高阶统计量地震子波估计建模

本文在反射系数序列为非高斯、平稳和统计独立的随机过程,地震子波为非因果、混合相位的假设条件下,分别应用滑动平均(MA)和自回归滑动平均(ARMA)模型对地震记录进行建模,并采用运算代价较小的基于高阶累积量的线性化求解方法——累积量矩阵方程法进行了子波提取和模型适应性的研究。数值模拟结果和实际地震数据处理结果表明:自回归滑动平均(ARMA)模型比滑动平均(MA)模型具有参数节省、模型更为高效的特点;累积量矩阵方程法可以有效地压制加性高斯噪声,但对累积量样本估计的准确性要求较高;如果累积量样本估计的误差和方差适度,结合自回归滑动平均(ARMA)模型描述的累积量矩阵方程法可以高效、准确地估计出地震子波。     

A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics

Sample pathwise numerical integration of noise-driven engineering dynamical systems cannot generally be performed beyond a limited level of accuracy, especially when the noise processes are modelled using (filtered) white noises. Recently, a locally transversal linearization (LTL) strategy has been proposed by the author (Proc Roy Soc London A 2001; 457 :539–566) for direct integration of deterministic and stochastic non-linear dynamical systems. The present effort is focussed on a host of extensions along with detailed theoretical error analyses of the linearization approach, especially as applied to problems in non-linear stochastic engineering dynamics. Thus, to begin with, estimates of local and global error orders in the basic LTL scheme are obtained separately for the displacement and velocity vectors when the system is driven either by a set of additive noises or by an arbitrary combination of (independently evolving) additive and multiplicative noises. Following this, a new family of higher-order LTL schemes is proposed in order to improve upon the basic LTL method and the associated error orders are established. A stepwise implementation of the lower- and higher-order versions of the LTL method, along with certain computational aspects, is also outlined. The proposed schemes are numerically illustrated, to a limited extent, for a single degree-of-freedom (SDOF) and a two degree-of-freedom (TDOF) non-linear engineering systems under additive and/or multiplicative white noise excitations. Copyright © 2004 John Wiley & Sons, Ltd.     

一种基于循环小波累积量的谐波恢复方法

循环统计量是乘性和加性噪声中谐波恢复问题的主要分析工具之一。本文在其基础上提出了一种新的理论与方法——基于循环小波累积量的谐波恢复方法。首先,提出了循环小波累积量的定义。然后,建立了基于一阶、二阶、三阶循环小波累积量的谐波分量的频率和相位的估计方法。在此基础上,采用了一种可调参数的小波,通过调节其参数来改善传统方法中频率分辨率低的缺陷。最后给出了模拟实验结果。     

一种基于高阶统计信息的信噪比估计改进算法

针对多进制正交幅度调制(Multiple quadrature amplitude modulation,MQAM)信号在低信噪比条件下估计精度不高的问题,提出了一种基于综合利用高阶统计信息的信噪比估计改进算法。根据所选高阶统计量最高阶数的不同,建立了3种信噪比与多种高阶统计量运算式之间的线性关系,利用全回归线性分析方法将3种线性关系转化为3种全回归模型,并求解模型系数。该算法充分利用了多种高阶统计量的有用信息,提高了信噪比估计精度。MQAM的仿真结果表明:在低信噪比条件下,该算法减小了信噪比估计误差,其估计性能明显优于传统的其他算法,且3种模型估计性能依次增加,可依据不同的信噪比要求对3种模型进行选取。     

Higher-Order and Modal Logic as a Framework for Explanation-Based Generalization

Certain tasks, such as formal program development and theorem proving, fundamentally rely upon the manipulation of higher-order objects such as functions and predicates. Computing tools intended to assist in performing these tasks are at present inadequate in both the amount of knowledge they contain (i.e., the level of support they provide) and in their ability to learn (i.e., their capacity to enhance that support over time). The application of a relevant machine learning technique—explanation-based generalization (EBG)—has thus far been limited to first-order problem representations. We extend EBG to generalize higher-order values, thereby enabling its application to higher-order problem encodings.Logic programming provides a uniform framework in which all aspects of explanation-based generalization and learning may be defined and carried out. First-order Horn logics (e.g., Prolog) are not, however, well suited to higher-order applications. Instead, we employ Prolog, a higher-order logic programming language, as our basic framework for realizing higher-order EBG. In order to capture the distinction between domain theory and training instance upon which EBG relies, we extend Prolog with the necessity operator of modal logic. We develop a meta-interpreter realizing EBG for the extended language, Prolog, and provide examples of higher-order EBG.     

FREQUENCY DOMAIN TESTS OF MULTIVARIATE GAUSSIANITY AND LINEARITY

A stationary multivariate time series { X _t } is defined as linear if it can be written in the form X _t = ∑^∞ _{j =−∞} A _j e _{t − j} where A _j are square matrices and e _t are independent and identically distributed random vectors. If the e _t } are normally distributed, then { X _t is a multivariate Gaussian linear process. This paper is concerned with the testing of departures of a vector stationary process from multivariate Gaussianity and linearity using the bispectral approach. First the definition and properties of cumulants of random matrices are used to obtain the expressions for the higher-order cumulant and spectral vectors of a linear vector process as defined above. Then it is shown that linearity of a vector process implies constancy of the modulus square of its normalized higher-order spectra whereas the component of such a vector process does not necessarily have a linear representation. Finally, statistics for the testing of multivariate Gaussianity and linearity are proposed.     

Speech-stream detection in short-wave channel based on empirical mode decomposition and higher-order statistics

To capture the presence of speech embedded in nonspeech events and background noise in short-wave non-cooperative communication,an algorithm for speech-stream detection in noisy environments is presented based on Empirical Mode Decomposition (EMD) and statistical properties of higher-order cumulants of speech signals.With the EMD,the noise signals can be decomposed into different numbers of IMFs.Then,the fourth-order cumulant (FOC) can be used to extract the desired feature of statistical properties for IMF components.Since the higher-order cumulants are blind for Gaussian signals,the proposed method is especially effective regarding the problem of speech-stream detection,where the speech signal is distorted by Gaussian noise.With the self-adaptive decomposition by EMD,the proposed method can also work well for non-Gaussian noise.The experiments show that the proposed algorithm can suppress different noise types with different SNRs,and the algorithm is robust in real signal tests.     

高阶逻辑下知识表示与聚类方法的研究*

针对一阶逻辑在复杂结构数据环境中存在模式搜索空间庞大和不能发明新谓词的缺点,提出了使用类型化的高阶逻辑知识表示语言Escher去表示各种复杂结构的数据,利用其强类型语法有效地约束知识发现过程中模式的搜索空间和高阶的特点去解决新谓词构造的问题。设计了以Escher为基础的复杂结构数据中的知识发现过程和基于复杂结构数据的聚类算法,并以实验验证了其有效性。     

一种面向密码芯片的旁路攻击防御方法

针对不同级别的旁路信息泄露,提出一种通用的旁路信息泄露容忍防御模型,并结合信息熵理论给出该模型的形式化描述.该模型采用(t,n)门限机制,使得部分旁路信息泄露不会影响系统的安全性.在该防御模型的基础上,结合高级加密标准AES-128算法的安全实现,设计了一种两阶段掩码的旁路攻击防御方法.与已有的防御方法相比,该方法能够同时防御高阶旁路攻击与模板攻击.通过理论分析与仿真实验验证了该方法的有效性.     

Bending-stretching analysis of thick functionally graded micro-plates using higher-order shear and normal deformable plate theory

In the present article, higher-order shear and normal deformable plate theory together with modified couple stress theory are developed to study the bending analysis of thick functionally graded rectangular micro-plates. One material length scale parameter is used for capturing the size effects. Utilizing the variational approach and also a principle of virtual displacement, a new form of equilibrium equations and the corresponding boundary conditions are derived. It is assumed that material properties vary through the thickness according to the power law function. Finally, an analytical solution for the bending problem of a simply supported FG rectangular micro-plate is presented.