基于均匀圆阵的信号二维方向角互相关估计

针对复值乘性和加性噪声同时存在的情况,提出一种基于均匀圆阵的信号二维方向角互相关估计方法.本文推导出互相关估计公式,分析了估计的统计性能,给出了最优参数选择原则.在不改变均匀圆阵阵列流形的情况下,此方法抑制了信号中的乘性和加性噪声,且计算量小.计算机仿真证明了此方法的有效性.     

关于Smarandache可乘函数的均值研究

本文的主要目的是利用初等方法研究Smarandache可乘函数在简单数集中的均值性质,并给出一个有趣的渐近公式。     

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.     

Polyspectral Analysis of Two-dimensional Mixed Processes and Coupled Harmonics

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Efficient and accurate approach for powder compaction problems

 In this paper, a new approach for powder cold compaction simulations is presented. A density-dependent plastic model within the framework of finite strain multiplicative hyperelastoplasticity is used to describe the highly nonlinear material behaviour; the Coulomb dry friction model is used to capture friction effects at die-powder contact; and an Arbitrary Lagrangian–Eulerian (ALE) formulation is used to avoid the (usual) excessive distortion of Lagrangian meshes caused by large mass fluxes. Several representative examples, involving structured and unstructured meshes are simulated. The results obtained agree with the experimental data and other numerical results reported in the literature. It is shown that, contrary to other Lagrangian and adaptive h-remeshing approaches recently reported for this type of problems, the present approach verifies the mass conservation principle with very low relative errors (less than 1% in all ALE examples and exactly in the pure Lagrangian examples). Moreover, thanks to the use of an ALE formulation and in contrast with other simulations, the presented density distributions do not present spurious oscillations. Received: 20 March 2002 / Accepted: 15 October 2002 The partial financial support of the Ministerio de Ciencia y Tecnología (grant number DPI 2001-2204) is gratefully acknowledged.     

Multiplicative Operator Splittings in Nonlinear Diffusion: From Spatial Splitting to Multiple Timesteps

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives.We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives.We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process.     

基于非参数乘法回归模型的农业景观步甲空间分布模拟

农业生产引起的景观变化是导致生物多样性丧失的重要原因,为评估农业景观结构变化对物种多样性的影响,探索农业景观物种空间模拟的方法,研究应用非参数乘法回归(NPMR)模型结合田间步甲取样数据,分析了步甲群落多样性、主要物种存在/不存在与取样点周围边长为200 m景观内景观结构之间的关系,建立研究区物种-景观分布预测模型,结合地理信息系统(GIS)技术建立研究区群落/物种空间分布预测图。结果表明:在群落水平上,景观结构对步甲群落多样性的影响不显著; 在物种水平上,黄斑青步甲(Chlaenius micans)、淡鞘婪步甲(Harpalus pallidipennis)受斑块密度的影响显著(p<0.05),黄斑青步甲、后斑青步甲(Chlaenius posticalis)和单齿婪步甲(Harpalus simplicide)受半自然生境类型数的影响显著(p<0.05),单齿蝼步甲(Scarites terricola)受半自然生境比例的影响显著(p<0.05),而蠋步甲(Dolichus halensis)受景观结构的影响较为复杂。通过模型预测,输出研究区域6个主要物种的空间分布模拟图,进一步分析发现在研究区域内,对景观结构较为敏感的6个步甲物种主要分布在农田与半自然生境相接的狭长地带。因此,利用非参数乘法回归模型可以很好地模拟步甲物种对农田景观结构的响应及其在景观中的空间分布变化。200 m×200 m尺度下,尽管步甲群落多样性不受景观结构的显著影响,但是存在部分步甲物种对景观结构响应显著,但不同物种对景观结构的响应不同。增加农田地块间半自然生境,并合理改善景观配置异质性将有利于对景观结构变化敏感步甲物种的维持。     

强度传输方程和神经网络融合的三维重构算法

针对原有强度传输方程法所恢复的相位精度不够精确的缺点,提出强度传输方程和神经网络融合的三维重构算法. 利用强度传输方程求解出物体不同角度的初始相位,利用神经网络算法进行优化,根据不同角度的最终恢复相位结合乘法技术重构出三维体信息. 该算法具有精度高的特点,可以为三维成像技术的应用提供参考. 对于实验中的示例图像,该算法将强度传输方程得到的相位误差从21.40%降低为5.26%,重构三维物体与模拟真实物体的相关程度为显著相关.     

A Modified Nonparametric Prewhitened Covariance Estimator

Abstract. This paper proposes a fully modified version of the spectral matrix estimator (and the long‐run variance estimator as a special case) proposed originally by Xiao and Linton [Journal of Time Series Analysis (2002) Vol. 23, pp. 215–250], and derives its asymptotic results. A striking feature of the modified spectral matrix estimator is to achieve the convergence rate of O(T ^?8/9) in the mean squared error (MSE), which is usually achieved under the fourth‐order spectral window. However, this estimator does not sacrifice the positive definiteness of the resulting estimate for the rate improvement; it is Hermitian and positive definite in finite samples by construction. The faster convergence rate is established by a multiplicative bias correction of the crude spectral estimator under the second‐order spectral window. The approximations to some sensible definitions of the MSE of the estimator and the bandwidths that minimize the asymptotic MSEs are also derived. Monte Carlo results indicate that for a wide variety of processes the modified spectral matrix estimator reduces the bias without inflating the variance and thus improves the MSE, compared with the crude, bias‐uncorrected estimator.     

具有数据包丢失的离散随机不确定系统的线性最优满阶估值器

研究了具有数据包丢失和随机不确定性离散随机线性系统的状态估计问题.其中数据包丢失是随机的,且满足Bernoulli分布,系统矩阵中的随机不确定性由一个白色乘性噪声来描述.首先,通过配方方法,提出了最小均方意义下的无偏最优线性递推满阶滤波器.所提出的滤波器用到了当前时刻和最近时刻接收到的观测来保证线性最优性.与多项式滤波和增广滤波器相比,本文的滤波器具有较小的计算负担.然后,基于所获得的线性滤波器推导了线性最优预报器和平滑器.进一步研究了线性最优估值器的渐近稳定性,给出了稳态特性存在的一个充分条件.最后,通过两个仿真例子验证了所提估计算法的优越性.