Accurate higher-order analytical approximate solutions to nonconservative nonlinear oscillators and application to van der Pol damped oscillators

In general, this paper deals with general nonlinear oscillations of a nonconservative and single degree-of-freedom system with odd nonlinearity and, in particular, it presents accurate higher-order analytical approximate solutions to van der Pol damped nonlinear oscillators having odd nonlinearity and the Rayleigh equation. By combining the linearization of the governing equation with harmonic balancing and the method of averaging, we establish accurate analytical approximate solutions for the general weakly damped nonlinear systems. Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. The combination of these two methods results in very accurate transient response of the periodic solution. In addition and for the first time, this paper also presents a method for deducing fourth-, fifth- and higher-order linearized governing equations from the lower-order equations without the requirement of formulating the problem from the first principle. Three examples including the van der Pol damped nonlinear oscillator are presented to illustrate the excellent agreement with approximate solution using the exact frequency.     

Two-degree-of-freedom output feedback controllers for discrete-time nonlinear systems

A discrete-time, model-based output feedback control structure for nonlinear processes is developed in the present work. The structure makes use of a closed-loop observer, while at the same time it guarantees that the overall feedback controller possesses integral action. An algebraic transformation is applied on the observer states to insure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The resulting control algorithm is a two-degree-of-freedom control law, in the sense that the output and the set point are processed in different ways. The control structure is shown not only to have the same properties as the standard model-state feedback structure, but also that it emerges from a model algorithmic control framework. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to evaluate the closed-loop performance of the proposed method.     

Adaptive observers as nonlinear internal models

This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of adaptive output regulation, by allowing for not necessarily stable zero dynamics of the controlled plant and by weakening the standard assumption of having the steady-state control input generated by a linear system.     

Using Lyapunov's direct method for wave suppression in reactive systems

This paper proposes a new approach for stabilizing a homogeneous solution in reaction–convection–diffusion system with oscillatory kinetics, in which moving or stationary patterns emerge in the absence of control. Specifically, we aim to suppress patterns by using a spatially weighted finite-dimensional feedback control that assures stability of the solution according to Lyapunov's direct method. A practical design procedure, based on spectral representation of the system and dissipative nature of parabolic PDEs, is presented.     

Determination of optimal feedback terminal controllers for general boundary conditions using generating functions

Given a nonlinear system and a performance index to be minimized, we present a general approach to expressing the finite time optimal feedback control law applicable to different types of boundary conditions. Starting from the necessary conditions for optimality represented by a Hamiltonian system, we solve the Hamilton-Jacobi equation for a generating function for a specific canonical transformation. This enables us to obtain the optimal feedback control for fundamentally different sets of boundary conditions only using a series of algebraic manipulations and partial differentiations. Furthermore, the proposed approach reveals an insight that the optimal cost functions for a given dynamical system can be decomposed into a single generating function that is only a function of the dynamics plus a term representing the boundary conditions. This result is formalized as a theorem. The whole procedure provides an advantage over methods rooted in dynamic programming, which require one to solve the Hamilton-Jacobi-Bellman equation repetitively for each type of boundary condition. The cost of this favorable versatility is doubling the dimension of the partial differential equation to be solved.     

基于Eigenspace的面瘫判定系统

本文将特征空间分类方法应用于面瘫图像的判定。结合应用的特点，引入多特征空间分类，比较图像与它们到两个特征空间的投影之间的距离作出判定，并在系统中加入灰度图变换，脸部子区域分割，确定对称轴和输入向量计算等前处理步骤。实验证明，本文的改进提高了系统判定的正确性。     

Influence of Membrane Stresses on Postbuckling of Rectangular Plates Using a Nonlinear Elastic 3-D Cosserat Brick Element

This paper has two main objectives. The first is to examine the influence of membrane stresses on postbuckled deformations of nonlinear elastic isotropic rectangular plates. The second is to further examine the accuracy of a new 3-D Cosserat eight noded brick element (Nadler and Rubin in Int J Solids Struct 40: 4585–4614, 2003) which was developed within the context of the theory of a Cosserat point. The equations of the Cosserat element include both material and geometric nonlinearities. A number of example problems are considered which examine predictions of the Cosserat element for beams and plates and comparison has been made with results from the commercial codes ANSYS and ADINA. Also, the approximate nonlinear postbuckling solution described in Timoshenko and Gere (Theory of elastic stability, Mc Graw-Hill, New York) is shown to be more limited than originally expected. These results suggest that the Cosserat element is robust, can perform well under extreme conditions and is capable of modeling combinations of three-dimensional bodies with attached thin structures.     

Chalcogenide Glasses Based on Germanium Disulfide for Second Harmonic Generation

High second‐order susceptibilities are created by thermal poling in bulk germanium disulfide based chalcogenide glasses. Experimental conditions of the poling treatment (temperature, voltage, time) were optimized for each glass composition. The second‐order nonlinear signals were recorded by using the Maker fringes experiment and a second‐order coefficient χ⁽²⁾ up to 8 pm V^–1 was measured in the Ge₂₅Sb₁₀S₆₅ glass. This value is obtained using a simulation based on accurate knowledge of the thickness of the nonlinear layer. Two mechanisms are proposed to explain the creation of a nonlinear layer under the anode: the formation and the migration of charged defects towards the anode may mainly occur in Ge₂₀Ga₅Sb₁₀S₆₅ and Ge₂₅Ga₅S₇₀ glasses, whereas the migration of Na⁺ ions towards the cathode may be responsible for the accumulation of negative charges under the anode in Ge₃₃S₆₇ and Ge₂₅Sb₁₀S₆₅ glasses. Different electronic conductivity behaviors seem to be at the origin of the phenomenon. In parallel, the potential effect of the poling treatment on the structural and electronic properties is studied using Raman spectroscopy and secondary ion mass spectroscopy measurements.     

Nonlinear Thermal Analysis for Qing-Tibet Railway Embankments in Cold Regions

Heat convection in ballast mass in railway embankments is a problem of heat convection in porous media. In order to calculate the temperature distribution of the Qing-Tibet railway embankment from the governing equations used to study forced convection for incompressible fluids porous media, detailed finite-element formulas for heat convection in porous media are derived using Galerkin’s method. The temperature distributions on central lines of the traditional railway embankment, the ripped-rock embankment, and the ripped-rock revetment embankment that were constructed on July 15, 2002 have been analyzed and compared on July 15, October 15 in the 24th year after construction, and January 15 in the 25th year after construction under the climatic and geological conditions on the Qing-Tibet Railway. The calculated results indicate that the traditional railway embankment will raise the permafrost temperature under the embankment base and make the permafrost embankment thermally unstable. The ripped-rock embankment and the ripped-rock revetment embankment will reduce the permafrost temperature under the embankment base in cold regions, therefore maintaining the thermal stability of permafrost. However, the ripped-rock embankment needs more rock mass while the ripped-rock revetment embankment need less rock mass, and its construction cost is lower than that of the former. Therefore, it is highly recommended that the ripped-rock revetment embankment be used for the Qing-Tibet railway embankment structure in high temperature permafrost regions so that the permafrost embankment can be protected as much as possible.