A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements, the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.     

On the Uniform Convergence of the Empirical Density of an Ergodic Diffusion

We investigate the uniform convergence of the density of the empirical measure of an ergodic diffusion. It is known that under certain conditions on the drift and diffusion coefficients of the diffusion, the empirical density f _t converges in probability to the invariant density f, uniformly on the entire real line. We show that under the same conditions, uniform convergence of f _t to f on compact intervals takes place almost surely. Moreover, we prove that under much milder conditions (the usual linear growth condition on the drift and diffusion coefficients and a finite second moment of the invariant measure suffice), we have the uniform convergence of f _t to f on compacta in probability. This revised version was published online in June 2006 with corrections to the Cover Date.     

积分方程特征值的一个下界估计式及其应用

导出了具有正定对称核的积分方程最小特征值的一个下界估计式，为此为基础，获得了相应特征值的一种算法。     

无穷方差厚尾过程变点的小波估计

研究随机设计下噪声为厚尾随机变量时非参数函数中的变点估计问题.首先,通过设计变换将随机设计转化为等间距固定设计,进而利用小波方法估计变换后的变点的位置,再利用逆设计变换求得随机设计下变点位置的估计,并给出估计的收敛速度.模拟研究结果说明对于无穷方差厚尾过程中的变点估计问题小波方法是有效的.     

半变系数模型约束PLS估计的渐近正态性

变系数模型已获得了广泛的应用,半变系数模型是变系数模型的有效推广,本文给出半变系数模型在线性约束条件下的PLS估计,并证明了常系数和函数系数估计的渐近正态性.     

A complete class for linear estimation in a general linear model

Summary It is shown that in linear estimation both unbiased and biased, all unique (up to equivalence with respect to risk) locally best estimators and their limits constitute a complete class.     

SAGE信道估计算法在部分相关STTC-MIMO系统中的应用

利用天线空间相关函数和方向特性将完全不相关的信道衰落矩阵映射为更符合实际的部分相关MIMO(multiple input multiple output)信道衰落矩阵,结合STTC(space-time trellis code)空时编码方式建立部分相关的STTC-MIMO系统,并将基于SAGE(space-alternating generalized expectation-maximization)的信道估计算法应用在这一系统中.结果显示,和ML(most-likelihood)估计相比,部分相关信道中使用SAGE估计算法可以使系统信噪比提高约1 dB.此外,空时编码(space-time codes)的纠错性能对MIMO系统的信噪比也有极大的影响.     

Estimating the intensity of a cyclic Poisson process in the presence of linear trend

We construct and investigate a consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process in the presence of linear trend. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance, and the mean-squared error of the proposed estimator are also computed. A simulation study shows that the first order asymptotic approximations to the bias and variance of the estimator are not accurate enough. Second order terms for bias and variance were derived in order to be able to predict the numerical results in the simulation. Bias reduction of our estimator is also proposed.     

一种特殊条件下的扩散方程的数值解法及物理分析

利用有限差分方法中的预估校正格式求解裂变产物在燃料芯块中的扩散方程,并进行了灵活的边界条件处理,取得了令人满意的计算精度,为有效开展对反应堆燃料元件破损探测信号的定量分析提供了条件.对数值计算过程进行了一定的物理分析,从物理意义上解释了数值计算过程中一些特殊处理的合理性.     

Testing Serial Correlation in Semiparametric Varying-Coefficient Partially Linear EV Models

This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,η^T）^T] =0, Cov[（ε,η^T）^T] = σ^2Ip＋1. The estimators of interested regression parameters /3 , and the model error variance σ2, as well as the nonparametric components α（T）, are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α（T） achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.