STABILITY OF TRANSONIC SHOCKS TO THE EULER-POISSON SYSTEM WITH VARYING BACKGROUND CHARGES

This paper is devoted to studying the stability of transonic shock solutions to the Euler-Poisson system in a one-dimensional nozzle of finite length.The background charge in the Poisson equation is a piecewise constant function.The structural stability of the steady transonic shock solution is obtained by the monotonicity argument.Furthermore,this transonic shock is proved to be dynamically and exponentially stable with respect to small perturbations of the initial data.One of the crucial ingredients of the analysis is to establish the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions.

Probabilistic Global Maximum Power Point Tracking Algorithm for Continuously Varying Partial Shading Conditions on Autonomous PV Systems

A photovoltaic (PV) string with multiple modules with bypass diodes frequently deployed on a variety of autonomous PV systems may present multiple power peaks under uneven shading. For optimal solar harvesting, there is a need for a control schema to force the PV string to operate at global maximum power point (GMPP). While a lot of tracking methods have been proposed in the literature, they are usually complex and do not fully take advantage of the available characteristics of the PV array. This work highlights how the voltage at operating point and the forward voltage of the bypass diode are considered to design a global maximum power point tracking (GMPPT) algorithm with a very limited global search phase called Fast GMPPT. This algorithm successfully tracks GMPP between 94% and 98% of the time under a theoretical evaluation. It is then compared against Perturb and Observe, Deterministic Particle Swarm Optimization, and Grey Wolf Optimization under a sequence of irradiance steps as well as a power-over-voltage characteristics profile that mimics the electrical characteristics of a PV string under varying partial shading conditions. Overall, the simulation with the sequence of irradiance steps shows that while Fast GMPPT does not have the best convergence time, it has an excellent convergence rate as well as causes the least amount of power loss during the global search phase. Experimental test under varying partial shading conditions shows that while the GMPPT proposal is simple and lightweight, it is very performant under a wide range of dynamically varying partial shading conditions and boasts the best energy efficiency (94.74%) out of the 4 tested algorithms.

Investigations on Fluid Resonance Within A Narrow Gap Formed by Two Fixed Bodies with Varying Breadth Ratios

The resonant motion of the fluid inside a narrow gap between two fixed boxes induced by incident regular waves with various wave heights is investigated by adopting a two-dimensional numerical wave flume based on an opensourced CFD package,OpenFOAM.The two boxes have identical draft and height,but the upstream box has a variable breadth.This article focuses on the influences of the breadth ratio,defined as the ratio of the breadth of the upstream box to that of the downstream box,on the following three aspects of hydrodynamic characteristics of gap resonance:(1)the wave height amplifications inside the gap,and in front and at the rear of the structure system,(2)the reflection,transmission,and energy loss coefficients of the structure system,and(3)the response and damping time of the fluid resonance.It is found that the fluid resonant frequency,the amplification factor of the resonant wave height inside the gap and the maximum energy loss coefficient of the structure system are shown to gradually decrease with the increase of the breadth ratio.The response time of gap resonance is shown to first increase and then decrease with the breadth ratio overall,regardless of the incident wave height,and the configuration that the two boxes have the same breadth would bring the largest response time of gap resonance.

Equilibrium Control Theory and Direct Method of Feedback Linearization for Nonlinear Time Varying Systems

Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.

Resonance analysis of single DOF parameter-varying system of magnetic-liquid double suspension bearing

Magnetic-liquid double suspension bearing(MLDSB)is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting.Its bearing capacity and stiffness can be greatly improved,and then it is suitable for the occasions of medium speed,heavy load.When the bearing system is excited by periodic force,the flow q and current i regulated by the double-closed-loop control mechanism change periodically.Then the risk of parametric resonance in MLDSB is greatly aggravated by the change of the parameter system,which seriously affects its operation stabil-ity and reliability.Therefore,this paper intends to study the resonance characteristics of the parame-ter system of MLDSB.Firstly,Marshall-Duffing equation of the parametric system is established by taking the flow q and the current i as variables respectively.Then,by using the asymptotic method,the occurrence condition and variation rule of the principal,1/2 Harmonic and 1/3 Harmonic para-metric resonance are solved.The results show that only the 1/2 Harmonic resonance of the flow q parameter varying system occurs accompanied by the resonance condition of high frequency.The principal,1/2 Harmonic and 1/3 Harmonic parametric resonance of the current i occur accompanied by the resonance condition of high frequency.And the 1/2 Harmonic resonance of the current i oc-curs accompanied by the non-single value bifurcation and dynamic bifurcation.The paper can pro-vide theoretical reference for the parameter design and stable operation of MLDSB.

Time varying congestion pricing for multi-class and multi-mode transportation system with asymmetric cost functions

This paper considers the problem of time varying congestion pricing to determine optimal time-varying tolls at peak periods for a queuing network with the interactions between buses and private cars.Through the combined applications of the space-time expanded network（STEN） and the conventional network equilibrium modeling techniques,a multi-class,multi-mode and multi-criteria traffic network equilibrium model is developed.Travelers of different classes have distinctive value of times（VOTs）,and travelers from the same class perceive their travel disutility or generalized costs on a route according to different weights of travel time and travel costs.Moreover,the symmetric cost function model is extended to deal with the interactions between buses and private cars.It is found that there exists a uniform（anonymous） link toll pattern which can drive a multi-class,multi-mode and multi-criteria user equilibrium flow pattern to a system optimum when the system＇s objective function is measured in terms of money.It is also found that the marginal cost pricing models with a symmetric travel cost function do not reflect the interactions between traffic flows of different road sections,and the obtained congestion pricing toll is smaller than the real value.

IDENTIFICATION OF NONLINEAR TIME VARYING SYSTEM USING FEEDFORWARD NEURAL NETWORKS

As it is well known,it is difficult to identify a nonlinear time varying system using traditional identification approaches,especially under unknown nonlinear function.Neural networks have recently emerged as a successful tool in the area of identification and control of time invariant nonlinear systems.However,it is still difficult to apply them to complicated time varying system identification.In this paper we present a learning algorithm for identification of the nonlinear time varying system using feedforward neural networks.The main idea of this approach is that we regard the weights of the network as a state of a time varying system,then use a Kalman filter to estimate the state.Thus the network implements nonlinear and time varying mapping.We derived both the global and local learning algorithms.Simulation results demonstrate the effectiveness of this approach.

High-Order Models of Nonlinear and Dispersive Wave in Water of Varying Depth with Arbitrary Sloping Bottom

High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).

FM interference suppression for PRC-CW radar based on adaptive STFT and time-varying filtering

The influence of frequency modulation （FM） interfer- ence on correlation detection performance of the pseudo random code continuous wave （PRC-CW） radar is analyzed. It is found that the correlation output deteriorates greatly when the FM inter- ference power exceeds the anti-jamming limit of the radar. Accord- ing to the fact that the PRC-CW radar echo is a wideband pseudo random signal occupying the whole TF plane, while the FM in- terference only concentrates in a small portion, a new method is proposed based on adaptive short-time Fourier transform （STFT） and time-varying filtering for FM interference suppression. This method filters the received signal by using a binary mask to excise only the portion of the TF plane corrupted by the interference. Two types of interference, linear FM （LFM） and sinusoidal FM （SFM）, under different signal-to-jamming ratio （S JR） are studied. It is shown that the proposed method can effectively suppress the FM interference and improve the performance of target detection.

A Topological Magueijo-Smolin Varying Speed of Light Theory, the Accelerated Cosmic Expansion and the Dark Energy of Pure Gravity

The paper presents a detailed analysis of ordinary and dark energy density of the cosmos based on two different but complimentary theories. First, and starting from the concept of the speed of light being an average over multi-fractals, we use Magueijo-Smolin’s ingenious revision of Einstein’s special relativity famous formula E = mc2 to a doubly special formula which includes the Planck energy as invariant to derive the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) wheremis the mass andcis the speed of light. Second we use the topological theory of pure gravity to reach the same result thus confirming the correctness of the theory of varying speed of light as well as the COBE, WMAP and Type 1a supernova cosmological measurements.

Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thickness

Structural components of varying thickness draw increasing attention these days due to economy and light-weight considerations. In view of the absence of research in vibration analysis of viscoelastic plate with varying thickness, this study devotes to investigate the dynamic behaviors of axially moving viscoelastic plate with varying thickness. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate is derived, the plate constituted by Kelvin-Voigt model has linearly varying thickness in the y-direction. The dimensionless complex frequencies of axially moving viscoelastic plate with four edges simply supported are calculated by the differential quadrature method, curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies versus dimensionless moving speed are obtained, the effects of the aspect ratio, thickness ratio, the dimensionless moving speed and delay time on the dynamic behaviors of the axially moving viscoelastic rectangular plate with varying thickness are analyzed. When other parameters keep constant, with the decrease of thickness ratio, the real parts of the first three-order natural frequencies decrease, and the critical divergence speeds of various modes decrease too, moreover, whether the delay time is large or small, the frequencies are all complex numbers.

Approximation approach to the SRM based on root decomposition in the simulation of spatially varying ground motions

The spectral representation method （SRM） is widely used to simulate spatially varying ground motions. This study focuses on the approximation approach to the SRM based on root decomposition, which can improve the efficiency of the simulation. The accuracy of the approximation approach may be affected by three factors： matrix for decomposition, distribution of frequency interpolation nodes and elements for interpolation. The influence of these factors on the accuracy of this approach is examined and the following conclusions are drawn. The SRM based on the root decomposition of the lagged coherency matrix exhibits greater accuracy than the SRM based on the root decomposition of the cross spectral matrix. The equal energy distribution of frequency interpolation nodes proposed in this study is more effective than the counter pith with an equal spacing. Elements for interpolation do not have much of an effect on the accuracy, so interpolation of the elements of the decomposed matrix is recommended because it is less complicated from a computational efficiency perspective.

Roll shifting strategy with varying stroke and step in hot strip mill

A new roll shifting strategy with varying stroke and varying step was investigated,Two characteristic parameters including cat ear height and gap contour smoothness were introduced to assess the effect of shifting strategy on roll wear,and the relation between characteristic parameters and shifting strategy was established.Both varying stroke and varying step can reduce cat ear height and gap contour smoothness,so the shifting strategy with varying stroke and varying step is better than the one with either varying stroke or varying step,Based on the effect of shifting control parameters on characteristic parameters of roll wear,the selection principle of these shifting control parameters was gained.A case study was conducted to validate the proposed roll shifting strategy,reducing uncontrollable quartic loading gap contour,improving strip profile and extending rolling length of a rolling campaign.

Running safety assessment of a train traversing a three-tower cable-stayed bridge under spatially varying ground motion

To explore the influence of spatially varying ground motion on the dynamic behavior of a train passing through a three-tower cable-stayed bridge,a 3D train–track–bridge coupled model is established for accurately simulating the train–bridge interaction under earthquake excitation,which is made up of a vehicle model built by multi-body dynamics,a track–bridge finite element model,and a 3D rolling wheel–rail contact model.A conditional simulation method,which takes into consideration the wave passage effect,incoherence effect,and site-response effect,is adopted to simulate the spatially varying ground motion under different soil conditions.The multi-time-step method previously proposed by the authors is also adopted to improve computational efficiency.The dynamic responses of the train running on a three-tower cablestayed bridge are calculated with differing earthquake excitations and train speeds.The results indicate that(1)the earthquake excitation significantly increases the responses of the train–bridge system,but at a design speed,all the running safety indices meet the code requirements;(2)the incoherence and site-response effects should also be considered in the seismic analysis for long-span bridges though there is no fixed pattern for determining their influences;(3)different train speeds that vary the vibration characteristics of the train–bridge system affect the vibration frequencies of the car body and bridge.

Wave Loading on Concentric Porous Cylinders with Varying Porosity

Wave diffraction of two concentric porous cylinders with varying porosity was studied by using an analytical method based on eigenfunction matching.The fluid domain around the cylinders is divided into three sub-domains and in each sub-domain an eigenfunction expansion of the velocity potential is obtained by satisfying the Laplace equation,the boundary conditions on the free surface and on the sea bed.The unknown coefficients of eigenfunction expansions are determined by boundary conditions on the porous hulls.In the paper,the boundary conditions are based upon the assumption that the flow in the porous medium is governed by Darcy's law.Two porous-effect parameters applied on two porous cylinders are functions of the vertical coordinate instead of the constant.Wave loading on the outer and inner cylinder is presented in the numerical results.

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).

RIEMANN-HILBERT CHARACTERIZATION FOR MAIN BESSEL POLYNOMIALS WITH VARYING LARGE NEGATIVE PARAMETERS

In this article, we establish the Bessel polynomials with varying large negative parameters and discuss their orthogonality based on the generalized Bessel polynomials. By using the Riemann-Hilbert boundary value problem on the positive real axis, we get the Riemann-Hilbert characterization of the main Bessel polynomials with varying large negative parameters.

A Mooring System Deployment Design Methodology for Vessels at Varying Water Depths

In this paper,a methodology for designing mooring system deployment for vessels at varying water depths is proposed.The Non-dominated Sorting Genetic Algorithm-II(NSGA-II)is combined with a self-dependently developed vessel-mooring coupled program to find the optimal mooring system deployment considering both station-keeping requirements and the safety of the mooring system.Two case studies are presented to demonstrate the methodology by designing the mooring system deployments for a very large floating structure(VLFS)module and a semi-submersible platform respectively at three different water depths.It can be concluded from the obtained results that the mooring system can achieve a better station-keeping ability with relatively shorter mooring line when deployed in the shallow water.The safety factor of mooring line is mainly dominated by the maximum instantaneous tension increment in the shallow water,while the pre-tension has a decisive influence on the safety factor of the mooring line in the deep water.

Model Parameter Transfer for Gear Fault Diagnosis under Varying Working Conditions

Gear fault diagnosis technologies have received rapid development and been effectively implemented in many engineering applications.However,the various working conditions would degrade the diagnostic performance and make gear fault diagnosis(GFD)more and more challenging.In this paper,a novel model parameter transfer(NMPT)is proposed to boost the performance of GFD under varying working conditions.Based on the previous transfer strategy that controls empirical risk of source domain,this method further integrates the superiorities of multi-task learning with the idea of transfer learning(TL)to acquire transferable knowledge by minimizing the discrepancies of separating hyperplanes between one specific working condition(target domain)and another(source domain),and then transferring both commonality and specialty parameters over tasks to make use of source domain samples to assist target GFD task when sufficient labeled samples from target domain are unavailable.For NMPT implementation,insufficient target domain features and abundant source domain features with supervised information are fed into NMPT model to train a robust classifier for target GFD task.Related experiments prove that NMPT is expected to be a valuable technology to boost practical GFD performance under various working conditions.The proposed methods provides a transfer learning-based framework to handle the problem of insufficient training samples in target task caused by variable operation conditions.

Dynamic simulation of a flexible spinning vehicle with the periodic varying thrust

The dynamic response of a flexible spinning vehicle with the varying thrust was investigated. The varying thrust was modeled as a series of simple harmonic components superimposed on a constant thrust. The analytical solutions for longitudinal motion were obtained by combining the motion equations and boundary conditions, and then, the transverse bending of rocket was examined solved by considering a coupled forcing vibration with varying parameters. Numerical solutions for a rocket with end-varying thrust were studied. It is shown that the lateral vibrations and motion attitudes of rocket depend on the frequencies of varying thrust to great extent, and an important phenomenon, beating, maybe take place. The proposed approach is more accurate and efficient in comparison to those standard numerical techniques.