Improved Perturbation Method Research Articles

Modeling the deterioration of the stiffness and of the collagen fibril distribution in a discrete model of the cornea microstructure

We present a stochastic approach to model the mechanical deterioration of the reinforcing microstructure of the human cornea. The fundamental structural micro-components of the stroma, collagen and crosslinks, are assembled deterministically into an elementary trusswork cell, multiply repeated and distorted to form a three-dimensional shell with the shape of a cornea. The spatial orientation of the collagen-like elements of each cell is thus characterized stochastically with a non correlated random angle field, obeying an assigned probability density function, leading to a non-deterministic structural stiffness. It follows that the mechanical response of the model to the action of deterministic forces equivalent to the intraocular pressure is stochastic due to the random spatial orientation of collagen fibers. The deterioration of the mechanical stiffness of the collagen components is described through a scalar variable field, evolving in space and in time, representative of a progressive damage which causes heterogeneity and asymmetric behavior. The damage variable acts in two ways on the global stiffness: (i) by reducing the stiffness of the collagen components; (ii) by modifying the dispersion coefficient of the probability density function. The equilibrium equations of the damaging model are solved at discrete time steps, with a fully explicit solution scheme, by means of the stochastic finite element improved perturbation method. The results show that when the collagen fibril stiffness reduces to 10% of the healthy value, as expected in the case of the vision-impairing condition known as keratoconus, the displacement field due to intraocular pressure is significantly affected in terms of both average and variance distributions. This effect confers a typical conical shape to the cornea. In particular, the analysis shows that high values of the response variances are confined in the keratoconus area, which agrees with a high level of uncertainties due to loss of fibril organization and thickness reduction under pathologic conditions.

Research on Sub-Synchronous-Oscillation Energy Analysis and Traceability Method Based on Refined Energy

At present, most studies use the direct method to analyze the oscillation problem of modern power systems. However, these studies often only simplify the external characteristics of the wind turbine and lack an in-depth understanding of its internal refined energy structure. In this paper, based on the direct-drive permanent magnetic synchronous generator’s detailed model (D-PMSG), combined with the dynamic energy of its port, layers of analysis are performed on the wind turbine’s internal connections, and a detailed model of the energy structure is created. Then, the interaction mechanism of each control link in the wind turbine is analyzed by combining the energy function of the wind turbine with the improved perturbation method. Finally, this paper constructs a sub-synchronous oscillation (SSO) scenario of weak damping and a forcing type and proves the accuracy and effectiveness of the traceability method based on the refined energy of D-PMSG. This traceability method based on refined energy is expected to provide a new solution to the stability problem caused by the integration of new energy.

A numerical model of the human cornea accounting for the fiber-distributed collagen microstructure

We present a fiber-distributed model of the reinforcing collagen of the human cornea. The model describes the basic connections between the components of the tissue by defining an elementary block (cell) and upscaling it to the physical size of the cornea. The cell is defined by two sets of collagen fibrils running in approximately orthogonal directions, characterized by a random distribution of the spatial orientation and connected by chemical bonds of two kinds. The bonds of the first kind describe the lamellar crosslinks, forming the ribbon-like lamellae; while the bonds of the second kind describe the stacking crosslinks, piling up the lamellae to form the structure of the stroma. The spatial replication of the cell produces a truss structure with a considerable number of degrees of freedom. The statistical characterization of the collagen fibrils leads to a mechanical model that reacts to the action of the deterministic intraocular pressure with a stochastic distribution of the displacements, here characterized by their mean value and variance. The strategy to address the solution of the heavy resulting numerical problem is to use the so-called stochastic finite element improved perturbation method combined with a fully explicit solver. The results demonstrate that the variability of the mechanical properties affects in a non-negligible manner the expected response of the structure to the physiological action.

Physical Formation Mechanisms of the Southwest China Vortex

On the basis of the Prandtl boundary layer theory and an improved perturbation method, the process of laminar flow bifurcating into the Southwest China vortex (SWV) in the Hengduan Mountains is studied. The results show that the formation of SWV is mainly determined by the speed of incoming airflow in the direction of the main axis of the Hengduan Mountains. The vortex is generated in the leeward area of the Hengduan Mountains when the speed of incoming airflow is greater than the critical velocity. Moreover, it means that the laminar flow bifurcates into a vortex. The formation position of the SWV is mainly determined by the relative position of the incoming airflow in the windward area of the Hengduan Mountains and the main axis of the Hengduan Mountains. The seasonal distribution of SWVs is determined by both the velocity of the incoming airflow and the relative position of the incoming airflow to the main axis of the Hengduan Mountains. These findings are consistent with the SWV observation facts, which not only adequately explain the physical formation mechanisms and processes of SWVs, but also present the formation location and seasonal distribution of SWVs. Meanwhile, a solution from laminar to vortex in circumflow motion is also presented.

Design and analysis of a three-dimensional discrete memristive chaotic map with infinitely wide parameter range

In this paper, a new discrete memristive chaotic map with infinitely wide parameter range is designed. Firstly, a discrete memristor based on a triangular wave function is constructed. The memristor conforms to the definition of generalized memristor, and a new three-dimensional memristive chaotic map is designed based on it. Numerical simulations show that the map has complex dynamic behavior. An improved perturbation method is proposed to estimate the output sequence of the chaotic system. At the same time, it is proved mathematically that the new map can always be in chaotic or hyperchaotic state with infinitely wide parameter range under certain conditions. By observing the Lyapunov exponent spectrum and the phase diagram, it is found as the absolute value of the parameter increases, the output range and ergodicity of the new map are also enhanced. We demonstrate that the new map has an initial-boosting behavior that depends on the initial conditions of the memristor. By changing the initial values of the memristor, we can control the appearance of attractor at different locations without loss. At the same time, this paper analyzes the mechanism of the discrete memristive chaotic map generating initial-boosting behavior, puts forward a method to make ordinary chaotic maps easier to obtain this behavior. Finally, the DSP hardware platform is used to implement the new map, which proves the physical existence and realizability of the map.

A novel perturbation method to reduce the dynamical degradation of digital chaotic maps

A chaotic map, which is realized on finite precision device, such as computer, will suffer dynamical degradation. Such chaotic maps cannot be regarded as rigorous chaos anymore, since their chaotic characteristics are degraded, and naturally, these kinds of chaotic maps are not secure enough for cryptographic use. Therefore, in this paper, a novel perturbation method is proposed to reduce the dynamical degradation of digital chaotic maps. Once the state is repeated during the iteration, the parameter and state are both perturbed to make the state jump out from a cycle. This method is convenient to implement without any external sources and can be used for different kinds of digital chaotic maps. The most widely used logistic map is used as an example to prove the effectiveness of this method. Several numerical experiments are provided to prove the effectiveness of this method. Under the same precision, the number of iterations when entering a cycle and the period of the improved map are greater than those of the original one. The complexity analysis shows that the improved map can get an ideal complexity level under a lower precision. All these results prove that this perturbed method can greatly improve the dynamical characteristics of original chaotic map and is competitive with other remedies. Furthermore, we improve this method by using a variable perturbation, where the perturbation is affected according to the number of iteration steps. Numerical experiments further prove that this improved perturbation method has a better performance in suppressing dynamical degradation.

Study of Autonomous Conservative Oscillator Using an Improved Perturbation Method

In a recent article \cite{manimegalai2019}, Aboodh transform based homotopy perturbation method ($AT$) has been found to produce approximate analytical solutions in a simple way but with better accuracy in comparison to those obtained from some of the established approximation methods \cite{mehdipour2010application,nofal2013analytical} for some physically relevant anharmonic oscillators such as autonomous conservative oscillator (ACO). In the present article, expansion of frequency ($\omega$) and an auxiliary parameter ($h$) are incorporated in the framework of the homotopy perturbation method (HPM) to improve the accuracy by retaining its simplicity. Laplace transform is used to make the calculation simpler. This improved HPM ($LH$) is simple but provides highly accurate results for ACO in comparison to those obtained from $AT$. The error in the values of frequency and displacement calculated using the $LH$ is found to be one or two order of magnitude less than those obtained from $AT$ for the considered parameter sets.

Static analysis of a circular nanotube made of functionally graded bi-semi-tubes using nonlocal strain gradient theory and a refined shear model

We in this article put forward a novel size-dependent beam model for static bending deformation of a functionally graded bi-semi-tube subjected to different boundary conditions based on the nonlocal strain gradient theory. The tube is formed by bonding together a ZrO2/Ti–6Al–4V functionally graded lower semi-tube and a Si3N4/SUS304 functionally graded upper one. The effective material properties Pf of FG bi-semi-tubes are assumed to vary along the radius of tube. We propose a refined shear model without requiring a shear correction factor for bars with circular cross section. Next the model is used to derive the governing equations of the tube based on the Hamilton's principle. The obtained equations form present a detailed analysis include a nonlocal parameter as well as a material length scale parameter, so much that they can account for the size-dependent in static bending of FG bi-semi-tubes. Later, these equations are resolved analytically by using an improved perturbation method. The analytical solutions are used to discuss the influence of various physical parameters on static mechanical performance of nanotubes, such as double volume fraction indexes, inner radius, the variation of temperature, strain gradient parameter, nonlocal parameter, scale parameter ratio. At last, compared with the conventional approaches, the novel approach is suggested in such work to lead to more accurate bending deformation in the same dimensionless size of tubes.

Parallel and Perpendicular Diffusion Coefficients of Energetic Charged Particles with Adiabatic Focusing

Abstract It is very important to understand stochastic diffusion of energetic charged particles in the nonuniform background magnetic field in plasmas of astrophysics and fusion devices. Using different methods considering an along-field adiabatic focusing effect, various authors derived a parallel diffusion coefficient and its correction T to , where is the parallel diffusion coefficient without an adiabatic focusing effect. In this paper, using the improved perturbation method developed by He & Schlickeiser and iteration process, we obtain a new correction to . Furthermore, by employing the isotropic pitch-angle scattering model , we find that has a different sign from that of T. In this paper, the spatial perpendicular diffusion coefficient with the adiabatic focusing effect is also obtained.

Optimal Income Taxation with Composition Effects

Providing estimable sufficient statistics to give policy prescriptions has become a widespread approach over the recent years. A well-known limitation of this approach is the endogeneity of sufficient statistics to the policy. In this paper, using optimal tax policy as our field of application, we highlight a new source of endogeneity. It arises since, under multidimensional heterogeneity, optimal tax formulas are expressed as a function of weighted means of sufficient statistics computed at the individual level and the weights are endogenous to tax policy. We analytically show that ignoring these composition effects leads to underestimate the optimal linear tax and, under a restrictive set of assumptions, the optimal nonlinear tax as well. To relax these assumptions, we use an improved tax perturbation approach to study composition effects in the latter case. Our numerical simulations using U.S. data suggest the optimal tax rate may be underestimated by 6 percentage points for high incomes levels. As a secondary result, we show the equivalence between our improved tax perturbation method and the first order mechanism design method, two methods which have hitherto been used separately to derive optimal tax schedules.

Intelligent Photovoltaic Systems by Combining the Improved Perturbation Method of Observation and Sun Location Tracking.

Currently, tracking in photovoltaic (PV) systems suffers from some problems such as high energy consumption, poor anti-interference performance, and large tracking errors. This paper presents a solar PV tracking system on the basis of an improved perturbation and observation method, which maximizes photoelectric conversion efficiency. According to the projection principle, we design a sensor module with a light-intensity-detection module for environmental light-intensity measurement. The effect of environmental factors on the system operation is reduced, and intelligent identification of the weather is realized. This system adopts the discrete-type tracking method to reduce power consumption. A mechanical structure with a level-pitch double-degree-of-freedom is designed, and attitude correction is performed by closed-loop control. A worm-and-gear mechanism is added, and the reliability, stability, and precision of the system are improved. Finally, the perturbation and observation method designed and improved by this study was tested by simulated experiments. The experiments verified that the photoelectric sensor resolution can reach 0.344°, the tracking error is less than 2.5°, the largest improvement in the charge efficiency can reach 44.5%, and the system steadily and reliably works.

A class of asymptotic solution for the time delay wind field model of an ocean

A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturbation method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-latitude wind field, and the physical meaning of the corresponding solution is also discussed.

Perturbation Analysis for a New Omni-Directional Antenna Consisted of Circular Rod Corrugations Gloved with a DNG Shell

A new omni-directional leaky-wave antenna is proposed in the paper, which is consisted of circular rod corrugations gloved with a Double-negative (DNG) shell. The leaky characteristics of the new antenna are analyzed by improved perturbation method. The electromagnetic fields are described in terms of a radial transmission-line network, which tremendously simplifies the analysis procedure with good calculation accuracy and brings considerable physical insight into the overall behavior of the dielectric grating antenna. The case where the n = −1 space harmonic of TE01 mode radiating into the space is carefully investigated, it is demonstrated that the gloved cylindrical DNG shell greatly enhances the leaky strength of the antenna. As a result, the dimension of the antenna could be largely reduced keeping the radiation efficiency unchanged, which is of practical significance for some applications.

An improved perturbation method for stochastic finite element model updating

AbstractIn this paper, an improved perturbation method is developed for the statistical identification of structural parameters by using the measured modal parameters with randomness. On the basis of the first‐order perturbation method and sensitivity‐based finite element (FE) model updating, two recursive systems of equations are derived for estimating the first two moments of random structural parameters from the statistics of the measured modal parameters. Regularization technique is introduced to alleviate the ill‐conditioning in solving the equations. The numerical studies of stochastic FE model updating of a truss bridge are presented to verify the improved perturbation method under three different types of uncertainties, namely natural randomness, measurement noise, and the combination of the two. The results obtained using the perturbation method are in good agreement with, although less accurate than, those obtained using the Monte Carlo simulation (MCS) method. It is also revealed that neglecting the correlation of the measured modal parameters may result in an unreliable estimation of the covariance matrix of updating parameters. The statistically updated FE model enables structural design and analysis, damage detection, condition assessment, and evaluation in the framework of probability and statistics. Copyright © 2007 John Wiley & Sons, Ltd.

Improved perturbation method and its application to the IIB matrix model

We present a new scheme for extracting approximate values in “the improved perturbation method”, which is a sort of resummation technique capable of evaluating a series outside the radius of convergence. We employ the distribution profile of the series that is weighted by nth-order derivatives with respect to the artificially introduced parameters. By those weightings the distribution becomes more sensitive to the “plateau” structure in which the consistency condition of the method is satisfied. The scheme works effectively even in such cases that the system involves many parameters. We also propose that this scheme has to be applied to each observable separately and be analyzed comprehensively. We apply this scheme to the analysis of the IIB matrix model by the improved perturbation method obtained up to eighth order of perturbation in the former works. We consider here the possibility of spontaneous breakdown of Lorentz symmetry, and evaluate the free energy and the anisotropy of space–time extent. In the present analysis, we find an SO ( 10 ) -symmetric vacuum besides the SO ( 4 ) - and SO ( 7 ) -symmetric vacua that have been observed. It is also found that there are two distinct SO ( 4 ) -symmetric vacua that have almost the same value of free energy but the extent of space–time is different. From the approximate values of free energy, we conclude that the SO ( 4 ) -symmetric vacua are most preferred among those three types of vacua.

An Improved Perturbation Analysis of a New Omnidirectional Circular Rod Antenna with Double Dielectric Gratings for Millimeterwave Application

The leakage characteristics of a new millimeter-wave omnidirectional circular rod antenna with double dielectric gratings are analyzed by an improved perturbation method. The electromagnetic fields are described in terms of a radial transmission-line network, which brings considerable physical insight into the overall behaviour of the leaky wave antenna. The analysis yields expression for the leakage constant in a closed form so that the design procedure of the antenna becomes very convenient. It is found that under the condition of the same radiation intensity, the double dielectric-grating antenna has relatively smaller dimension than that of the single one. The results obtained by the present analysis are compared with the exact solution based on the mode matching method; it is found that the improved perturbation analysis yields as accurate results as the rigorous method with extreme simplicity of the analysis and calculations.

Improved perturbation analysis of a new omnidirectional circular rod antenna with multi dielectric gratings for millimeter‐wave application

AbstractThe leakage characteristics of a new millimeter‐wave omnidirectional circular rod antenna with multi‐dielectric gratings are analyzed by an improved perturbation method. The analysis yields an expression for the leakage constant in a closed form so that the design procedure of the antenna becomes very convenient. It is found that under conditions of the same dimension of the antenna, the multi‐layer grating antenna has more radiation efficiency than that of the single one. Its accuracy has been verified with the exact solution based on the mode matching method. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 53–55, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10668

Dynamic response of a rectangular beam with a known non-propagating crack of certain or uncertain depth

In this paper the deterministic behaviour of a beam with a transverse on edge non-propagating crack is first studied. Moreover the stochastic setting pertaining the case in which the crack has an uncertain depth is investigated. The beam is discretized by finite elements in which a so-called closing crack model, with fully open or fully closed crack, is used to describe the damaged element. Once the mathematical model of the beam is defined, the dynamic response is evaluated by applying a numerical procedure based on the philosophy of structural systems with dynamic modification. In the stochastic case the improved perturbation method is modified in order to solve efficiently the stochastic non-linear differential equations.

Improved perturbation analysis for a new omnidirectional periodic dielectric rod leaky‐wave antenna for millimeter‐wave application

AbstractThe leakage characteristics of a new millimeter wave omnidirectional periodic circular dielectric rod leaky‐wave antenna are analyzed by an improved perturbation method. The electromagnetic fields are described in terms of a radial transmission‐line network, which brings considerable physical insight into the overall behavior of the leaky‐wave antenna. The analysis yields expression for the leakage constant in a closed form so that the design procedure of the antenna becomes very convenient. It was found that the circular dielectric shell layer greatly affects the leaky characteristics of the antenna. The results obtained by the present analysis are compared with the exact solution based on the mode‐matching method. It is justified that the improved perturbation procedure yields as accurate results as the rigorous method, with extreme simplicity of the analysis and calculations. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 344–346, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10316

Static and Dynamic Analysis of Non-Linear Uncertain Structures

The procedures usually adopted in the evaluation of the stochastic response of structures with uncertain parameters, the so-called stochastic structures, are affected by some limits. Namely, the major drawbacks are: the conspicuous computational time required for the analysis of many degree of freedom systems and the loss of accuracy in the case of large uncertainty in the parameters. A method able to reduce the previous inconveniences was recently introduced in the study of statically loaded linear structures. The method, named improved perturbation method, was also extended to the field of linear dynamics. In both cases, the improved perturbation method provides a good approximation, even in the case of moderately large deviation of the uncertain parameters, and the computational time required is comparable to conventional first order perturbation. The present paper intends to apply the improved perturbation method in the second order analysis of geometrically non-linear uncertain systems subjected to static and dynamic deterministic forces.