混合初边值问题解的渐近性质及其差分解

 本文讨论了当t→∞时拟线性方程组初边值解的一些渐近性质。在假设非定常问题的解唯一、定常问题的解存在时,对同一边界条件,证明了当t→∞时非定常方程组的解趋于定常问题的解,讨论了用差分方法求解这种问题时,边界点上一些量的精确算法;为了消除在物体尖角附近出现的局部非物理解,得到正确解,我们还给出了一个简单的耗散型物面边界格式;最后给出了一些尖角凹形体的算例。     

基于Bayes理论的多源可靠性数据融合方法应用研究

对Bayes方法在多源可靠性数据融合中的应用进行了分析。将Bootstrap方法和随机抽样法应用于确定不同先验信息下的先验分布或先验分布中的超参数。论证了采用线性加权进行多源先验分布融合的合理性,并提出了将样本的边缘分布作为该方法中确定权重的一个衡量尺度。最后,采用上述方法对某飞机组件的寿命进行了统计推断。     

物理质团法关于可压流计算的程序验证

为了评估无网格物理质团法(PECM)对可压流计算的可信性,结合物理认识对该方法的设计思想和数值格式进行了先验分析,基于9个一维模型数值解与参照解的对比信息,通过后验分析方法对PECM进行了程序验证,参照解包括无网格再生核粒子法(RKPM)的数值解以及精确解。验证结果表明:各种物理参数以及状态方程的强烈间断会导致RKPM严重的失稳或失真,而PECM在包括极大密度比在内的各种强间断条件下仍保持稳定和收敛并具有较高的准确度。      

独立指数分布期望参数的Γ极小极大估计

在参数的部分先验信息已知的条件下所获得的Γ极小极大估计是一种介于有确定的先验分布函数的Bayes估计和无先验信息的极小极大估计之间的估计方法,因而更切合实际.以往的研究对二项分布参数的线性组合及负二项分布的参数在某些限制条件下的Γ极小极大估计做了讨论.本文给出了独立指数分布的期望参数在一般的先验矩限制下的Γ极小极大估计,同时讨论了两种特殊情况,即给出了在仅有先验二阶矩限制下的以及有确定的先验一阶矩和二阶矩限制下的指数分布的期望参数的Γ极小极大估计.     

独立指数分布期望参数的Г极小极大估计

在参数的部分先验信息已知的条件下所获得的Г极小极大估计是一种介于有确定的先验分布函数的Bayes估计和无先验信息的极小极大估计之间的估计方法，因而更切合实际。以往的研究对二项分布参数的线性组合及负二项分布的参数在某些限制条件下的Г极小极大估计做了讨论。本文给出了独立指数分布的期望参数在一般的先验矩限制下的Г极小极大估计，同时讨论了两种特殊情况，即给出了在仅有先验二阶矩限制下的以及有确定的先验一阶矩和二阶矩限制下的指数分布的期望参数的Г极小极大估计。     

基于先验知识及其定量评估的自适应杂波抑制研究

 为了改善训练样本数受限的非均匀杂波环境中的系统检测性能,研究了基于先验知识及其定量评估的自适应杂波抑制算法。提出了使用经真实杂波信息白化后的先验杂波协方差矩阵与单位矩阵之差的谱范数,来定量评估杂波先验知识的准确程度,并给出了真实杂波协方差矩阵未知时的矩阵谱范数估计方法。结合先验知识定量评估结果,获得了具有先验知识约束时的杂波协方差矩阵最大似然估计方法。分别基于多脉冲相参雷达以及空时自适应雷达进行了杂波建模,在此基础之上分析了算法性能。仿真结果证实了该算法优于使用样本协方差矩阵及先验杂波信息形成杂波抑制权值的性能。     

关于跨音速定常小扰动平面势流线松弛的稳定性和收敛性的讨论

引言 对跨音速势流方程采用混合差分线松弛求解,常碰到稳定性和收敛性问题。差分方程的舍入误差,若在求解过程中不会增长,则格式稳定。当选取的步长趋于零时,差分方程的解趋于微分方程的解,则格式收敛。要得到所要求的解,必须使差分格式既稳定又收敛。由于跨音速势流方程的非线性,严格的稳定性与收敛性证明十分困难。大量的计算实验指出:在松弛求解中,计算是否稳定,是否收敛和当收敛时的收敛速度,     

一阶微分方程终值问题拟解的存在性

利用拟上下解方法,研究了一阶微分方程终值问题u′(t)=f()t,u(t),u(T)=xT拟解的存在性,并通过构造单调迭代序列得到该终值问题的最大最小拟解。     

小子样条件下正态先验信息的融合

对于Bayes小子样检验方法,先验信息的有效性影响着统计推断的准确性。在对多源正态先验信息进行融合时,采用自助法将之转换为先验子分布,其中采用了改进的经验分布函数法进行再抽样。然后,基于专家水平确定其权重,再结合专家估计法确定各先验子分布的权重。最后,通过计算综合先验分布与假设的正态分布的差异部分的面积,对综合先验分布为正态分布的假设进行检验。案例分析表明此融合方法是有效的。     

安全关键软件可靠性验证测试方法研究

为了在不降低安全关键软件可靠性验证测试结果可信性的前提下减少测试用例量,在分析经典统计假设测试和无先验贝叶斯统计方法的基础上,提出了一种先验知识动态整合的贝叶斯推断统计测试方法;并提供了软件失效概率的概率密度函数先验分布参数的详细求解办法。实验表明,所提供的安全关键软件可靠性验证测试方法可以用较少的测试用例获得同样的结果可信性。     

Extensions and critique of minimum-relative-entropy spectralestimation

Insight is provided into minimum-relative-entropy spectral estimation (MRESE), which has proved very successful in some applications. There are, however, shortcoming inherent in MRESE as it has so far developed; e.g. it would be desirable to incorporated objective, absolute (rather than subjective, relative) weighting for prior estimates. Such problems are pointed out, and solutions are offered for some of them. A few of these problems are common to MRESE and minimum-entropy spectral estimation. The unsolved problems are offered as topics for further research     

Accuracy Limitations of Hyperbolic Multilateration Systems

A recently developed procedure [1] for assessing the accuracy of hyperbolic multilateration systems makes it easy to determine basic limitations on accuracy. This paper illustrates how such bounds can be derived. The results include bounds for a variety of geometries that are representative of practical ground-based and satellite-based hyperbolic systems. The results are applicable whenever the ranging errors can be treated as uncorrelated zeromean random variables. In some cases the bounds quantify general knowledge (e. g., the directional dependence of errors). In other cases the bounds represent entirely new limitations (e. g., optimum accuracies for sector-restricted and cone-restricted transmitter/receiver configurations).     

Performance Bounds for Continuous-time Filters in the Presence of Modeling Errors

We are concerned with obtaining bounds on the performance of Kalman-type, linear, continuous-time filters susceptible to modeling errors. Limiting the discussion to stationary performance, we obtain bounds on the performance index, the mean square error of estimates for suboptimal and optimal (Kalman) filters. The bounds are expressed in terms of the model matrices and the range of errors of the matrices. The results are useful to a designer in comparing the performance of a suboptimal filter with that of the optimal filter when he has information on the range of modeling errors. The tightness of the bounds is shown by an application of the results in the estimation of the motion of an aircraft carrier at sea.     

高超声速飞行器飞行动力学特性不确定分析

 高超声速飞行器分析模型存在较大不确定性,其给出的动力学特性与真实值之间存在偏差,因此研究飞行动力学特性分析结果的可信度水平对控制系统设计具有重要意义。针对典型的乘波体构型高超声速飞行器,在建立气动/结构/推进相互耦合的动力学模型基础上,利用非概率区间来描述模型中的不确定参数,并将复特征根不确定范围求解问题转化为频率和阻尼比两个实数的不确定区间分别求解,给出了动力学模态特征根、频率及阻尼比的不确定边界。分别采用直接蒙特卡罗(DMC)模拟方法、基于泰勒展开的区间分析方法(TIAM)和基于多项式逼近的区间分析方法(CIAM)对高超声速飞行器飞行动力学不确定性进行了研究。结果表明:CIAM计算时间适中,且给出的边界更为准确、安全,适合在控制系统设计和验证过程中使用。     

Output voltage bounds of a three-phase boost rectifier

A general closed-form duty cycle control law is derived based on the linear combination of two sets of continuous duty cycle control laws. From this general solution one can generate infinitely many pulsewidth modulation (PWM) control strategies to achieve the same ideal performance. Then, from the resulting closed-form solution, a general explicit lower bound and a general explicit upper bound of the output dc voltage are derived. Besides the academic interests, these bounds are very useful practically as a convenient guideline for helping quickly design the three-phase boost rectifier. Finally, some illustrative examples are given and some experimental results provided for verifying the derived bounds     

一类中立型高维周期微分系统的周期解

文中利用指数型二分法,结合不动点定理考虑如下形式的中立型高维周期系统: 苦d/dt[x(t)+cx1]=A(t,x(t))x(t)+f(t,x1),得到其T-周期解存在的充分性条件,所得结论改进或推广了早先文献中周期解存在的相应结论。     

一类具有时滞的细胞繁殖模型的正周期解的存在性

研究了一类血红细胞生存模型的时滞微分方程y（t）=-a（t）y（t）＋6（t）e^-r（t）y（r-τ（t））,t≥0的正周期解的存在性,给出其存在的充分条件。     

Security applications of computer vision

In an age which bears witness to a proliferation of Closed Circuit Television (CCTV) cameras for security and surveillance monitoring, the use of image processing and computer vision techniques which were provided as top end bespoke solutions can now be realised using desktop PC processing. Commercial Video Motion Detection (VMD) and Intelligent Scene Monitoring (ISM) systems are becoming increasingly sophisticated, aided, in no small way, by a technology transfer from previously exclusively military research sectors. Image processing is traditionally concerned with pre-processing operations such as Fourier filtering, edge detection and morphological operations. Computer vision extends the image processing paradigm to include understanding of scene content, tracking and object classification. Examples of computer vision applications include Automatic Number Plate Recognition (ANPR), people and vehicle tracking, crowd analysis and model based vision. Often image processing and computer vision techniques are developed with highly specific applications in mind and the goal of a more global understanding computer vision system remains, at least for now, outside the bounds of present technology. This paper will review some of the most recent developments in computer vision and image processing for challenging outdoor perimeter security applications. It also describes the efforts of development teams to integrate some of these advanced ideas into coherent prototype development systems     

Analytic example of a Schweppe likelihood-ratio detector

A low-dimensional test problem with a known solution is used to verify various computer implementations of F.C. Schweppe's likelihood detector (1965). In this case a closed-form solution is provided for a Schweppe likelihood detector in terms of an intermediate Kalman filter, as utilized in its implementation, for detecting the presence of a two-state signal model in Gaussian white noise. The associated error probabilities are also evaluated following a procedure that utilizes optimized Chernoff-like bounds for a tight approximation. A methodology is demonstrated for appropriately setting the decision threshold for this example as a tradeoff against allowable observation time. By using this or similar examples, certain qualitative and quantitative aspects of the software implementation can be checked for conformance to anticipated behavior as an intermediate benchmark, prior to modular replacement of the various high-order matrices appropriate to the particular application     

Hard-constrained versus soft-constrained parameter estimation

The paper aims at contrasting two different ways of incorporating a priori information in parameter estimation, i.e., hard-constrained and soft-constrained estimation. Hard-constrained estimation can be interpreted, in the Bayesian framework, as maximum a posteriori probability (MAP) estimation with uniform prior distribution over the constraining set, and amounts to a constrained least-squares (LS) optimization. Novel analytical results on the statistics of the hard-constrained estimator are presented for a linear regression model subject to lower and upper bounds on a single parameter. This analysis allows to quantify the mean squared error (MSE) reduction implied by constraints and to see how this depends on the size of the constraining set compared with the confidence regions of the unconstrained estimator. Contrastingly, soft-constrained estimation can be regarded as MAP estimation with Gaussian prior distribution and amounts to a less computationally demanding unconstrained LS optimization with a cost suitably modified by the mean and covariance of the Gaussian distribution. Results on the design of the prior covariance of the soft-constrained estimator for optimal MSE performance are also given. Finally, a practical case-study concerning a line fitting estimation problem is presented in order to validate the theoretical results derived in the paper as well as to compare the performance of the hard-constrained and soft-constrained approaches under different settings