Deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions

In this paper, we investigate the approximation of completely resonant nonlinear wave systems via deterministic learning. The plants are distributed parameter systems (DPS) describing homogeneous and isotropic elastic vibrating strings with fixed endpoints. The purpose of the paper is to approximate the infinite-dimensional dynamics, rather than the parameters of the wave systems. To solve the problem, the wave systems are first transformed into finite-dimensional dynamical systems described by ordinary differential equation (ODE). The properties of the finite-dimensional systems, including the convergence of the solution, as well as the dominance of partial system dynamics according to point-wise measurements, are analyzed. Based on the properties, second, by using the deterministic learning algorithm, an approximately accurate neural network (NN) approximation of the the finite-dimensional system dynamics is achieved in a local region along the recurrent trajectories. Simulation studies are included to demonstrate the effectiveness of the proposed approach.     

一种降低电离层梯度影响的Hatch滤波算法

目前,地基增强系统（Ground-Based Augment System,GBAS）中的主要问题是：尽管使用载波平滑降低了伪距噪,利用差分技术消除了用户和基准站间的大部分共同误差,从而减少了差分改正值中的误差。但是电离层时间梯度和空间梯度于这两个过程中产生了额外的误差,阻碍了差分改正值质量的进一步提高。基于对电离层时间和空间梯度引起的额外误差的分析,并考虑平滑伪距噪声,文章提出了一种新的Hatch滤波方法,该滤波器的时间常数是随卫星仰角、电离层时间和空间梯度以及用户与参考站之间的距离而实时变化的。该方法降低了差分改正值误差,提高了定位精度。并且通过差分定位仿真并对比传统的单频Hatch滤波方法,发现使用该方法后,减小了差分校正值的误差。     

Thermodynamics-inspired inverse halftoning viamultiple halftone images

Based on an analogy between thermodynamics and Bayesian inference,inverse halftoning was formulated using multiple halftone images based on Bayesian inference using the maximizer of the posterior marginal(MPM) estimate.Applying Monte Carlo simulation to a set of snapshots of the Q-Ising model,it was demonstrated that optimal performance is achieved around the Bayes-optimal condition within statistical uncertainty and that the performance of the Bayes-optimal solution is superior to that of the maximum-a-posteriori(MAP) estimation which is a deterministic limit of the MPM estimate.These properties were qualitatively confirmed by the mean-field theory using an infinite-range model established in statistical mechanics.Additionally,a practical and useful method was constructed using the statistical mechanical iterative method via the Bethe approximation.Numerical simulations for a 256-grayscale standard image show that Bethe approximation works as good as the MPM estimation if the parameters are set appropriately.     

基于中值滤波和梯度锐化的边缘检测

实现一种基于中值滤波和梯度锐化的边缘检测方法。首先采用既能过滤噪声又能保护边缘信息的中值滤波对图像进行平滑处理。然后采用梯度锐化加强边缘像素强度,通过简单的二值化获得图像的初始边缘,系统采用连通区域标记的方法去除位于图像封闭边界内的残留黑块。最后通过实验结果与人工提取的结果比较,进行误差分析,找出本文算法的不足之处,以便对该算法进行改进。实践证明,本文的边缘检测方法对含有噪声点且灰度分布比较均匀的图像有很好的效果。     

基于横纵向联合控制的多目标优化车辆跟驰研究

为解决车辆在拥堵环境中因车速波动较大所带来的跟驰平稳性较差、跟踪无效或不安全等问题,提出了基于车辆模型和深度强化学习的多目标优化跟驰方案。首先基于车辆横纵向动力学建立车辆跟驰模型,然后根据车间距误差、速度误差、横向偏差及相对偏航角等,利用深度确定性策略梯度算法得到跟驰车的加速度和转向角,以更平稳安全地控制跟驰车辆。经NGSIM公开驾驶数据集进行测试与验证,该方案可有效地提升跟驰车辆的稳定、舒适与安全性,对保证交通安全和提升道路通行能力具有重要意义。     

基于人类视觉模型的各向异性扩散滤波方法

针对各向异性扩散模型中扩散系数的梯度阈值确定问题进行了研究,提出了一种基于人类视觉模型的各向异性扩散滤波器。首先在PM方程的基础上研究了各向异性扩散系数中梯度阈值的取值问题。根据仿生学原理,分析了韦伯比曲线,将图像根据背景亮度划分为不同的区域,分别采用不同的公式计算梯度阈值。然后讨论了改进后算法在8邻域内的离散实现问题。仿真结果表明,与传统的恒常梯度阈值扩散模型相比,改进后的算法在有效保留图像重要信息的同时对噪声的抑制效果更为理想。     

线性矩阵方程异类约束最小二乘解的迭代算法

多矩阵变量线性矩阵方程(LME)约束解的计算问题在参数识别、结构设计、振动理论、自动控制理论等领域都有广泛应用。本文借鉴求线性矩阵方程(LME)同类约束最小二乘解的迭代算法,通过构造等价的线性矩阵方程组,建立了求多矩阵变量LME的一种异类约束最小二乘解的迭代算法,并证明了该算法的收敛性。在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LME的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LME的极小范数异类约束最小二乘解。另外,还可求得指定矩阵在该LME的异类约束最小二乘解集合中的最佳逼近解。算例表明,该算法是有效的。     

Ultrasonic crack characterization via a constrained inversion algorithm

The Kirchhoff approximation is used to show that the time domain impulse response of an isolated flat crack can be given a simple geometrical interpretation in terms of the derivative of a projected length function. For an elliptical crack, this derivative can be obtained explicitly to yield the two edge-diffracted waves which originate from the flashpoints of the crack. An explicit coordinate invariant expression is obtained from this elliptical crack solution which relates the time difference, t, between the arrival of these edge-diffracted waves and the crack size and orientation. Previously, we have proposed that this expression, together with t measurements in different scattering directions, could be used in a regression analysis as the basis for performing a constrained inversion of crack scattering data (i.e., where we attempt to obtain the best equivalent flat elliptical crack that fits the scattering measurements). Here we will demonstrate some results of applying the proposed algorithm using noisy synthetic data. The sensitivity of the results to both, number of measurements and transducer orientation, will be discussed.     

温度梯度机理下激光参数对激光成形的影响

以纯铝板和低碳钢板为主要研究对象，对温度梯度机理下激光输入功率、扫描速度、离焦量以及扫描次数等参数与成形弯曲角之间的关系进行了试验研究，深入分析了温度梯度机理下影响成形的主要因素。     

自适应Fourier分解思想在再生核W2 1 [a,b]空间的应用

在再生核$W_2^1[a, b]$空间中研究自适应正交贪婪分解算法, 利用能量下降最快的原理自适应性地构造出最佳$n$项逼近函数, 并从理论上证明其收敛性成立。最后, 实验验证了在$W_2^1[a, b]$再生核空间中, 利用正交贪婪原理构造的$n$项数值原函数比用等分结点构造出的最佳$n$项数值原函数收敛效果更优。