混合高斯有色数据的生成方法

详细介绍了混合高斯有色数据生成中的各类抽样及色化方法后,结合一组仿真实例,验证了混合高斯有色数据的各种具体生成方法及其性能。     

一种新的非高斯随机振动数值模拟方法

在振动工程领域,采用蒙特卡洛仿真方法求解复杂随机动力学问题时需要精确模拟各种随机振动激励信号。当随机振动激励具有显著的非高斯特征时,用传统的高斯振动去近似将产生较大的分析误差,需要研究精确的非高斯振动数值模拟技术。现有各种非高斯随机模拟方法一般只能模拟具有高峰值特征的随机振动,即超高斯随机振动,并且算法复杂不够直观,需要进行多次反复迭代,模拟精度和效率都有待提高。本文提出了一种新的基于幅值调制和相位重构的非高斯随机振动数值模拟方法,算法简洁直观,并充分利用快速傅里叶变换算法提高模拟效率,不仅可以模拟具有指定统计特性和频谱特性的超高斯随机振动,还能模拟亚高斯随机振动,具有广泛的适应性。数值仿真实验验证了该方法的有效性和精确性。     

非高斯数据的高斯化滤波

在信号检测、图像处理等领域有时需要对非高斯数据进行高斯化滤波处理。给出高斯化滤波定义和它的一般工作机理，重点介绍评估滤波效果的Q-Q图检验方法，然后对比研究了基于概率密度函数及其导数的U滤波和基于概率密度函数反函数的G滤波两种高斯化实现的方法、原理与性能，并给出了一组湖试数据实例。     

一种基于累积量的ESPRIT型盲波束形成算法

讨论一种用于非高斯信号源方位估计的盲波束形成算法。假设背景噪声是二阶统计未知的有色(空间相关)高斯噪声,基于“阵元对”模型的ESPRIT方位估计算法可以通过用累积量矩阵取代自相关矩阵完成信号空间的重建。经过这种处理,加性有色高斯噪声可被滤除,因此算法不需要相关噪声矩阵的知识。当加性噪声源是空间相关矩阵未知的有色高斯噪声时,计算机仿真比较了基于累积量的ESPRIT算法与基于二阶统计的ESPRIT算法的性能。     

涡旋光束通过非高斯随机粗糙面的场分布特性

基于角谱衍射理论,利用Johnson传递系统数值模拟非高斯粗糙面,研究了拉盖尔-高斯涡旋光束通过随机非高斯粗糙表面的场分布特性。在分析了非高斯粗糙面方向自相关长度、峰度、偏斜以及均方根粗糙度对涡旋光束场分布影响的基础上,研究了涡旋光束通过随机粗糙表面后光束光强分布变化时的均方根粗糙度取值范围,并通过实验,将实验数据与仿真结果进行了对比分析。结果表明:当非高斯粗糙面方向相关长度为20 mm,偏斜为0.001,峰度为6,均方根粗糙度大于0.12 mm时,拉盖尔-高斯光束透过随机表面的光强分布不再保持空心分布,对应的相位奇点消失。     

偏斜非高斯随机振动信号幅值概率密度函数研究

偏斜非高斯振动信号幅值概率密度没有明确、简洁的解析表达式。研究概率密度的解析表达式,对于非高斯振动理论研究具有重要意义。针对以上需求,提出了一种基于高斯混合模型的概率密度函数表示方法。首先,通过时间样本序列得到偏斜非高斯振动信号前五阶矩的估计值。其次,根据平稳高斯随机过程各阶矩之间的定量关系,结合二阶高斯混合模型的数学表达式建立方程组,求解得到混合模型中每个高斯分量的均值、标准差和权重系数。然后,将每个高斯分量的参数代入高斯混合模型,得到偏斜非高斯振动信号的幅值概率密度的解析表达式。最后,将所提出的方法应用于仿真非高斯加速度信号和实测非高斯振动应力信号,充分验证了该方法的有效性和适用性。     

一种非高斯随机振动过程数值模拟方法

目的 考虑真实随机振动的非高斯特性,提出一种根据已知信息生成与其相符的非高斯随机振动过程的数值模拟方法。方法 基于均值、方差、偏斜度、峭度及功率谱密度函数（或自相关函数）等约束条件,对非高斯随机振动进行模拟。根据功率谱获取非高斯过程的自相关矩阵;通过Hermite多项式的正交性质和多项式混沌展开方法推导出的公式,构造满足标准正态分布随机过程的协方差矩阵,并对其进行谱分解和主成分分析;最后,利用Karhunen-Loeve展开和多项式混沌展开来表示所模拟的非高斯振动过程。结果 随着采样点个数的增加,实测数据与模拟数据之间的误差越来越小,该方法具有较好的模拟精度。结论 应用多项式混沌展开、Karhunen-Loeve展开以及蒙特卡洛等方法,可生成非高斯随机振动过程,并得到准确有效的各项统计参数模拟值。     

混响背景下GTM回波检测算法研究

为改善混响背景下传统匹配滤波算法效果不佳问题,在分析其非平稳性、有色性和非高斯性的基础上,提出了混合高斯时变自回归模型(Gaussian mixture Tvar Model,GTM),推导了模型公式及其参数求解方法,形成了GTM回波检测算法。为对混响特性及滤波效果进行定量描述进而验证算法性能,给出了一种定量衡量混响非平稳性、有色性、非高斯特性的滤波效果评价方法。通过实测混响分析表明,GTM模型能够较好地拟合实测混响的概率密度曲线和功率谱密度曲线,实现了混响背景下回波的有效检测并改善混响特性。     

非高斯噪声激励下分段非线性系统的平均首次穿越时间

噪声诱导的逃逸问题出现在众多研究领域,平均首次穿越时间作为用来表征粒子逃逸现象的重要特征量,现已被广泛应用于电子器件的开关时间及双稳器件的寿命等问题的研究之中.本文研究了由乘性非高斯噪声和加性高斯白噪声共同驱动下分段非线性系统的平均首次穿越时间问题.运用路径积分法、统一色噪声近似和最速下降法,得到了系统平均首次穿越时间的表达式.通过数值计算发现,在非高斯噪声偏离参数、噪声关联时间和互关联强度的作用下,非高斯噪声强度的增加会导致平均首次穿越时间曲线出现单峰结构,而加性噪声强度的增加会导致平均首次穿越时间的单调减小,这表明在该模型中非高斯噪声和高斯噪声对平均首次穿越时间的影响是不同的.此外还进一步讨论了非高斯噪声偏离参数、噪声关联时间和噪声互关联强度对平均首次穿越时间的影响.     

包装运输试验中非平稳随机振动表征和模拟方法

目的研究量化表征非平稳随机振动的方法,模拟包装物实际运输振动环境中的非平稳和非高斯特征。方法通过引入“运行测试”非参数统计检验方法,对均方根值时变非平稳过程进行量化表征,利用贝塔分布随机数的幅值调制方法模拟生成非平稳非高斯随机过程。结果通过数值验证贝塔分布方法,能够基于目标峭度和功率谱密度函数等约束条件灵活生成具有不同平稳程度的非平稳非高斯随机过程。结论该方法可以对非平稳特征进行定量表征,并可用于真实模拟包装件的运输振动环境,避免“欠试验”和“过试验”问题的发生。     

Estimation Performance for the Cubature Particle Filter under Nonlinear/Non-Gaussian Environments

This paper evaluates the state estimation performance for processing nonlinear/non-Gaussian systems using the cubature particle filter (CPF), which is an estimation algorithm that combines the cubature Kalman filter (CKF) and the particle filter (PF). The CPF is essentially a realization of PF where the third-degree cubature rule based on numerical integration method is adopted to approximate the proposal distribution. It is beneficial where the CKF is used to generate the importance density function in the PF framework for effectively resolving the nonlinear/non-Gaussian problems. Based on the spherical-radial transformation to generate an even number of equally weighted cubature points, the CKF uses cubature points with the same weights through the spherical-radial integration rule and employs an analytical probability density function (pdf) to capture the mean and covariance of the posterior distribution using the total probability theorem and subsequently uses the measurement to update with Bayes’ rule. It is capable of acquiring a maximum a posteriori probability estimate of the nonlinear system, and thus the importance density function can be used to approximate the true posterior density distribution. In Bayesian filtering, the nonlinear filter performs well when all conditional densities are assumed Gaussian. When applied to the nonlinear/non-Gaussian distribution systems, the CPF algorithm can remarkably improve the estimation accuracy as compared to the other particle filter-based approaches, such as the extended particle filter (EPF), and unscented particle filter (UPF), and also the Kalman filter (KF)-type approaches, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF) and CKF. Two illustrative examples are presented showing that the CPF achieves better performance as compared to the other approaches.     

改进的粒子滤波在深空探测自主天文导航中的应用

针对深空自主天文导航中可能存在初始状态误差较大、状态分布非高斯分布等问题,基于轨道6根数描述形式,提出了利用星光角距观测信息和UPF（Unscented Particle Filter）算法确定探测器轨道的方法.通过控制重采样频率,使UPF获得更高的滤波精度和更少的计算量.最后经仿真计算,验证了所给出的自主天文导航方法以及改进的粒子滤波算法的可行性和有效性.     

Simulation of a non-Gaussian stochastic process based on a combined distribution of the UHPM and the GBD

To simulate non-Gaussian stochastic processes based on the first four moments, various simulation methods are presented, in which the determination of the transformation model and the calculation of the correlation coefficients between non-Gaussian stochastic processes and Gaussian stochastic processes are the critical procedures in these simulation methods. However, some existing simulation methods are limited to specific ranges. Furthermore, their practical applications are affected negatively due to the expensive cost of determining the transformation model and the correlation coefficients between non-Gaussian and Gaussian stochastic processes. Therefore, an accurate and efficient simulation method of a non-Gaussian stochastic process with a broader range is proposed in this article. Since the simulation of non-Gaussian processes and the Nataf transformation of non-Gaussian variables have some similar characteristics, a new combined distribution is proposed based on the unified Hermite polynomial model (UHPM) and the generalized beta distribution (GBD). Then, the combined distribution is employed in the simulation of non-Gaussian stochastic processes, in which the transformation model is deduced by the combined distribution. The correlation coefficient transformation function (CCTF) between the Gaussian and non-Gaussian stochastic processes can be evaluated through the interpolation method. Furthermore, numerical examples are presented to show the accuracy and effectiveness of the proposed simulation method for non-Gaussian stochastic processes.     

Evaluation of bistable systems for binary signal detection in symmetric non-Gaussian noise

For detecting binary signals in symmetric noise with unknown probability density functions (PDF), a nonlinear receiver is proposed based on the bistable systems with autoregressive models of order 1 [AR(1)]. The bistable systems are utilized to pre-process the noisy observations ahead of the linear correlation (LC) detector. The permutations of the observations are utilized to bypass the design of the optimal LC vector which depends on the noise PDF. The detection performances, in the form of probabilities of error, in some non-Gaussian noise are evaluated versus the matched filter (MF) and Volterra filter (VF) through numerical simulations. The results show that the bistable receiver performs better than MF receiver when the noise deviates from Gaussian distribution, and seems more robust compared to the VF receiver.     

Importance sampling for reliability assessment of dynamic systems under general random process excitation

This paper develops a reliability assessment method for dynamic systems subjected to a general random process excitation. Safety assessment using direct Monte Carlo simulation is computationally expensive, particularly when estimating low probabilities of failure. The Girsanov transformation-based reliability assessment method is a computationally efficient approach intended for dynamic systems driven by Gaussian white noise, and this approach can be extended to random process inputs that can be represented as transformations of Gaussian white noise. In practice, dynamic systems may be subjected to inputs that may be better modeled as non-Gaussian and/or non-stationary random processes, which are not easily transformable to Gaussian white noise. We propose a computationally efficient scheme, based on importance sampling, which can be implemented directly on a general class of random processes — both Gaussian and non-Gaussian, and stationary and non-stationary. We demonstrate that this approach is in fact equivalent to Girsanov transformation when the uncertain inputs are Gaussian white noise processes. The proposed approach is demonstrated on a linear dynamic system driven by Gaussian white noise and Brownian bridge processes, a multi-physics aero-thermo-elastic model of a flexible panel subjected to hypersonic flow, and a nonlinear building frame subjected to non-stationary non-Gaussian random process excitation.     

Generation of non-Gaussian stochastic processes using nonlinear filters

Non-Gaussian stochastic processes are generated using nonlinear filters in terms of Itô differential equations. In generating the stochastic processes, two most important characteristics, the spectral density and the probability density, are taken into consideration. The drift coefficients in the Itô differential equations can be adjusted to match the spectral density, while the diffusion coefficients are chosen according to the probability density. The method is capable to generate a stochastic process with a spectral density of one peak or multiple peaks. The locations of the peaks and the band widths can be tuned by adjusting model parameters. For a low-pass process with the spectrum peak at zero frequency, the nonlinear filter can match any probability distribution, defined either in an infinite interval, a semi-infinite interval, or a finite interval. For a process with a spectrum peak at a non-zero frequency or with multiple peaks, the nonlinear filter model also offers a variety of profiles for probability distributions. The non-Gaussian stochastic processes generated by the nonlinear filters can be used for analysis, as well as Monte Carlo simulation.     

Automatic black and white film colorization using texture features and artificial neural networks

Abstract

This study represents an innovative automatic method for black and white films colorization using texture features and a multilayer perceptron artificial neural network. In the proposed method, efforts are made to remove human interference in the process of colorization and replace it with an artificial neural network (ANN) which is trained using the features of the reference frame. Later, this network is employed for automatic colorization of the remained black and white frames. The reference frames of the black and white film are manually colored. Using a Gabor filter bank, texture features of all the pixels of the reference frame are extracted and used as the input feature vector of the ANN, while the output will be the color vector of the corresponding pixel. Finally, the next frames’ feature vectors are fed respectively to the trained neural network, and color vectors of those frames are the output. Applying AVI videos and using various color spaces, a series of experiments are conducted to evaluate the proposed colorization process. This method needs considerable time to provide a reasonable output, given rapidly changing scenes. Fortunately however, due to the high correlation between consecutive frames in typical video footage, the overall performance is promising regarding both visual appearance and the calculated MSE error. Apart from the application, we also aim to show the importance of the low level features in a mainly high level process, and the mapping ability of a neural network.     

Bayesian state and parameter estimation of uncertain dynamical systems

The focus of this paper is Bayesian state and parameter estimation using nonlinear models. A recently developed method, the particle filter, is studied that is based on stochastic simulation. Unlike the well-known extended Kalman filter, the particle filter is applicable to highly nonlinear models with non-Gaussian uncertainties. Recently developed techniques that improve the convergence of the particle filter simulations are introduced and discussed. Comparisons between the particle filter and the extended Kalman filter are made using several numerical examples of nonlinear systems. The results indicate that the particle filter provides consistent state and parameter estimates for highly nonlinear models, while the extended Kalman filter does not.     

Research on Time Synchronization Method Under Arbitrary Network Delay in Wireless Sensor Networks

To cope with the arbitrariness of the network delays, a novel method, referred to as the composite particle filter approach based on variational Bayesian (VB-CPF), is proposed herein to estimate the clock skew and clock offset in wireless sensor networks. VB-CPF is an improvement of the Gaussian mixture kalman particle filter (GMKPF) algorithm. In GMKPF, Expectation-Maximization (EM) algorithm needs to determine the number of mixture components in advance, and it is easy to generate overfitting and underfitting. Variational Bayesian EM (VB-EM) algorithm is introduced in this paper to determine the number of mixture components adaptively according to the observations. Moreover, to solve the problem of data packet loss caused by unreliable links, we propose a robust time synchronization (RTS) method in this paper. RTS establishes an autoregressive model for clock skew, and calculates the clock parameters based on the established autoregressive model in case of packet loss. The final simulation results illustrate that VB-CPF yields much more accurate results relative to GMKPF when the network delays are modeled in terms of an asymmetric Gaussian distribution. Moreover, RTS shows good robustness to the continuous and random dropout of time messages.