A robust principal component analysis

A robust principal component analysis for samples from a bivariate distribution function is described. The method is based on robust estimators for dispersion in the univariate case along with a certain linearization of the bivariate structure. Besides the continuity of the functional defining the direction of the suitably modified principal axis, we prove consistency of the corresponding sequence of estimators. Asymptotic normality is established under some additional conditions.     

高超音速飞行器鲁棒控制器设计

军事变革和信息化战场环境的变化,促使空天攻防作战成为未来作战的战场之一。临近空间高超音速飞机和导弹会对传统攻防体系带来颠覆性冲击。复杂环境对高超音速飞行器控制技术的发展提出了严峻的挑战,本文针对吸气式高超音速飞行器在飞行包线内动态特性易变、稳定性较差、不确定因素较多以及对外界扰动敏感以及整个执行机构控制能力弱和动态特性低等的控制问题,首次提出了一种能同时抑制扰动和模型不确定性的基于优化控制的鲁棒控制方法,保证飞行器能得到很好地控制,快速响应环境变化并很快回到稳定飞行的状态。采用线性矩阵不等式方法来设计飞行控制系统,给出了不确定系统稳定的条件, 将反馈稳定问题转化为了一个最优控制问题。同时将闭环极点在一定区域内参与优化,进一步提高优化效率。与文献方法仿真对比结果证实了本文方法的优越性。     

High-temperature site preference and atomic short-range ordering characteristics of ternary alloying elements in γ’-Ni3Al intermetallics

Abstract

Remarkable high-temperature mechanical properties of nickel-based superalloys are correlated with the arrangement of ternary alloying elements in L1₂-type-ordered γ′-Ni₃Al intermetallics. In the current study, therefore, high-temperature site occupancy preference and energetic-structural characteristics of atomic short-range ordering (SRO) of ternary alloying X elements (X = Mo, W, Ta, Hf, Re, Ru, Pt or Co) in Ni₇₅Al_21.875X_3.125 alloy systems have been studied by combining the statistico-thermodynamical theory of ordering and electronic theory of alloys in the pseudopotential approximation. Temperature dependence of site occupancy tendencies of alloying X element atoms has been predicted by calculating partial ordering energies and SRO parameters of Ni-Al, Ni-X and Al-X atomic pairs. It is shown that, all ternary alloying element atoms (except Pt) tend to occupy Al, whereas Pt atoms prefer to substitute for Ni sub-lattice sites of Ni₃Al intermetallics. However, in contrast to other X elements, sub-lattice site occupancy characteristics of Re atoms appear to be both temperature- and composition-dependent. Theoretical calculations reveal that site occupancy preference of Re atoms switches from Al to both Ni and Al sites at critical temperatures, T_c, for Re > 2.35 at%. Distribution of Re atoms at both Ni and Al sub-lattice sites above T_c may lead to localised supersaturation of the parent Ni₃Al phase and makes possible the formation of topologically close-packed (TCP) phases. The results of the current theoretical and simulation study are consistent with other theoretical and experimental investigations published in the literature.     

基于哈密顿函数的永磁同步电机混沌系统鲁棒控制

哈密顿系统理论是研究非线性系统的一种重要工具, 近年来在电机调速、控制等方面得到广泛应用. 本文针对永磁同步电机运行中存在的混沌现象, 提出一种基于哈密顿函数的永磁同步电机混沌系统鲁棒控制器设计方法. 将永磁同步电机动态模型变换为类Lorenz混沌方程, 在特定参数下, 通过Lyapunov指数和Lyapunov维数的计算可知系统是混沌的. 令电机转速跟踪给定值得误差方程. 由于误差方程并不具有标准哈密顿函数形式, 将其转化为具有扰动不确定项的哈密顿系统, 并与负载扰动一起作为系统的总扰动量, 设计了一种鲁棒控制器. 控制器由两部分组成, 一部分基于互联与阻尼配置法, 实现任意转速的有效跟踪, 另一部分实现扰动补偿. 仿真表明, 控制器使电机迅速脱离混沌状态, 并能实现转速趋近跟踪, 验证了控制器的可行性与有效性. 该方法扩展了哈密顿函数的适用范围, 具有一定的优越性.     

基于叠层衍射的数字水印算法研究

基于叠层衍射成像原理提出了一种新的衍射数字水印算法:叠层水印. 通过双随机相位编码和探针, 实现对水印图像的分块加密, 密文经过衰减处理, 加载在振幅型宿主图像的空域上, 伪探针记录下宿主图像, 并加载到传输图像的相位上. 模拟实验结果表明: 首先, 叠层水印可以很好地提取水印图像的振幅、相位信息. 其次, 叠层水印可以解决水印不可感知性与密文信息提取质量之间的矛盾. 最后, 通过鲁棒性研究验证了: 叠层水印具有很好的抗噪声和抗剪切能力, 并且可以通过增加探针的数目和交叠率进一步提高其鲁棒性, 并给出其在GIF图像上的应用.     

Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem

The goal of the Label Ranking (LR) problem is to learn preference models that predict the preferred ranking of class labels for a given unlabeled instance. Different well-known machine learning algorithms have been adapted to deal with the LR problem. In particular, fine-tuned instance-based algorithms (e.g., k-nearest neighbors) and model-based algorithms (e.g., decision trees) have performed remarkably well in tackling the LR problem. Probabilistic Graphical Models (PGMs, e.g., Bayesian networks) have not been considered to deal with this problem because of the difficulty of modeling permutations in that framework. In this paper, we propose a Hidden Naive Bayes classifier (HNB) to cope with the LR problem. By introducing a hidden variable, we can design a hybrid Bayesian network in which several types of distributions can be combined: multinomial for discrete variables, Gaussian for numerical variables, and Mallows for permutations. We consider two kinds of probabilistic models: one based on a Naive Bayes graphical structure (where only univariate probability distributions are estimated for each state of the hidden variable) and another where we allow interactions among the predictive attributes (using a multivariate Gaussian distribution for the parameter estimation). The experimental evaluation shows that our proposals are competitive with the start-of-the-art algorithms in both accuracy and in CPU time requirements.     

Soliton solution to the complex modified Korteweg–de Vries equation on both zero and nonzero background via the robust inverse scattering method

In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero background. Especially, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time $t$ is large, then we give the comparison between the exact solution and the asymptotic solution.     

Experimentation and Learning in Repeated Cooperation

We study an agency model, in which the principal has only incomplete information about the agent's preferences, in a dynamic setting. Through repeated interaction with the agent, the principal learns about the agent's preferences and can thus adjust the inventive system. In a dynamic computational model, we compare different learning strategies of the principal when facing different types of agents. The results indicate that better learning of preferences can improve the situation of both parties, but the learning process is rather sensitive to random disturbances.     

Robust discrete optimization and network flows

We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. In particular, when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. When only the cost coefficients are subject to uncertainty and the problem is a 0–1 discrete optimization problem on n variables, then we solve the robust counterpart by solving at most n+1 instances of the original problem. Thus, the robust counterpart of a polynomially solvable 0–1 discrete optimization problem remains polynomially solvable. In particular, robust matching, spanning tree, shortest path, matroid intersection, etc. are polynomially solvable. We also show that the robust counterpart of an NP-hard -approximable 0–1 discrete optimization problem, remains -approximable. Finally, we propose an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network. The research of the author was partially supported by the Singapore-MIT alliance.The research of the author is supported by a graduate scholarship from the National University of Singapore.Mathematics Subject Classification (2000): 90C10, 90C15     

Robust Model Averaging Method Based on LOF Algorithm

Model averaging is a good alternative to model selection, which can deal with the uncertainty from model selection process and make full use of the information from various candidate models. However, most of the existing model averaging criteria do not consider the influence of outliers on the estimation procedures. The purpose of this paper is to develop a robust model averaging approach based on the local outlier factor (LOF) algorithm which can downweight the outliers in the covariates. Asymptotic optimality of the proposed robust model averaging estimator is derived under some regularity conditions. Further, we prove the consistency of the LOF-based weight estimator tending to the theoretically optimal weight vector. Numerical studies including Monte Carlo simulations and a real data example are provided to illustrate our proposed methodology.