动力学光谱数据解析的奇异值分解最小二乘法

奇异值分解最小二乘法用于解析模拟的二组份可见／紫外动力学光谱数据。该方法不仅可获得组成动力学光谱变化的组份分数及其光谱,而且能够给出各组份随时间的变化规律。与动力学和非线性回归相结合,可用于处理复杂体系动力学光谱数据。     

Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.     

Vibration analysis of harmonically excited non-linear system using the method of multiple scales

An analytical method is presented for evaluation of the steady state periodic behavior of non-linear systems. This method is based on the substructure synthesis formulation and a multiple scales procedure, which is applied to the analysis of non-linear responses. A complex non-linear system is divided into substructures, of which equations are approximately transformed to modal co-ordinates including non-linear term under the reasonable procedure. Then, the equations are synthesized into the overall system and the solution of the non-linear system can be obtained. Based on the method of multiple scales, the proposed procedure reduces the size of large-degree-of-freedom problem in solving the non-linear equations. Feasibility and advantages of the proposed method are illustrated by the application of the analytic procedure to the non-linear rotating machine system as a large mechanical structure system. Results obtained are reported to be an efficient approach with respect to non-linear response prediction when compared with other conventional methods.     

Non-linear effect of wall linings on sound attenuation in ducts

The equivalent surface source method is extended to the analysis of high intensity sound propagation in a duct whose wall is partially treated with a sound absorbing material. The propagation of sound in the gas is assumed to be linear, but the acoustic resistance of the sound absorbing material is assumed to be a function of the normal acoustic velocity. The problem is reduced to a non-linear integro-differential equation for the fluid particle displacement at the lined wall surface, which can be solved by a successive approximation method. Numerical examples show that the non-linear effect decreases or increases the peak sound attenuation rate of the lowest mode depending upon the linear component of the resistance. The dependence of the attenuation spectrum on modal phase difference of multi-mode incident waves is heavily affected by the non-linear effect. In the case of incident waves of multi-circumferential modes, different circumferential modes are generated by the non-linear effect.     

Two-component description of dynamical systems that can be approximated by solitons: The case of the ion acoustic wave equations of plasma physics

A new approach to the perturbative analysis of dynamical systems, which can be described approximately by soliton solutions of integrable non-linear wave equations, is employed in the case of small-amplitude solutions of the ion acoustic wave equations of plasma physics. Instead of pursuing the traditional derivation of a perturbed KdV equation, the ion velocity is written as a sum of two components: elastic and inelastic. In the single-soliton case, the elastic component is the full solution. In the multiple-soliton case, it is complemented by the inelastic component. The original system is transformed into two evolution equations: An asymptotically integrable Normal Form for ordinary KdV solitons, and an equation for the inelastic component. The zero-order term of the elastic component is a single-soliton or multiple-soliton solution of the Normal Form. The inelastic component asymptotes into a linear combination of single-soliton solutions of the Normal Form, with amplitudes determined by soliton interactions, plus a second-order decaying dispersive wave. Satisfaction of a conservation law by the inelastic component and of mass conservation by the disturbance to the ion density is determined solely by the initial data and/or boundary conditions imposed on the inelastic component. The electrostatic potential is a first-order quantity. It is affected by the inelastic component only in second order. The charge density displays a triple-layer structure. The analysis is carried out through the third order.     

STATISTICAL SEISMIC RESPONSE ANALYSIS AND RELIABILITY DESIGN OF NONLINEAR STRUCTURE SYSTEM

Industrial structure systems may have non-linearity, and are also sometimes exposed to the danger of earthquake. In the design of such system, these factors should be accounted for from the viewpoint of reliability. This paper proposes a method to analyze seismic response and reliability design of a complex non-linear structure system under random excitation. The actual random excitation is represented to the corresponding Gaussian process for the statistical analysis. Then, the non-linear system is subjected to this random process. The non-linear structure system is modelled by substructure synthesis method (SSM) procedure. The non-linear equations are expanded sequentially. Then, the perturbed equations are solved in probabilistic method. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with the non-linear stochastic problem. The system performance condition in the design of system is that responses caused by random excitation be limited within safe bounds. Thus, the reliability of the system is considered according to the crossing theory. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.     

Analytical method for steady state vibration of system with localized non-linearities using convolution integral and Galerkin method

The analytical method using transfer function or impulse response is very effective for analyzing non-linear systems with localized non-linearities. This is because the number of non-linear equations can be reduced to that of the equations with respect to points connected with the non-linear element. In the present paper, analytical method for the steady state vibration of non-linear system including subharmonic vibration is proposed by utilizing convolution integral and the impulse response. The Galerkin method is introduced to solve the non-linear equations formulated by the convolution integral, and then the steady state vibration is obtained. An advantage of the present method is that stability or instability of the steady state vibration can be discriminated by the transient analysis from convolution integral. The three-degree-of-freedom mass-spring system is shown as a numerical example and the proposed method is verified by comparing with the result by Runge-Kutta-Gill method.     

NON-LINEAR GENERALIZATION OF PRINCIPAL COMPONENT ANALYSIS: FROM A GLOBAL TO A LOCAL APPROACH

Principal component analysis (PCA), also known as proper orthogonal decomposition or Karhunen-Loève transform, is commonly used to reduce the dimensionality of a data set with a large number of interdependent variables. PCA is the optimal linear transformation with respect to minimizing the mean square reconstruction error but it only considers second-order statistics. If the data have non-linear dependencies, an important issue is to develop a technique which takes higher order statistics into account and which can eliminate dependencies not removed by PCA. Recognizing the shortcomings of PCA, researchers in the field of statistics and neural networks have developed non-linear extensions of PCA. The purpose of this paper is to present a non-linear generalization of PCA, called VQPCA. This algorithm builds local linear models by combining PCA with clustering of the input space. This paper concludes by observing from two illustrative examples that VQPCA is potentially a more effective tool than conventional PCA.     

Three-dimensional finite element simulation of closed delaminations in composite materials

Early stage delaminations in composite materials tend to be closed at rest. Inspection with traditional linear ultrasonic techniques generally fails to diagnose and locate such imperfections. However, if undetected and left untreated, incipient defects may gradually grow within the material and eventually lead to failure of the component. Kissing bonds or clapping contacts inherently demand a non-linear diagnostic method, applying a finite excitation amplitude that is able to overcome an activation threshold to open and close the contact. In order to obtain a better understanding and analysis of the macroscopic non-linear behavior that can be observed at the component level, we developed and investigated the results of a finite element model for a composite material containing a single circular delamination. The model makes use of local node splitting and the non-linear constitutive behavior is implemented by means of spring-damper elements at the delamination interface. The results of this parametric study allow a better insight in the behavior of the excited delamination in experimental conditions, including the appearance of localized subharmonics and harmonics of the excitation frequency. Based on the developed model, two different detection and localization techniques (using either a single frequency or a sweep excitation) were demonstrated to determine position, shape, depth and orientation of one or multiple delaminations.     

The effect of spin on the non-linear resonant motions of a dynamical system

The motions of a two degree of freedom mechanical oscillator in a state of internal resonance due to the non-linear coupling between its modes are analyzed by the method of multiple scales. The system is connected by a motor to a vertical shaft driven at a constant spin rate relative to inertial space. It is shown that the non-linear resonance phenomenon can effectively be controlled by properly changing the spin rate of the motor. In addition, the transition curves that separate the non-linear resonant and the non-resonant motions of the system are also determined analytically by a straightforward perturbation method. The analytical expression for the transition curves is used in connection with the multiple scale analysis to yield a refined approximation for the main characteristics of the non-linear resonant motion.     

Data detection for the P-SLAM optical data storage system

This paper presents an intersymbol interference (ISI) and system noise analysis of the P-SLAM (parallel-sub-lambda) optical data storage system. Data are stored in sub-wavelength features accessed by transmitting light through the structure and collecting optical power measurements in the near-field. The non-linear ISI caused by the interactions of light between these features is characterized using finite-difference time-domain (FDTD) simulations. A system noise analysis is also presented that quantifies the effects of imperfections in fabrication and material properties. Previously, the authors proposed a detection scheme that dealt with the non-linear ISI by physically reducing it with air gaps. In this paper a signal processing method, the Viterbi algorithm, is proposed to overcome ISI. A modification is proposed to the Viterbi algorithm that is designed to deal with both the non-linear ISI and system noise. System simulations are used to show the uncoded bit error rate of the system is similar to current technologies. Conservative predictions estimate a data density of 5 Gbits/cm² for the system which exceeds densities achievable by current optical technologies.     

Seismic response of bridge piers on elasto-plastic Winkler foundation allowed to uplift

When the bridge piers with shallow foundation are subject to intensive earthquake excitations, uplift of foundations will occur and the foundation soil will partly become plastic. It is very difficult to use an accurate method to simulate the uplifting and yielding of supporting soil. An improved Winkler foundation model, which could be used to consider the uplift and yield, was employed in the analysis. The 1940 El Centro earthquake record is inputted to a rigid pier with shallow foundation so that the non-linear history response is obtained. From the non-linear analysis, it is concluded that the non-linear effect is very remarkable when uplifting and yielding of supporting soil are considered. Compared with the linear analysis, the stiffness of bridge pier-soil system degrades in each cycle after considering uplifting and yielding. It is shown that the non-linear analysis can get larger rotational angles and smaller bending moments compared with the linear analysis.     

Application of the maximum likelihood principle to separate exponential terms in T2 relaxation of nuclear magnetic resonance

The method of maximum likelihood has been implemented for the estimation of multiple exponential components of T2 decay curves in spin echo NMR measurements on biologic tissues. Each Each component contributes an exponential term described by two parameters (initial amplitude and T2) to the T2 decay curve. The maximum likelihood method estimates the parameters and their standard errors for all terms simultaneously, avoiding the subjectivity inherent in methods such as graphical peeling. In the model used, it was assumed that water protons are compartmentalized and that the measured spin echo signals from the protons undergoing relaxation obey the Poisson distribution. A system of non-linear equations was derived and solved iteratively for the values of the exponential parameters which maximize the likelihood of obtaining the observed data under these assumptions. The approach was implemented for bi- and tri-exponential models on a MicroVAX II computer (Digital Equipment Corporation, Maynard, MA). Simulations of bi- and tri-exponential data, with and without system noise, were analyzed to assess the accuracy and reproducibility of the method. A subset of the simulations was repeated with non-linear least squares techniques and was compared to the results obtained with maximum likelihood. Rabbit muscle and gerbil brain samples were measured and analyzed with the maximum likelihood method. The simulations showed that within specific limits on relative sizes and relaxation rates of components, these parameters can be estimated with errors less than 5%. The comparison to non-linear least squares analysis showed that the maximum likelihood method is generally superior in estimating the parameters in difficult cases. The results from tissue measurements demonstrate that the method is effective even in cases where graphical peeling would clearly not yield reliable results.     

The effects of large vibration amplitudes on the dynamic strain response of a clamped-clamped beam with consideration of fatigue life

The effects of large vibration amplitudes on the dynamic strain response, near to the fundamental resonance, of a clamped-clamped, thin beam is examined. Complementary theoretical and experimental studies showed that the harmonic distortion of the induced total strain, due to sinusoidal excitation at mid-span, is mainly due to the axial strain component. A limited set of fatigue experiments showed the considerable decrease in fatigue life, which occurs due to non-linear vibration, compared to that of a cantilevered beam of the same material. The statistical approach to the analysis of non-linear vibration induced by random loading is examined theoretically and experimentally, good correlation being achieved between predicted and measured fatigue lives.     

A semi-classical approach to two-frequency solitons in a three-level cascade atomic system

A semi-classical theory of two intense optical fields interacting with a third-order non-linear medium composed of a three-level cascade atomic system is presented. It is predicted that non-linear atom-field interactions allow the formation of two-frequency bright, dark and grey spatial solitons. We demonstrate through numerical simulations and analytic stability analysis that the bright and grey solitons are stable.     

Track infrared point targets based on projection coefficient templates and non-linear correlation combined with Kalman prediction

For a long time, tracking IR point targets is a great challenge task. We propose a tracking framework based on template matching combined with Kalman prediction. Firstly, a novel template matching method for detecting infrared point targets is presented. Different from the classic template matching, the projection coefficients obtained from principal component analysis are used as templates and the non-linear correlation coefficient is used to measure the matching degree. The non-linear correlation can capture the higher-order statistics. So the detection performance is improved greatly. Secondly, a framework of tracking point targets, based on the proposed detection method and Kalman prediction, is developed. Kalman prediction reduces the searching region for the detection method and, in turn, the detection method provides the more precise measurement for Kalman prediction. They bring out the best in each other. Results of experiments show that this framework is competent to track infrared point targets.     

Recovery of reflectance spectra from colorimetric data using principal component analysis embedded regression technique

The classical principal component analysis technique is enhanced for reconstruction of reflectance spectra of surface colors from the corresponding tristimulus values under a given set of viewing conditions, i.e., D65 illuminant and 1964 standard observer. In this paper, the number of implemented eigenvectors has been virtually extended from three to six by estimation of another set of tristimulus values under illuminant A and 1964 standard observer. The second set of colorimetric data was predicted by the conventional non-linear regression method and used in the spectral reconstruction to produce a fully determined system in the case of six eigenvectors. The improvement obtained from the proposed modification was examined for the recovery of the reflectance spectra of Munsell color chips as well as ColorChecker DC samples. The performance is evaluated by the mean, maximum and standard deviation of color difference values under other sets of light sources. The values of mean, maximum and standard deviation of root mean square (RMS) errors between the reproduced and the actual spectra were also calculated. Results are compared with those obtained from traditional methods using the principal component analysis (PCA) routine. All metrics show that the suggested method leads to considerable improvements in comparison with the standard PCA approach.     

Flexible polyurethane foam modelling and identification of viscoelastic parameters for automotive seating applications

A hereditary model and a fractional derivative model for the dynamic properties of flexible polyurethane foams used in automotive seat cushions are presented. Non-linear elastic and linear viscoelastic properties are incorporated into these two models. A polynomial function of compression is used to represent the non-linear elastic behavior. The viscoelastic property is modelled by a hereditary integral with a relaxation kernel consisting of two exponential terms in the hereditary model and by a fractional derivative term in the fractional derivative model. The foam is used as the only viscoelastic component in a foam-mass system undergoing uniaxial compression. One-term harmonic balance solutions are developed to approximate the steady state response of the foam-mass system to the harmonic base excitation. System identification procedures based on the direct non-linear optimization and a sub-optimal method are formulated to estimate the material parameters. The effects of the choice of the cost function, frequency resolution of data and imperfections in experiments are discussed. The system identification procedures are also applied to experimental data from a foam-mass system. The performances of the two models for data at different compression and input excitation levels are compared, and modifications to the structure of the fractional derivative model are briefly explored. The role of the viscous damping term in both types of model is discussed.     

Study of the Performance of an All-Optical Half-Adder Based on Three-Core Non-Linear Directional Fiber Coupler Under Delayed and Instantaneous Non-Linear Kerr Responses

Abstract

Recently, much attention has been given to the influence of the relaxation process of the non-linear response, because the usual assumption of instantaneous non-linear response fails for ultra-short pulses, and additional contributions coming from non-linear dispersion and delayed non-linearity have to be taken into account. This article presents a numerical analysis of the symmetric planar and asymmetric planar three-core non-linear directional fiber couplers operating with a soliton pulse, where effects of both delayed and instantaneous non-linear Kerr responses are analyzed for implementation of an all-optical half-adder. To implement this all-optical half-adder, eight configurations were analyzed for the non-linear directional fiber coupler, with two symmetric and six asymmetric configurations. The half-adder is the key building block for many digital processing functions, such as shift register, binary counter, and serial parallel data converters. The optical coupler is an important component for applications in optical-fiber telecommunication systems and all integrated optical circuit because of its very high switching speeds. In this numerical simulation, the symmetric/asymmetric planar presents a structure with three cores in a parallel equidistant arrangement, three logical inputs, and two output energy. To prove the effectiveness of the theoretical model for generation of the all-optical half-adder, the best phase to be applied to the control pulse was sought, and a study was done of the extinction ratio level as a function of the Δ > parameter, the normalized time duration, and the Sum and Carry outputs of the (symmetric planar/asymmetric planar) non-linear directional fiber coupler. In this article, the interest is in transmission characteristics, extinction ratio level, normalized time duration, and pulse evolution along the non-linear directional fiber coupler. To compare the performance of the all-optical half-adders, the figure of merit of the logic gates was used. All results were obtained numerically, considering a simple model for generation of an all-optical half-adder.     

STOCHASTIC AVERAGING OF DUHEM HYSTERETIC SYSTEMS

The response of Duhem hysteretic system to externally and/or parametrically non-white random excitations is investigated by using the stochastic averaging method. A class of integrable Duhem hysteresis models covering many existing hysteresis models is identified and the potential energy and dissipated energy of Duhem hysteretic component are determined. The Duhem hysteretic system under random excitations is replaced equivalently by a non-hysteretic non-linear random system. The averaged Ito's stochastic differential equation for the total energy is derived and the Fokker-Planck-Kolmogorov equation associated with the averaged Ito's equation is solved to yield stationary probability density of total energy, from which the statistics of system response can be evaluated. It is observed that the numerical results by using the stochastic averaging method is in good agreement with that from digital simulation.