压缩感知中高斯矩阵的优化研究

为了优化高斯矩阵,对部分哈达玛矩阵与高斯矩阵的统计学参数作了对比分析,确定了导致部分哈达玛矩阵信号重构能力好的主要因素,并提出了高斯矩阵优化算法.验证了优化算法对不同规模高斯矩阵的通用性和有效性,确定了优化矩阵对各种稀疏信号重构算法的适用性.最后对优化矩阵的性能作了初步的理论和实验分析,优化矩阵的信号重构能力可达到、甚至超过哈达玛矩阵.研究成果为测量矩阵的分析、设计和优化提供了新的思路和方法.     

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.     

基于GPGPU的实体表面实时提取

为实时提取三维实体表面,提出一种基于GPGPU并行计算的实体表面实时提取方法。在分析深度剥离算法原理和GPU图形绘制管线的基础上,给出在GPU上利用深度剥离算法实现实时提取三维实体表面的算法;通过OpenGL的高级着色语言GLSL控制GPU的图形绘制管线实现了该算法,给出其伪代码。以龙、叶轮和刀具扫描体的模型为应用实例验证了该算法效果良好,特别是对于刀具扫描体表面的提取,可满足实时性要求。     

无理数字典码的测试数据压缩方案

提出了一种无理数字典码的测试数据压缩方案,能有效地压缩芯片测试数据。方案利用无理数序列建立字典,编码时只需进行相容性检查,无需填充无关位,简化了操作步骤;同时,选择局部压缩率最大的一组数据作为最终编码结果,保证压缩效果可以达到局部最优。对ISCAS 89标准电路Mintest集的实验结果显示,该方案的压缩效果优于传统压缩方法,如Golomb码、FDR码、混合定变长码等。     

多传感器数据采集系统中的数据融合研究

针对多传感器数据采集系统的准确性与可靠性的要求,提出了单传感器分批估计融合与模糊理论中的相关性函数与加权自适应算法相结合的数据融合方法。首先,对每一只传感器进行分批估计融合,得到了较为可靠的局部决策值。然后,利用模糊理论中的相关性函数,计算出每只传感器与其它传感器的相关程度,并剔除掉那些相关程度较低的传感器的局部决策值。最后,在权的最优分配原则下,利用加权自适应算法对剩下的局部决策值进行数据融合。该方法能在数据先验知识未知的情况下,客观地反映各个传感器的可靠程度。数据分析结果表明:与同类融合方法相比,该方法具有更高的精度。     

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.     

Order-k α-hulls and α-shapes

We introduce order-k α-hulls and α-shapes – generalizations of α-hulls and α-shapes. Being also a generalization of k-hull (known in statistics as “k-depth contour”), order-k α-hull provides a link between shape reconstruction and statistical depth. As a generalization of α-hull, order-k α-hull gives a robust shape estimation by ignoring locally up to k outliers in a point set. Order-k α-shape produces an “inner” shape of the set, with the amount of “digging” into the points controlled by k. As a generalization of k-hull, order-k α-hull is capable of determining “deep” points amidst samples from a multimodal distribution: it correctly identifies points which lie outside clusters of samples.The order-k α-hulls and α-shapes are related to order-k Voronoi diagrams in the same way in which α-hulls and α-shapes are related to Voronoi diagrams. This implies that order-k α-hull and α-shape can be readily built from order-k Voronoi diagram, and that the number of different order-k α-shapes for all possible values of α is proportional to the complexity of order-k Voronoi diagram.     

Coordinating efficiency and equity in disaster relief logistics via information updates

This paper addresses a multi-supplier, multi-affected area, multi-relief, and multi-vehicle relief allocation problem in disaster relief logistics. A multi-objective optimisation model based on disaster scenario information updates is proposed in an attempt to coordinate efficiency and equity through timely and appropriate decisions regarding issues such as vehicle routing and relief allocation. An optimal stopping rule is also proposed to determine the optimum period of delay before responding to disaster, because decision making requires accurate disaster information. The main contribution of this paper is solving relief allocation problem in a novel way by correlating operational research with statistical decision making and Bayesian sequential analysis. Finally, a case is presented based on the post-disaster rescue in Eastern China after supertyphoon Saomai to test the applicability and show the potential advantages of the proposed model.     

Explicit solution of relative entropy weighted control

We consider the minimization over probability measures of the expected value of a random variable, regularized by relative entropy with respect to a given probability distribution. In the general setting we provide a complete characterization of the situations in which a finite optimal value exists and the situations in which a minimizing probability distribution exists. Specializing to the case where the underlying probability distribution is Wiener measure, we characterize finite relative entropy changes of measure in terms of square integrability of the corresponding change of drift. For the optimal change of measure for the relative entropy weighted optimization, an expression involving the Malliavin derivative of the cost random variable is derived. The theory is illustrated by its application to several examples, including the case where the cost variable is the maximum of a standard Brownian motion over a finite time horizon. For this example we obtain an exact optimal drift, as well as an approximation of the optimal drift through a Monte-Carlo algorithm.     

太阳能供热系统优化设计的相关问题研究

随着我国建筑总量和建筑能耗的快速增长,传统的供热方式已难以满足建筑供热的需求,而利用太阳能为建筑物供热,则可获得良好的节能和环保效益。就太阳能供热系统优化设计的相关问题进行了分析和研究,以期能为太阳能供热技术的推广和应用提供一定的理论依据。