Higher-Order Convex Approximations of Young Measures in Optimal Control

The general theory of approximation of (possibly generalized) Young measures is presented, and concrete cases are investigated. An adjoint-operator approach, combined with quasi-interpolation of test integrands, is systematically used. Applicability is demonstrated on an optimal control problem for an elliptic system, together with one-dimensional illustrative calculations of various options.     

The Bootstrap Methodology in Statistics of Extremes—Choice of the Optimal Sample Fraction

The main objective of statistics of extremes is the prediction of rare events, and its primary problem has been the estimation of the tail index , usually performed on the basis of the largest k order statistics in the sample or on the excesses over a high level u. The question that has been often addressed in practical applications of extreme value theory is the choice of either k or u, and an adaptive estimation of . We shall be here mainly interested in the use of the bootstrap methodology to estimate adaptively, and although the methods provided may be applied, with adequate modifications, to the general domain of attraction of G, , we shall here illustrate the methods for heavy right tails, i.e. for > 0. Special relevance will be given to the use of an auxiliary statistic that is merely the difference of two estimators with the same functional form as the estimator under study, computed at two different levels. We shall also compare, through Monte Carlo simulation, these bootstrap methodologies with other data-driven choices of the optimal sample fraction available in the literature.     

Nonparametric Inference for a Class of Stochastic Partial Differential Equations II

Consider the stochastic partial differential equationdu (t,x) = (t)u (t, x)dt + dW _Q(t,x), 0 t T where = ₂/x ₂, and is a class of positive valued functions. We obtain an estimator for the linear multiplier (t) and establish the consistency, rate of convergence and asymptotic normality of this estimator as 0.     

Boundary Bias Correction for Nonparametric Deconvolution

In this paper we consider the deconvolution problem in nonparametric density estimation. That is, one wishes to estimate the unknown density of a random variable X, say f _X , based on the observed variables Y's, where Y = X + with being the error. Previous results on this problem have considered the estimation of f _X at interior points. Here we study the deconvolution problem for boundary points. A kernel-type estimator is proposed, and its mean squared error properties, including the rates of convergence, are investigated for supersmooth and ordinary smooth error distributions. Results of a simulation study are also presented.     

Simulation optimization of buffer allocations in production lines with unreliable machines

We use a recent simulationbased optimization method, sample path optimization, to find optimal buffer allocations in tandem production lines where machines are subject to random breakdowns and repairs, and the product is fluidtype. We explore some of the functional properties of throughput of such systems and exploit these properties to prove the almost sure convergence of our optimization technique, under a regularity condition on the steady state. Utilizing a generalized semiMarkov process (GSMP) representation of the system, we derive recursive expressions to compute onesided directional derivatives of throughput, from a single simulation run. Finally, we give computational results for lines with up to 50 machines. We also compare results for smaller lines with the results from a more conventional method, stochastic approximation, whenever applicable. In these numerical studies, our method performed quite well on problems that are considered difficult by current computational standards.     

红外中带滤光片的结构、带宽估算及调整

中波红外波段在航天、气象、遥感等领域有着重要的应用，为了提高信噪比，系统中经常使用高质量的红外中带滤光片。相对带宽是红外中带滤光片重要的指标，主要取决于光学薄膜的膜系结构和具体设计。首先给出双截止组合型、F-P型、多半波型等几种膜系结构，归纳了相对带宽估算公式。同时从实用性出发，对一些具体膜系结构进行了相对带宽估算和综合分析，结果表明多半波结构最为可行。针对多半波结构，提出了间隔层膜料和光学厚度的选择、采用等效膜、调整膜层折射率等相对带宽调整的方法。最后，利用上述相对带宽调整方法对红外中带滤光片进行了设计，给出了实际镀制结果，滤光片相对带宽指标满足设计要求。     

On stochastic parameter estimation using data assimilation

Data assimilation-based parameter estimation can be used to deterministically tune forecast models. This work demonstrates that it can also be used to provide parameter distributions for use by stochastic parameterization schemes. While parameter estimation is (theoretically) straightforward to perform, it is not clear how one should physically interpret the parameter values obtained. Structural model inadequacy implies that one should not search for a deterministic “best” set of parameter values, but rather allow the parameter values to change as a function of state; different parameter values will be needed to compensate for the state-dependent variations of realistic model inadequacy. Over time, a distribution of parameter values will be generated and this distribution can be sampled during forecasts. The current work addresses the ability of ensemble-based parameter estimation techniques utilizing a deterministic model to estimate the moments of stochastic parameters. It is shown that when the system of interest is stochastic the expected variability of a stochastic parameter is biased when a deterministic model is employed for parameter estimation. However, this bias is ameliorated through application of the Central Limit Theorem, and good estimates of both the first and second moments of the stochastic parameter can be obtained. It is also shown that the biased variability information can be utilized to construct a hybrid stochastic/deterministic integration scheme that is able to accurately approximate the evolution of the true stochastic system.     

Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite-difference Newton method

An inverse radiation problem was considered to estimate boundary conditions such as temperature distribution and emissivity in axisymmetric absorbing, emitting, and scattering medium, given the measured incident radiative heat fluxes. The finite-volume method was employed to solve a direct radiative transfer equation for a two-dimensional axisymmetric geometry. Various parameter estimators, such as conjugate-gradient method, hybrid genetic algorithm, and finite-difference Newton method, were employed to solve the inverse problems, while discussing their performances in terms of estimation accuracy and computational efficiency. Based on this, we proposed, as a best inverse analysis tool, a new combined method that adopted the hybrid genetic algorithm as an initial value selector and used the finite-difference Newton method as a parameter estimator.     

立方星剩磁在轨辨识与主动补偿技术

立方星的姿态测量与控制系统常采用磁测磁控结合偏置动量轮的方案,整星剩磁干扰力矩是影响姿态控制精度的重要因素之一。提出了一种利用磁强计实现剩磁矩在轨辨识与利用磁力矩器实现剩磁矩主动补偿的新方案:基于磁强计输出和卫星姿态动力学建立了剩磁矩在轨辨识模型,并利用采样滤波器(UKF)提高单磁强计条件下的辨识效果;把控制对象简化成线性定常系统,分析了剩磁干扰力矩对姿态的影响数学模型,并针对磁力矩器和磁强计分时工作的特点,基于叠加性原理提出了基于角速度的剩磁矩主动补偿算法。仿真研究表明,在1000 s内剩磁矩在轨辨识精度为0.001 A×m~2量级,主动补偿后,偏航角、滚动角与俯仰角控制误差分别从4.3°、4.6°与2.1°均减少至0.4°以内。提出的方法为类似配置卫星减少剩磁干扰力矩的影响提供了一种新思路。