertainties is high and when the system is highly nonlinear. The approach should be valuable for reliability-based optimization and reliability sensitivity analysis.     

Kernel density maximum entropy method with generalized moments for evaluating probability distributions,including tails,from a small sample of data

In this paper, a novel method to determine the distribution of a random variable from a sample of data is presented. The approach is called generalized kernel density maximum entropy method, because it adopts a kernel density representation of the target distribution, while its free parameters are determined through the principle of maximum entropy (ME). Here, the ME solution is determined by assuming that the available information is represented from generalized moments, which include as their subsets the power and the fractional ones. The proposed method has several important features: (1) applicable to distributions with any kind of support, (2) computational efficiency because the ME solution is simply obtained as a set of systems of linear equations, (3) good trade‐off between bias and variance, and (4) good estimates of the tails of the distribution, in the presence of samples of small size. Moreover, the joint application of generalized kernel density maximum entropy with a bootstrap resampling allows to define credible bounds of the target distribution. The method is first benchmarked through an example of stochastic dynamic analysis. Subsequently, it is used to evaluate the seismic fragility functions of a reinforced concrete frame, from the knowledge of a small set of available ground motions.     

On the existence of maximum entropy distributions with four and more assigned moments

It is known that the probability distribution satisfy the Maximum Entropy Principle (MEP) if the available data consist in four moments of probability density function. Two problems are typically associated with use of MEP: the definition of the range of acceptable values for the moments M_i; the evaluation of the coefficients a_j. Both problems have already been accurately resolved by analytical procedures when the first two moments of the distribution are known.

In this work, the analytical solution in the case of four known moments is provided and a criterion for confronting the general case (whatever the number of known moments) is expounded. The first four moments are expressed in nondimensional form through the expectation and the coefficients of variation, skewness and kurtosis. The range of their acceptable values is obtained from the analytical properties of the differential equations which govern the problem and from the Schwarz inequality.     

Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes,random fields and random matrices

The construction of probabilistic models in computational mechanics requires the effective construction of probability distributions of random variables in high dimension. This paper deals with the effective construction of the probability distribution in high dimension of a vector‐valued random variable using the maximum entropy principle. The integrals in high dimension are then calculated in constructing the stationary solution of an Itô stochastic differential equation associated with its invariant measure. A random generator of independent realizations is explicitly constructed in this paper. Three fundamental applications are presented. The first one is a new formulation of the stochastic inverse problem related to the construction of the probability distribution in high dimension of an unknown non‐stationary random time series (random accelerograms) for which the velocity response spectrum is given. The second one is also a new formulation related to the construction of the probability distribution of positive‐definite band random matrices. Finally, we present an extension of the theory when the support of the probability distribution is not all the space but is any part of the space. The third application is then a new formulation related to the construction of the probability distribution of the Karhunen–Loeve expansion of non‐Gaussian positive‐valued random fields. Copyright © 2008 John Wiley & Sons, Ltd.     

Different forms of entropy dimension for zero entropy systems

The aim of this paper is to introduce the lower s-topological entropy to distinguish zero entropy systems. That this quantity is an invariant factor under topological conjugacy and a power rule is shown. Some examples are given to show that the lower entropy dimension can attain any value in (0, 1), and are different with the upper one and the entropy dimension in the sense of Bowen. A counterexample is used to indicate that the product rule does not hold, and the lower s-topological entropy of the subsystem for the non-wandering set can be strictly less than that of the system when 0 < s < 1. Finally, this study also constructs a dynamical system to show that the transitive system with zero entropy dimension may not be minimal.     

An efficient metamodeling approach for uncertainty quantification of complex systems with arbitrary parameter probability distributions

This paper proposes an efficient metamodeling approach for uncertainty quantification of complex system based on Gaussian process model (GPM). The proposed GPM‐based method is able to efficiently and accurately calculate the mean and variance of model outputs with uncertain parameters specified by arbitrary probability distributions. Because of the use of GPM, the closed form expressions of mean and variance can be derived by decomposing high‐dimensional integrals into one‐dimensional integrals. This paper details on how to efficiently compute the one‐dimensional integrals. When the parameters are either uniformly or normally distributed, the one‐dimensional integrals can be analytically evaluated, while when parameters do not follow normal or uniform distributions, this paper adopts the effective Gaussian quadrature technique for the fast computation of the one‐dimensional integrals. As a result, the developed GPM method is able to calculate mean and variance of model outputs in an efficient manner independent of parameter distributions. The proposed GPM method is applied to a collection of examples. And its accuracy and efficiency is compared with Monte Carlo simulation, which is used as benchmark solution. Results show that the proposed GPM method is feasible and reliable for efficient uncertainty quantification of complex systems in terms of the computational accuracy and efficiency. Copyright © 2016 John Wiley & Sons, Ltd.     

An Enhanced Formulation of the Maximum Entropy Method for Structural Optimization

A numerical optimization method was proposed time ago by Templeman based on the maximum entropy principle. That approach combined the Kuhn-Tucker condition and the information theory postulates to create a probabilistic formulation of the optimality criteria techniques. Such approach has been enhanced in this research organizing the mathematical process in a single optimization loop and linearizing the constraints. It turns out that such procedure transforms the optimization process in a sequence of systems of linear equations which is a very efficient way of obtaining the optimum solution of the problem. Some examples of structural optimization, namely, a planar truss, a spatial truss and a composite stiffened panel, are presented to demonstrate the capabilities of the methodology.     

基于分解法的最大熵随机有限元法

摘要：提出了一种新的基于分解法的最大熵随机有限元方法,利用单变量分解将多维随机响应函数表述为单维随机响应函数的组合形式,从而将求解随机结构响应统计矩的多维积分表达式转化为单维积分式,对单维积分采用高斯-埃尔米特积分格式求解。在获得结构响应的统计矩之后,利用最大熵原理求得结构响应的概率密度函数解析表达式。该法不涉及求导运算,对于非线性随机问题非常适用。算例结果表明,本文方法具有较好的精度与计算效率。
     

Using partial probability weighted moments and partial maximum entropy to estimate quantiles from censored samples

The maximum entropy principle constrained by probability weighted moments is an useful technique for unbiasedly and efficiently estimating the quantile function of a random variable from a sample of complete observations. However, censored or incomplete data are often encountered in engineering reliability and lifetime distribution analysis. This paper presents a new distribution free method for the estimation of the quantile function of a non-negative random variable using a censored sample of data, which is based on the principle of partial maximum entropy (MaxEnt) in which partial probability weighted moments (PPWMs) are used as constraints. Numerical results and practical examples presented in the paper confirm the accuracy and efficiency of the proposed partial MaxEnt quantile function estimation method for censored samples.     

Efficient evaluation of the pdf of a random variable through the kernel density maximum entropy approach

In this paper, a new approach for the evaluation of the probability density function (pdf) of a random variable from the knowledge of its lower moments is presented. At first the classical moment problem (MP) is revisited, which gives the conditions such that the assigned sequence of sample moments represent really a sequence of moments of any distribution. Then an alternative approach is presented, termed as the kernel density maximum entropy (MaxEnt) method by the authors, which approximates the target pdf as a convex linear combination of kernel densities, transforming the original MP into a discrete MP, which is solved through a MaxEnt approach. In this way, simply solving a discrete MaxEnt problem, not requiring the evaluation of numerical integrals, an approximating pdf converging toward the MaxEnt pdf is obtained. The method is first demonstrated by approximating some known analytical pdfs (the chi‐square and the Gumbel pdfs) and then it is applied to some experimental engineering problems, namely for modelling the pdf of concrete strength, the circular frequency and the damping ratio of strong ground motions, the extreme wind speed in Messina's Strait region. All the developed numerical applications show the goodness and efficacy of the proposed procedure. Copyright © 2008 John Wiley & Sons, Ltd.     

Entropy and entropy of mixing

Entropy as a function of temperature at constant volume, S(T), can be determined by integrating the molar specific entropy capacity C_V/T (C_V: molar specific heat capacity at constant volume). As a second approach, S(T) at constant volume can be determined by differentiating the free energy with respect to the temperature, T. Recently, it has been shown for a system obeying Boltzmann statistics that these mathematical approaches are equivalent to applying the formula of the mixing entropy, if the ground and excited states of the same sub‐systems or elementary systems are considered as mixing objects or quantum components. This result considerably extends the applicability of the formula of the mixing entropy, which is derived in textbooks just for mixing real indifferent components. In the present paper, it is shown that the formula of the mixing entropy can also be applied to calculate the entropy of Bose and Fermi systems. Thus, all entropy can be calculated and interpreted as mixing entropy of real components or quantum components. In reverse, the transitions between the ground and the excited states of any system can be explained as mixing processes. This interpretation is applied to the melting transition of chemically bonded solids and in particular to the glass transition whereby upon cooling the mixing entropy of the melt is (at least partly) frozen in the configuration. These results suggest a new interpretation of the glass transition and a new definition of structural glass.