Stochastic Stability in a Model of Drilling

A random perturbation of a dynamical system serving as a model for the drilling process is studied. For this perturbation the existence of absolutely continuous stationary distributions is proved. It is shown that these distributions tend to a unique absolutely continuous invariant probability of the nonperturbed system as the magnitude of perturbation tends to zero.     

The dynamic response and perturbation of magnetic field vector of orthotropic cylinders under various shock loads

In this paper, an analytical method is introduced to solve the problem for the dynamic stress-focusing and centred-effect of perturbation of the magnetic field vector in orthotropic cylinders under thermal and mechanical shock loads. Analytical expressions for the dynamic stresses and the perturbation of the magnetic field vector are obtained by means of finite Hankel transforms and Laplace transforms. The response histories of dynamic stresses and the perturbation of the field vector are also obtained. In practical examples, the dynamic focusing effect on both magnetoelastic stress and perturbation of the axial magnetic field vector in an orthotropic cylinder subjected to various shock loads is presented and discussed.     

MAGNETOTHERMODYNAMIC STRESS AND PERTURBATION OF MAGNETIC FIELD VECTOR IN A SOLID CYLINDER

A theoretical method is presented to analyze magnetothermoelastic waves and perturbation of the magnetic field vector produced by thermal shock in a solid conducting cylinder. By means of finite integral transforms the exact expressions for magnetothermodynamic stress and perturbation response of an axial magnetic field vector in a solid cylinder were obtained. From sample numerical calculations the focusing effect on both magnetothermostress and perturbation of the axial magnetic field vector is revealed and is discussed.     

MAGNETOTHERMODYNAMIC STRESS AND PERTURBATION OF MAGNETIC FIELD VECTOR IN A HOLLOW CYLINDER

An analytical method is presented to investigate magnetothermoelastic waves and perturbation of the magnetic field vector produced by thermal shock in a hollow conducting cylinder. By means of finite integral transforms the exact expressions for magnetothermodynamic stress and perturbation response of an axial magnetic field vector in a hollow cylinder were obtained. From sample numerical calculations the dynamic effect on both magnetothermostress and perturbation of the axial magnetic field vector is revealed and is discussed.     

Modal re‐analysis of rotary wind turbine blades in refinement design

A modal re‐analysis approach is proposed for refinement designs of rotary wind turbine blades on the basis of matrix perturbation methods. The approach entails effects of stress stiffening, spin softening, uncertainty of material properties and structural modifications of blades. Three perturbation methods are used to conduct the re‐analysis approach, including the standard perturbation method and two improvements proposed by H. C. Hu and S. H. Chen, respectively. Numerical results of a typical wind turbine blade indicate that the two improved methods deliver better accuracy than the standard perturbation method in terms of eigenpairs. In application to blade designs, Chen's method is suitable for a multi‐step modal re‐analysis with explicit small parameters and cultivates the first‐order and second‐order perturbations of eigenpairs as well. In contrast, Hu's method is a better choice for a single‐step modal re‐analysis without determining any small parameter explicitly and directly offers approximate eigenpairs instead of somehow tedious perturbation processes. Copyright © 2012 John Wiley & Sons, Ltd.     

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The problem of imposing an in-line velocity perturbation on a uniform flow about a fixed cylinder is studied numerically. A finite volume method using SIMPLEC algorithm is applied on an O-type body-fitted co-located grid. The effect of frequency, amplitude, and shape of the velocity perturbation on the lift and drag coefficients and the Nusselt and Strouhal numbers were studied for the case of Reynolds number equal to 1000. It is noticed that lock-on is present and have a pronounced effect on the average Nusselt number, increasing it by 8.3 percent relative to the uniform flow value, though with a lower effect on drag and lift coefficients. In addition, it is concluded that a sinusoidal perturbation with a dimensionless frequency equal to 0.15 and dimensionless velocity perturbation equal to 0.2 is a better choice to enhance the heat transfer rate.     

Comparison of HAM and HPM solutions in heat radiation equations

In this paper it is proved that the perturbation and homotopy perturbation solutions for the two problems namely (i) unsteady convective–radiative equation and (ii) non-linear convective–radiative conduction equation are only valid for weak non-linearity. It is worth mentioning that homotopy perturbation method (HPM) does not provide exact and convergent solutions in most of the situations. Moreover, HPM have no criteria for establishing the convergence of the series solution. In the present study, it is shown and commented that the results in the two examples are valid only for small values of the parameters. The homotopy analysis method (HAM) is used in obtaining more meaningful and valid solutions.     

Perturbation solutions of planar diffusion-controlled moving-boundary problems

A new perturbation method is developed for the problems of solidification of liquid in a plane coordinate system. The method consists of (1) immobilizing the moving boundary by Landau's transformation, (2) replacing the time variable by the moving interface ${}_{\mathrm{f}}\text{(τ), (3)}$ applying the regular parameter perturbation technique. A quasi-steady state solution is shown to be the zero-order approximation. The perturbation solution for the planar solidification of a saturated liquid with constant wall temperature is shown to be identical with the exact solution. Comparison of the perturbation solutions for the solidification of a flowing warm liquid on a cooled flat plate with the experimental result of Siegel and Savino [8]is also given.     

基于神经网络的改进扰动观察法MPPT控制

为进一步提高光伏发电系统的输出效率和动态调节性能,设计基于神经网络的改进扰动观察法最大功率点跟踪(MPPT)控制.该方法在扰动观察法基础上引入神经网络算法,使得在环境剧烈变化时,系统动态调节速度加快.通过系统仿真和硬件实测,得出该改进扰动观察法相比于传统扰动观察法和神经网络法,在一定程度上能加快动态调节速度和减小稳态误...     

Perturbation estimation based robust state feedback control for grid connected DFIG wind energy conversion system

This paper develops a perturbation estimation based robust state feedback control (PER-SFC) scheme of doubly-fed induction generator (DFIG) for maximum power point tracking (MPPT). The combinatorial effect of nonlinearities originally stemmed from wind turbine aerodynamics, generator modelling uncertainties and wind speed randomness is aggregated as a perturbation, which is rapidly estimated online by a sliding-mode state and perturbation observer (SMSPO). Then, a linear state feedback controller is designed to fully compensate the perturbation estimate in real-time. Furthermore, only the measurement of rotor speed and reactive power is needed while no accurate DFIG model is required by the proposed approach. Under such framework, the elegant merits of conventional linear state feedback control (favourable implementation simplicity and high reliability) and nonlinear robust control (global control consistency and considerable robustness) can be wisely incorporated. Meanwhile, their inherent drawbacks could be significantly reduced. Case studies are undertaken which verify the effectiveness and superiority of PER-SFC compared to that of other classical methods.     

High-order perturbation solutions to a LH2 spreading model with continuous spill

High-order perturbation solutions have been obtained for the simple physical model describing the LH₂ spreading with a continuous spill, and are shown to improve over the first-order perturbation solutions. The non-dimensional governing equations for the model are derived to obtain more general solutions. Non-dimensional parameters are sought as the governing parameters for the non-dimensional equations, and the non-dimensional evaporation rate is used as the perturbation parameter. The results show that the second-order solutions exhibit an improvement over the first-order solutions with respect to the pool volume; however, there is still a difference between numerical solutions and second-order solutions in the late stage of spread. Finally, it is revealed that the third-order solutions almost agree with numerical solutions.     

混合流体对流中扰动的成长

通过流体力学扰动方程组的二维数值模拟,研究了混合流体Rayleigh-Benard对流运动中扰动的成长。发现扰动的线性阶段成长率是相对瑞利数r的函数。从线性阶段到非线性阶段的过渡存在三种斑图结构。     

Assessment of homotopy–perturbation and perturbation methods in heat radiation equations

One of the newest analytical methods to solve the nonlinear heat transfer equations is using both homotopy and perturbation methods in equations. Here, homotopy–perturbation method is applied to solve heat transfer problems with high nonlinearity order. The origin of using this method is the difficulties and limitations of perturbation or homotopy. It has been attempted to show the capabilities and wide-range applications of the homotopy–perturbation method in comparison with the previous ones in solving heat transfer problems. In this research, homotopy–perturbation method is used to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative conduction equation containing two small parameters of ε₁ and ε₂.     

Free Convective Flow of Electrically Conducting and Viscous Immiscible Fluid Flow in a Vertical Channel in the Presence of First‐Order Chemical Reaction

In this paper, the effects of chemical reaction on free convective flow of electrically conducting and viscous incompressible immiscible fluids are analyzed. The coupled nonlinear equations governing the heat and mass transfer are solved analytically and numerically with appropriate boundary conditions for each fluid and the solutions have been matched at the interface. The analytical solutions are solved by using regular perturbation method valid for small values of perturbation parameter and numerically by using finite difference method. The numerical results for various values of thermal Grashof number, mass Grashof number, Hartman number, viscosity ratio, width ratio, conductivity ratio, and chemical reaction parameter have been presented graphically in the presence and in the absence of electric field load parameter. In addition, the closed form expression for volumetric flow rate, Nusselt number, species concentration, and total heat rate added to the flow is also analyzed. The solutions obtained by finite difference method and perturbation method agree very well to the order of 10^?4 for small values of perturbation parameter.     

On Singularly Perturbed Partial Integro-Differential Equations with Irregular Singularity

We study exact asymptotic properties of solutions of singular, singularly perturbed partial integro-differential equations of irregular type in the complex domain in its perturbation parameter. A result on κ-summability is obtained for formal power series solutions of a given problem in the perturbation parameter.      

Magnetothermostress Wave Propagation and Perturbation of Magnetic Field Vector in an Orthotropic Laminated Hollow Cylinder

An analytical method is developed to determine the transient response of magneto-thermostress and perturbation of the magnetic field vector produced in orthotropic laminated hollow cylinders subjected to thermal shock, and permeated by a primarily uniform magnetic field. A magnetothermostress equation for each separate hollow cylinder is found by making use of a series of simply mathematical transform. Then, by using the interface continuity conditions between layers and the boundary conditions at the internal and external surfaces of the orthotropic laminated hollow cylinders, the unknown constants involved are determined. Thus, an exact expression for the magnetothermostress wave propagation and the perturbation response of magnetic field vector in the orthotropic laminated hollow cylinders are obtained. From sample numerical calculations, some characters of magnetothermodynamic stresses and perturbation of magnetic field vector in orthotropic laminated hollow cylinders are revealed and discussed.     

Unsteady flow of an incompressible fluid in a horizontal porous medium with suction

A theoretical analysis of two-dimensional unsteady flow in a porous medium bounded by a horizontal wall is presented as a perturbation on a basic flow. It is assumed that the perturbation is occasioned by a sudden suction at the wall. Even for a highly permeable medium, the characteristic Reynolds number in porous media flow is usually small and asymptotic solutions are developed by the Laplace transform technique. It is observed that the perturbed shear stress at the wall decays exponentially with time.     

Laminar-to-turbulent transition in supersonic boundary layer: Effects of initial perturbation and wall heat transfer

Direct numerical simulations of supersonic boundary layers (SBLs) over a flat plate for M_∞=2.2 are performed for adiabatic and isothermal (cooled and heated) walls. Receptivity analysis based on five criteria, namely skin-friction coefficient, Stanton number, Reynolds shear stress, wall-normal Reynolds heat flux, and modal decomposition are performed. Effect of perturbation intensity and wall heat transfer on the receptivity and the transitional growth of SBLs are presented. It is found out that increasing perturbation intensity moves the transition onset location upstream and increases the transition length. Additionally, below 1% perturbation intensity, wall cooling stabilizes the flow while beyond this value it has the opposite effect.     

结构行波功率流检测机理研究

研究了基于差分方法检测扰动功率流的可行性，研究结果表明用密布的速度、加速度传感器和相应的检测电路就可以检测出结构某点的扰动功率流的数值，为机械振动控制提供了一种新方法。     

Stabilizing controls for a doubly fed synchronous-induction machine

The stability of a doubly-fed synchronous-induction machine is investigated through small as well as large perturbation models. Two stabilizing control strategies have been proposed for the small perturbation bilinear model. The first is based on quadratic bilinear regulator theory, and the second provides a suboptimal control based on minimization of time. The responses are compared with the uncontrolled ones as well as those with conventional linear regulator control. While both the proposed strategies stabilize the system, the minimum-time suboptimal control is found to be superior