Convex Parametric Programming in Abstract Spaces

This article studies stability and optimality for convex parametric programming models in abstract spaces. Necessary conditions for continuity of the feasible set mapping are given in complete metric spaces. This continuity is characterized for models in which the space of decision variables is reflexive Banach space. The main result on optimality characterizes locally optimal parameters relative to stable perturbations of the parameter. The result is stated in terms of the existence of a saddle-point for a Lagrangian that uses a finite Borel measure. It does not hold for unstable perturbations even if the model is finite dimensional. The results are applicable to various formulations of control and optimal control problems.     

Large amplitude electron plasma oscillations

We consider a cold plasma in order to find new large-amplitude wave solutions in the long-wavelength limit. Accordingly we derive two generic coupled equations which describe the energy exchange between the electrostatic and electromagnetic waves. A new kind of quasi-periodic behavior is found. Our derivations may be considered as a prerequisite to extended studies of stimulated Raman scattering for cases where the wave amplitudes are so large that standard perturbation techniques are not applicable.     

Principal parametric resonances of non-linear mechanical system with two-frequency and self-excitations

The principal parametric resonance of a single-degree-of-freedom system with non-linear two-frequency parametric and self-excitations is investigated. In particular, the case in which the parametric excitation terms with close frequencies is examined. The method of multiple scales is used to determine the equations that describe to first-order the modulation of the amplitude and phase. Qualitative analysis and asymptotic expansion techniques are employed to predict the existence of steady state responses. Stability is investigated. The effect of damping, magnitudes of non-linear excitation and self-excitation are analyzed.     

Regular and Chaotic Vibrations of a Parametrically and Self-Excited System Under Internal Resonance Condition

Vibrations of a parametrically and self-excited system with two degrees of freedom have been analysed in this paper. The system is constituted by two parametrically coupled oscillators characterised by self-excitation and nonlinear Duffing’s type nonlinearities. Synchronisation phenomenon has been determined near the principal resonances in the neighbourhood of the first p₁ and the second p₂ natural frequencies, and near the combination resonance (p₁+p₂)/2. Vibrations have been investigated for parameters which satisfy the internal resonance condition p₂/p₁=3. The existence and break down of the synchronisation phenomenon have been revealed analytically by the multiple time scale method, whilst transition of the system to chaotic motion has been carried out numerically.     

Un modèle paramétrique d'évolution de surface pour matériaux contraints : modélisationA parametric model of surface evolution for materials under constraint; part I: modeling

We present a model describing the surface changes of an elastic preconstrained material which is valid for large deformations. The surface profile is described by a parametric curve that allows the emergence of infinite tangents and back return point as the surface evolves. The proposed model covers a number of classic models: Spencer (1994), Yang (1993), Kassner (1994), Chiu (1994). These latter models were limited to surface profiles with one-to-one representations and low amplitudes of deformation. To cite this article: M. Carrive, J. Grilhé, C. R. Mecanique 334 (2006).     

Stability chart of parametric vibrating systems using energy-rate method

Based on the integral of energy and numerical integration, we introduce, develop, and apply a general algorithm to predict parameters of a parametric equation to produce a periodic response. Using the new method, called energy-rate, we are able to find not only stability chart of a parametric equation which indicates the boundaries of stable and unstable regions, but also periodic responses that are embedded in stable or unstable regions.There are three main important advantages in energy-rate method. It can be applied not only to linear but also to non-linear parametric equations; most of the perturbation methods cannot. It can be applied to large values of parameters; most of the perturbation methods cannot. Depending on the accuracy of numerical integration method, it can also find the value of parameters for a periodic response more accurate than classical methods, no matter if the periodic response is on the boundary of stability and instability or it is a periodic response within the stable or unstable region.In order to introduce the energy-rate method and indicate its advantages we apply the method to the standard Mathieu's equation,

     

Bifurcation Control of Parametrically Excited Duffing System by a Combined Linear-Plus-Nonlinear Feedback Control

For a parametrically excited Duffing system we propose a bifurcation control method in order to stabilize the trivial steady state in the frequency response and in order to eliminate jump in the force response, by employing a combined linear-plus-nonlinear feedback control. Because the bifurcation of the system is characterized by its modulation equations, we first determine the order of the feedback gain so that the feedback modifies the modulation equations. By theoretically analyzing the modified modulation equations, we show that the unstable region of the trivial steady state can be shifted and the nonlinear character can be changed, by means of the bifurcation control with the above feedback. The shift of the unstable region permits the stabilization of the trivial steady state in the frequency response, and the suppression of the discontinuous bifurcation due to the change of the nonlinear character allows the elimination of the jump in the quasistationary force response. Furthermore, by performing numerical simulations, and by comparing the responses of the uncontrolled system and the controlled one, we clarify that the proposed bifurcation control is available for the stabilization of the trivial steady state in the frequency response and for the reduction of the jump in the nonstationary force response.     

New techniques of local damage detection in machinery based on stochastic modelling using adaptive Schur filter

Vibration signal analysis is one of the most effective techniques of monitoring machinery and detecting local damage in their parts, e.g. bearings and gearboxes. However, such detection is sometimes difficult, especially in heavy industrial machines, because of a small proportion of damage-induced components in relation to the remaining components of registered signals. Therefore, more effective signal processing algorithms are being looked for. Moreover, local damage (cracking, pitting, spalling, breakage, etc.) in bearings and gearboxes generates broad-spectrum impulse signals, while the other type can be effectively modelled as a sum of narrowband signals. In this article, techniques based on Schur adaptive filter are proposed for local damage detection. In such an approach, the analysed signal is modelled by means of autoregressive process and the filter is described by so-called reflection coefficients. Schur algorithm is an effective algorithm with very good numerical properties and it is capable of tracking rapid changes in second order statistics of the analysed signal. Thus, the method is well-suited to analysing non-stationary signals and it is potentially interesting for use in bearing and gearbox monitoring.Reflection coefficients describing the signal model, defined with the use of Schur algorithm, may be applied in a variety of ways, giving a chance of employing different solutions in different conditions. In the first proposed solution, detection is based on the weighted sum of derivatives of reflection coefficients, while in the other one – on new signal obtained as power in frequency bands calculated from a parametric spectrogram, whose starting point are reflection coefficients. All these operations are aimed at enhancing changes that occur in the signal at the moments when damage-induced impulses appear. The article also presents guidelines for methods of determining parameter values in the employed analyses. The proposed solutions have been applied for analysing signals coming from a two-stage gearbox of a large machine driving a mining belt conveyor and the obtained results were analysed. They prove the effectiveness of the proposed techniques. It is worth emphasizing that these techniques can be easily adapted for monitoring machinery in varying operating conditions.     

基于光纤光参量放大的光脉冲压窄技术的研究

在高重复频率的光窄脉冲源中,为了获得更窄的脉冲,需要增加泵浦功率|但泵浦功率的提高会使光放大器的增益趋于饱和,放大的自发辐射噪音增强,脉冲光信噪比下降.为此,提出了利用啁啾管理和光纤光参量放大相结合的脉冲压窄方案.将强度调制后的泵浦光通过相位调制引入线性负啁啾,由于经参量过程后在新的闲频光上啁啾会加倍,从而进一步增大了信号的谱宽,并通过色散补偿介质实现了光脉冲压缩.实验给出了10 GHz速率下的结果,通过泵浦光的相位调制在0.5 W平均泵浦光功率条件下得到了脉宽19 ps的光脉冲,结果与理论分析基本吻合.