A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

基于分段加权的反向稀疏跟踪算法研究

为提高稀疏表示跟踪模型性能，提出一种分段加权的反向稀疏跟踪算法，将跟踪问题转化为在贝叶斯框架下寻找概率最高的候选对象问题，构造不同的分段权重函数来分别度量候选目标与正负模板的判别特征系数。通过池化来降低跟踪结果的不确定性干扰，选择正负模板加权系数差值最大的候选表示作为跟踪结果。实验表明，在光照变化、遮挡、快速运动、运动模糊情况下，所提出的算法可以确保跟踪结果的准确性和鲁棒性。     

300 m级高拱坝设计与施工三维可视化仿真研究

双曲拱坝的C2连续曲面的三维模型表达困难,以双曲拱坝函数方程为基础引入CATIA三维软件,实现交互式设计和分析。同时,完成双曲拱坝细部模型的基于规则的智能化设计。基于大坝详细设计的三维成果,利用组件技术对模型数据进行提取和利用,制定施工方案并进行施工方案的动态可视化仿真。     

STATIONARY TANGENT: THE DISCRETE AND NON-SMOOTH CASE

Abstract. In Keich (2000 ),we define a stationary tangent process, or a locally optimal stationary approximation, to a real non-stationary smooth Gaussian process. This paper extends the idea by constructing a discrete tangent – a `locally' optimal stationary approximation – for a discrete time, real Gaussian process. Analogously to the smooth case, our construction relies on a generalization of the recursion formula for the orthogonal polynomials of the spectral distribution function. More precisely, we use a generalization of the Schur parameters to identify the stationary tangent. By way of discretizing, we later demonstrate how this tangent can be used to obtain `good' local stationary approximations to non-smooth continuous time, real Gaussian processes. Further, we demonstrate how, analogously to the curvatures in the smooth case, the Schur parameters can be used to determine the order of stationarity of a non-smooth process.     

G~2－连续的保凸插值三次Bezier样条曲线

本文引入曲率参数，描述了分段三次Ｂｅｚｉｅｒ插值样条曲线（开的和闭的）。这些插值曲线是Ｇ~２－连续的和保凸的，并且这些曲线可以作局部修改。最后，用本文的方法解决了一个实际问题。     

三峡地下电站变顶高尾水洞水动力特性

在国内首次应用模型水轮发电机组对三峡地下电站变顶高尾水洞方案进行水力过渡过程试验研究。对水轮机导叶实行分段关闭 ,并求出了二段关闭的最佳拐点 ,试验证实了二段关闭对减小尾水管进口的负压和机组转速上升有明显的作用。通过有关水力参数的测试 ,认为变顶高尾水洞可以满足各项技术要求 ,是一个减少山体开挖、节省投资的新型设计方案。在地下电站中具有广泛的应用前景     

Conceptual damage-sensitive features for structural health monitoring: Laboratory and field demonstrations

The use of damage-sensitive features to evaluate structural condition or health is a very critical aspect of structural health monitoring. The purpose of this paper is to investigate the potential of two different damage-sensitive features for detecting damage. Different damage scenarios are simulated on a large-scale laboratory structure and a three-span highway bridge for demonstration. The features presented in this paper are the modal flexibility-based deflection and curvature both of which are obtained directly from dynamic properties. In the literature, flexibility associated with mode shapes and mode shapes curvatures have been mostly explored. In this study, multi-input–multi-output dynamic data are used to obtain modal flexibility, which is a close approximation to the actual flexibility. A main novelty is that the curvature is calculated from the deflected shapes using the modal flexibility as opposed to using modal vectors. In this paper, the theory of the methodology is explained and then experimental studies and results are presented. For the experimental studies, the laboratory specimen and the three-span bridge were gradually damaged. It is shown that both deflection and curvature are conceptual and physically meaningful features for damage detection and localization. The issues and the requirements for these features to perform successfully are also presented.     

A direct stiffness analysis of a composite beam with partial interaction

The use of the conventional semi-analytical stiffness method in finite element analysis, in which interpolation polynomials are used to develop the stiffness relationships, leads to problems of curvature locking when beam-type elements are developed for composite members with partial interaction between the materials of which it is comprised. The curvature locking phenomenon that occurs for composite steel–concrete members is quite well reported, and the general approach to minimizing the undesirable ramifications of curvature locking has been to use higher-order polynomials with increasing numbers of internal nodes. This paper presents an alternate formulation based on a direct stiffness approach rather than starting from pre-defined interpolation polynomials, and which does not possess the undesirable locking characteristics. The formulation is based on a more general approach for a bi-material composite flexural member, whose constituent materials are joined by elastic shear connection so as to provide partial interaction. The stiffness relationships are derived, and these are applied to a simply supported and a continuous steel–concrete composite beam to demonstrate the efficacy of the method, and in particular its ability to model accurately both very flexible and very stiff shear connection that causes difficulties when implemented in competitive semi-analytical algorithms. Copyright © 2004 John Wiley & Sons, Ltd.     

Adaptive Edge Detectors for Piecewise Smooth Data Based on the minmod Limiter

We are concerned with the detection of edges—the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our previous work [Gelb and Tadmor, Appl. Comp. Harmonic Anal., 7, 101–135 (1999)] and realized in the dual Fourier space, is based on concentration factors; with a proper choice of concentration factors one can achieve higher-orders—in fact in [Gelb and Tadmor, SIAM J. Numer. Anal., 38, 1389–1408 (2001)] we constructed exponentially accurate edge detectors. Since the stencil of these highly-accurate detectors is global, an outside threshold parameter is required to avoid oscillations in the immediate neighborhood of discontinuities. In this paper we introduce an adaptive edge detection procedure based on a cross-breading between the local and global detectors. This is achieved by using the minmod limiter to suppress spurious oscillations near discontinuities while retaining high-order accuracy away from the jumps. The resulting method provides a family of robust, parameter-free edge-detectors for piecewise smooth data. We conclude with a series of one- and two-dimensional simulations.To David Gottlieb, on his 60th birthday, with friendship and appreciation.     

参数三次B样条曲线的一种整体光顺方法

本文在能量法的基础上，提出了一种新的目标函数，给出了参数三次Ｂ样条曲线的一种新的整体光顺方法。利用这种方法得到的曲线不仅具有较小的应变能，而且曲率变化比较均匀，具有很好的光顺效果。该方法能推广到对曲面的光顺。