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.     

Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications

This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises. The system presents the following main features: (1) one-step correlated and cross-correlated random parameter matrices in the observation equation are assumed; (2) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. Using an innovation approach and these correlation assumptions, a recursive algorithm with a simple computational procedure is derived for the optimal linear filter. As a significant application of the proposed results, the optimal recursive filtering problem in multi-sensor systems with missing measurements and random delays can be addressed. Numerical simulation examples are used to demonstrate the feasibility of the proposed filtering algorithm, which is also compared with other filters that have been proposed.     

Control of discrete-time HMM partially observed under fractional Gaussian noises

A discrete-time control problem of a finite-state hidden Markov chain partially observed in a fractional Gaussian process is discussed using filtering. The control problem is then recast as a separated problem with information variables given by the unnormalized conditional probabilities of the whole path of the hidden Markov chain. A dynamic programming result and a minimum principle are obtained.     

基于AGR提取PD信号的应用研究

提出了一种从混合有色背景噪声环境提取变压器局部放电信号的方法一自适应高斯基表示。自适应高斯基表示是一种参数化最优联合时频分析工具，它能够有效地去除交叉项干扰，滤除有色噪声。系统运行中存在的服从高斯或非高斯分布的有色噪声．具有不满足细节小波分解系数趋于零的特性，不能有效地被小波分解滤除。基于信号匹配原则，通过自适应估计最优高斯基分解参数，将信号分解为最优高斯基函数的线性组合，滤除噪声，无限逼近原信号．弥补了局部放电信号检测精确性的不足。大量的仿真结果表明自适应高斯基表示是一个有效的局部放电检测方法，它将在电力系统局部放电信号检测中得到广泛的应用。     

Necessary and sufficient conditions for bounded distributed mean square tracking of multi‐agent systems with noises

This paper is concerned with the distributed control problem of second‐order agents under directed network topology. The control input of each agent only depends on its own state and the states of its neighbors corrupted by white noises. By using the algebraic graph theory and stochastic analysis method, necessary and sufficient conditions are presented for mean square bounded tracking. Finally, several simulation examples are given to illustrate the results. Copyright © 2015 John Wiley & Sons, Ltd.     

CALIBRATION OF A 6-DOF SPACE ROBOT USING GENETIC ALGORITHM

The kinematic error model of a 6-DOF space robot is deduced, and the cost function of kinematic parameter identification is built. With the aid of the genetic algorithm （GA） that has the powerful global adaptive probabilistic search ability, 24 parameters of the robot are identified through simulation, which makes the pose （position and orientation） accuracy of the robot a great improvement. In the process of the calibration, stochastic measurement noises are considered. Lastly, generalization of the identified kinematic parameters in the whole workspace of the robot is discussed. The simulation results show that calibrating the robot with GA is very stable and not sensitive to measurement noise. Moreover, even if the robot＇s kinematic parameters are relative, GA still has strong search ability to find the optimum solution.     

图像增强在基于形状特征图像检索中的应用

基于内容的图像检索系统中需要提取图像的形状特征,通常情况下为得到形状特征,需要对图像分割来得到的目标边界。在对不均匀图像提取边界曲线时,噪声点和非噪声区域常会干扰导致小的边界变化。本文采取了一定的措施对该问题进行了改进:首先通过去掉图像的彩色成分,将图像进行灰度化处理,再通过图像增强技术,对图像进行平滑处理,然后提取图像的形状。由于图像增强对图像预制模糊时,已经对图像中的噪声点和颜色不均匀区域进行了处理,所以再次对图像进行形状处理时,可有效去除噪声点和非噪声干扰区域的影响。     

Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

This paper addresses the problem of designing robust fusion time‐varying Kalman estimators for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, missing measurements, packet dropouts, and uncertain‐variance linearly correlated measurement and process white noises. By the augmented approach, the original system is converted into a stochastic parameter system with uncertain noise variances. Furthermore, applying the fictitious noise approach, the original system is converted into one with constant parameters and uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of the noise variances, the five robust fusion time‐varying Kalman estimators (predictor, filter, and smoother) are presented by using a unified design approach that the robust filter and smoother are designed based on the robust Kalman predictor, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, and scalar weights, a modified robust covariance intersection fusion estimator, and robust centralized fusion estimator. Their robustness is proved by using a combination method, which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of nonnegative definite matrix, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. A simulation example is shown with application to the continuous stirred tank reactor system to show the effectiveness and correctness of the proposed results.     

相关白噪声激励下双稳态Duffing-Van der Pol系统的随机分岔

研究了相关乘性和加性高斯白噪声激励下,双稳态Duffing-Van der Pol系统的随机P-分岔和D-分岔;利用随机平均法,得出系统幅值稳态概率密度的理论表达式,以及随机P-分岔发生的临界参数条件;通过分析概率密度曲线形状的变化,发现阻尼系数、加性和乘性噪声强度均可诱导系统出现随机P-分岔,但对系统分岔区域的影响有着明显的不同,同时Monte-Carlo数值模拟验证了理论分析的有效性.此外,利用Wolf算法得到系统的最大Lyapunov指数,并分析了系统的稳定性和随机D-分岔,发现加性和乘性噪声强度以及阻尼系数α_1的增大,均会使系统趋于不稳定,而阻尼系数ε,α_2的增大,可以增强系统的稳定性.     

基于小波变换的图像条带噪声去除方法

条带噪声的存在不但妨碍高光谱图像的目视判读,而且制约高光谱遥感的定量应用。针对小波变换法条带噪声去除过程中遇到的条带噪声和图像有用信息难以有效分离的问题,根据小波变换的方向性和数学显微镜特性,提出了一种新的基于小波变换的条带噪声去除方法。这种方法首先对含有条带噪声的图像进行一定层数的小波分解;然后对每一层分解得到的与条带噪声分布方向相同的子图像再进行一定层数的小波分解,从而实现条带噪声和图像有用信息的有效分离,将含有条带噪声的子图像置零;最后利用小波反变换得到去除条带噪声的图像。以欧洲空间局PROBA卫星上搭载的CHRIS高光谱数据为例,采用相关系数(R)、结构相似度(SSIM)和峰值信噪比(PSNR)3个定量指标,对比分析了新方法与矩匹配法、傅立叶滤波法和小波阈值法的条带噪声去除效果。结果表明新方法去噪后的图像具有最高的R、SSIM和PSNR,新方法能够有效地去除高光谱图像中的条带噪声,同时较好地保留了原始图像的有用信息。
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