A Preisach-based hysteresis model for magnetic and ferroelectric hysteresis

In this paper we present a model for hysteretic nonlinearities with non-local memories. This model can be applied to describe hysteretic material behavior. Common applications are ferromagnetic or ferroelectric materials. Our model consists of an analytic function and a Preisach operator. We define a continuous Preisach weight function and introduce a method for the identification of the model parameters. The model parameters are customized to a set of symmetric hysteresis curves. We verify our model for a soft magnetic material, a hard magnetic material and the ferroelectric behavior of some piezoelectric material. After that, non-symmetric curves like the virgin curve are predicted very well by the model. It is especially useful, if forced magnetization or polarization, that appears beyond technical saturation, come into account.     

Stochastic joint time–frequency response analysis of nonlinear structural systems

A novel approximate analytical approach for determining the response evolutionary power spectrum (EPS) of nonlinear/hysteretic structural systems subject to stochastic excitation is developed. Specifically, relying on the theory of locally stationary processes and utilizing a recently proposed representation of non-stationary stochastic processes via wavelets, a versatile formula for determining the nonlinear system response EPS is derived; this is done in conjunction with a stochastic averaging treatment of the problem and by resorting to the orthogonality properties of harmonic wavelets. Further, the nonlinear system non-stationary response amplitude probability density function (PDF), which is required as input for the developed approach, is determined either by utilizing a numerical path integral scheme, or by employing a time-dependent Rayleigh PDF approximation technique. A significant advantage of the approach relates to the fact that it is readily applicable for treating not only separable but non-separable in time and frequency EPS as well. The hardening Duffing and the versatile Preisach (hysteretic) oscillators are considered in the numerical examples section. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the approach.     

Hysteresis-induced long-time tails

It is shown analytically that the output of the standard model for complex, nonlocal hysteresis, the Preisach model, exhibits long-time tails under quite general conditions. For uncorrelated input signals the exponent of the algebraic output correlation decay is determined solely by the tails of the input and the Preisach density. Correspondingly we identify universality classes leading to identical algebraic tails. These results predict the occurrence of 1/f noise for a large class of hysteretic systems.     

Nonlinear dynamics of complex hysteretic systems: Oscillator in a magnetic field

Complex hysteresis is a well-known phenomenon in many branches of science. The most prominent examples come from materials with a complex microscopic structure such as magnetic materials, shape-memory alloys, or, porous materials. Their hysteretic behavior is characterized by the existence of multiple internal system states for a given external parameter and by a non-local memory. The input-output behavior of such systems is well studied and in a standard phenomenological approach described by the so-called Preisach operator. What is not well understood, are situations, where such a hysteretic system is dynamically coupled to its environment. Since the hysteretic sub-system provides a complicated form of nonlinearity, one expects non-trivial, possibly chaotic behavior of the combined dynamical system. We study such a combined dynamical system with hysteretic nonlinearity. In this original contribution a simple differential-operator equation with hysteretic damping, which describes a magnetic pendulum is considered. We find, for instance, a fractal dependence of the asymptotic behavior as function of the starting values. The sensitivity of the system to perturbations is investigated by several methods, such as the 0–1 test for chaos and sub-Lyapunov exponents. The power spectral density is also calculated and compared with analytical results for simple input-output scenarios.     

On the response and dissipated energy of Bouc–Wen hysteretic model

An efficient formulation for the response and dissipated energy of Bouc–Wen hysteretic model is proposed. The displacement is associated with the hysteretic parameter in terms of Gauss’ hypergeometric function. The hysteretic equation is solved analytically for specific values of the exponential parameter that controls the transition between elastic and inelastic regime. This formulation is used to provide analytical expressions of the dissipated energy under symmetric cyclic excitation, based solely on the model parameters and the displacement amplitude. For arbitrary values of the exponential parameter, the equations are solved numerically. For fully yielding systems, approximate relations are determined using suitable curve fitting. The derived expressions facilitate considerably the preliminary design of hysteretic systems.     

Study of MPI based on parallel MOM on PC clusters for EM-beam scattering by 2-D PEC rough surfaces

This paper firstly applies the finite impulse response filter (FIR) theory combined with the fast Fourier transform (FFT) method to generate two-dimensional Gaussian rough surface. Using the electric field integral equation (EFIE), it introduces the method of moment (MOM) with RWG vector basis function and Galerkin's method to investigate the electromagnetic beam scattering by a two-dimensional PEC Gaussian rough surface on personal computer (PC) clusters. The details of the parallel conjugate gradient method (CGM) for solving the matrix equation are also presented and the numerical simulations are obtained through the message passing interface (MPI) platform on the PC clusters. It finds significantly that the parallel MOM supplies a novel technique for solving a two-dimensional rough surface electromagnetic-scattering problem. The influences of the root-mean-square height, the correlation length and the polarization on the beam scattering characteristics by two-dimensional PEC Gaussian rough surfaces are finally discussed.     

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.     

The stochastic collocation method for radiation transport in random media

Stochastic spectral expansions are used to represent random input parameters and the random unknown solution to describe radiation transport in random media. The total macroscopic cross section is taken to be a spatially continuous log-normal random process with known covariance function and expressed as a memoryless transformation of a Gaussian random process. The Karhunen-Loève expansion is applied to represent the spatially continuous random cross section in terms of a finite number of discrete Gaussian random variables. The angular flux is then expanded in terms of Hermite polynomials and, using a quadrature-based stochastic collocation method, the expansion coefficients are shown to satisfy uncoupled deterministic transport equations. Sparse grid Gauss quadrature rules are investigated to establish the efficacy of the polynomial chaos-collocation scheme. Numerical results for the mean and standard deviation of the scalar flux as well as probability density functions of the scalar flux and transmission function are obtained for a deterministic incident source, contrasting between absorbing and diffusive media.     

Heat conduction in a random medium

The method of time-ordered cumulants is used to investigate the behavior of heat pulses in a one-dimensional medium in which the thermal conductivity is random. A partial differential equation is obtained for the average temperature profile; it is the heat equation modified by the addition of a fourth-order spatial derivative. A solution is obtained by asymptotic series. The first two spatial moments of the average temperature profile are evaluated and are shown to tend to those of a Gaussian whent is large. Finally, an equation is obtained for the covariance function.Alfred P. Sloan Fellow.     

基于高斯过程的混沌时间序列单步与多步预测

针对混沌时间序列单步和多步预测,提出基于复合协方差函数的高斯过程 (GP)模型方法.GP模型的确立由协方差函数决定,通过对训练数据集的学习,在证据最大化框架内,利用矩阵运算和优化算法自适应地确定协方差函数和均值函数中的超参数.GP模型与神经网络、模糊模型相比,其可调整参数很少.将不同复合协方差函数的GP模型应用在混沌时间序列单步及多步提前预测中,并与单一协方差函数的GP、支持向量机、最小二乘支持向量机、径向基函数神经网络等方法进行了比较.仿真结果表明,基于不同复合协方差函数的GP方法能精确地预测混沌时间序 关键词： 高斯过程 混沌时间序列 预测 模型比较     

Thermo-magnetic history effects in the giant magnetostriction across the first-order transition and minor hysteresis loops modeling in Fe0.955Ni0.045Rh alloy

Results of temperature- and magnetic field-dependent strain measurements across the first-order antiferromagnetic to ferromagnetic phase transition in Fe(0.955)Ni(0.045)Rh are presented. Distinct thermal and magnetic field hystereses are observed in the measured strain across the phase transition. The minor hysteresis loops inside the hysteretic regime across the temperature-driven transition are modeled using the Preisach model of hysteresis. The applicability of the Preisach model to explain the general features of minor hysteresis loops is discussed for a disorder influenced first-order transition. The minor hysteresis loops show the property of retaining the memory of the starting or end point of the temperature cycle followed within the hysteretic region. A larger temperature excursion within the hysteretic region wipes out the memory of a smaller temperature cycle which contains one of the extrema of the larger cycle. The end-point memory and the wiping-out property of the minor hysteresis loops can be described quite well within the Preisach model, irrespective of the temperature history followed to reach a particular starting point. Thermo-magnetic history effects across the magnetic field-induced transition are explained, which will enable the choice of the starting point of an experimental cycle in the field-temperature phase space so as to achieve the desired functionality. Our results highlight the necessity to understand the influence of disorder on a first-order phase transition so as to achieve a repeatable performance of materials whose functionalities are based on such a transition.     

Modelling of creep hysteresis in ferroelectrics

In the current paper, a macroscopic model is proposed to simulate the hysteretic dynamics of ferroelectric ceramics with creep phenomenon incorporated. The creep phenomenon in the hysteretic dynamics is attributed to the rate-dependent characteristic of the polarisation switching processes induced in the materials. A non-convex Helmholtz free energy based on Landau theory is proposed to model the switching dynamics. The governing equation of single-crystal model is formulated by applying the Euler–Lagrange equation. The polycrystalline model is obtained by combining the single crystal dynamics with a density function which is constructed to model the weighted contributions of different grains with different principle axis orientations. In addition, numerical simulations of hysteretic dynamics with creep phenomenon are presented. Comparison of the numerical results and their experimental counterparts is also presented. It is shown that the creep phenomenon is captured precisely, validating the capability of the proposed model in a range of its potential applications.     

Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface

A current based hybrid method (HM) is proposed which combines the method of moment (MOM) with the Kirchhoff approximation (KA) for the analysis of scattering interaction between a two-dimensional (2D) infinitely long conducting target with arbitrary cross section and a one-dimensional (1D) Gaussian rough surface. The electromagnetic scattering region in the HM is split into KA region and MOM region. The electric field integral equation (EFIE) in MOM region (target) is derived, the computational time of the HM depends mainly on the number of unknowns of the target. The bistatic scattering coefficient for the infinitely long cylinder above the rough surface with Gaussian roughness spectrum is calculated, and the numerical results are compared and verified with those obtained by the conventional MOM, which shows the high efficiency of the HM. Finally, the influence of the size, location of the target, the rms height and correlation length of the rough surface on the bistatic scattering coefficient with different polarizations is discussed in detail.     

Down-mixing of multi-channel audio for sound field reproduction based on spatial covariance

This article describes a method for automatic down-mixing multi-channel audio content on the basis of spatial covariance. Such a down-mixing method should be able to convert the signal of the original multi-channel audio system into that for an alternative system with the lesser number of channels, while maintaining the spatial impression of sound. Moreover, it should take into account the listener’s position and transfer function. Wave surface control and convolving the head related transfer function are techniques used in sound field control or reproduction. We consider that the spatial impressions of a sound field, which we perceive through our ears, are reproduced by preserving the relative relationship between observation points even if the wave surface is not completely controlled. Takahashi et al. proposed a new sound field reproduction method that we named “SOund field Reproduction based on sPAtial Covariance” (SORPAC). SORPAC can control the point-to-point covariance in a sound field. We expect that this sound field reproduction method based on spatial covariance can be applied to down-mixing of multi-channel content because SORPAC does not require the listener’s position or transfer function. This article describes SORPAC and its characteristics. We used SORPAC for down-mixing audio content. We confirmed that SORPAC-based down-mixing could accurately reproduce the interaural cross correlation (IACC) in relation to the listener’s position.     

相关变量随机数序列产生方法

当采用蒙特卡罗方法对很多问题进行研究时,有时需要对多维相关随机变量进行抽样.之前的研究表明:在协方差矩阵满足正定条件时,可以采用Cholesky分解方法产生多维相关随机变量.本文首先对产生多维相关随机变量的理论公式进行了推导,发现采用Cholesky分解并不是产生多维相关随机变量的唯一方法,其他的矩阵分解方法只要能满足协方差矩阵的分解条件,同样可以用来产生多维相关随机变量.同时给出了采用协方差矩阵、相对协方差矩阵和相关系数矩阵产生多维随机变量的公式,以方便以后使用.在此基础上,利用一个简单测试题和Jacobi矩阵分解方法对上述理论进行了验证.通过对大亚湾中微子能谱进行抽样分析,Jacobi矩阵分解和Cholesky矩阵分解结果一致.针对核工程中的不确定性分析常用的~(238)U辐射俘获截面协方差矩阵进行分解时,由于协方差矩阵的矩阵本征值有负值,导致很多矩阵分解方法无法使用,在引入置零修正以后发现,与Cholesky对角线置零修正相比,Jacobi负本征值置零修正的误差更小.     

Stochastic response of vibro-impact Duffing oscillators under external and parametric Gaussian white noises

This study presents a solution procedure for the stationary probability density function (PDF) of the response of vibro-impact Duffing oscillators under external and parametric Gaussian white noises. First the Zhuravlev non-smooth coordinate transformation is adopted to convert a vibro-impact oscillator into an oscillator without barriers. The stationary PDF of the converted oscillator is governed by the Fokker–Planck (FP) equation. The FP equation is solved by the exponential-polynomial closure (EPC) method. Illustrative examples are presented with vibro-impact Duffing oscillators under external and parametric Gaussian white noises to show the effectiveness of the solution procedure. The parametric excitation is acting in displacement and the constraint is a unilateral zero-offset barrier. The restitution coefficient of impacts is taken as 0.90. Comparison with the simulated results shows that the proposed solution procedure can provide good approximate PDFs for displacement and velocity although a little difference exists in the tail of these PDFs. This difference may be due to the weak approximation on the response of the vibro-impact oscillators using a continuous Markov process when the restitution coefficient is not very close to unity.     

Eine neue methode der konstruktion des verallgemeinerten preisach-diagramms

The author proposes the construction of a generalized Preisach diagram which is valid in the whole interval of fields coming into consideration in processes of technical magnetization. Fundamentally, the paper uses the method of variable probability density used in the papers by Feldtkeller-Wilde [2], Wilde-Girke [3] and later by Biorci-Pescetti [4]. A contribution of this paper is the method permitting the determination of the probability density distribution in the Preisach diagram by means of the experimentally obtained anhysteretic and primary magnetization curve. The advantage of this method compared with that of [4] is that the original Preisach diagram is used as the basis, permitting a clearer physical interpretation of the two separated components of the probability density than the method based on a modification of the Preisach diagram given in [4]. Some more complicated curves of magnetization reversal, calculated by means of the P-diagram proposed here, are compared in the figures with the corresponding measured curves. The values obtained by the method after Biorci-Pescetti are given for comparison.     

On the product Preisach model of hysteresis

The product model is an output-dependent modification of the traditional Preisach model in order to remove its non-real congruency property. The differential susceptibility is proposed to be a product of a magnetization-dependent factor and an expression containing two terms: one for the reversible process and the other an integral of a Preisach type distribution for the irreversible part. Thus the magnetization is an indirect function, in which the saturation is a natural property of the hysteresis model, and the reversible and irreversible parts of the magnetization are added up indirectly. The envelope function is related to the paramagnetic process and in the specific case of uni-axial anisotropy it is a hyperbolic tangent function. The measurement of the anhysteretic curve may provide the direct link to the evaluation methods of experimental data applied for traditional Preisach modeling.     

Mass operator for wave scattering from a slightly random surface

This paper deals with the mass operator representing multiple-scattering effects in the theory of wave scattering from a slightly random surface. By means of the stochastic-functional approach, a recurrence equation for the mass operator is obtained in the form of an iterative integral. However, its solution oscillates in a non-physical manner against the number of iterations. Next, the recurrence equation may be regarded as a nonlinear integral equation, when the number of iterations goes to infinity. An analytical solution of the nonlinear integral equation is presented for a special case in which the roughness spectrum is the Dirac delta function. Then, the nonlinear integral equation is solved numerically for the Gaussian roughness spectrum by iteration, starting from such an analytical solution. It is shown that only a few iterations are required to obtain the mass operator, even when the correlation distance is small. Effects of the mass operators on the coherent reflection coefficient and the incoherent scattering cross section are calculated and shown in figures.     

Dependence of the anhysteretic magnetization on the demagnetization factor

A method is presented to measure the dependence of the anhysteretic magnetization curve (the anhysteretic magnetization as a function of the internal field after degaussing) on the demagnetization factor N without physically varying N. The relation between the Preisach distribution and the N dependence of the anhysteretic magnetization curve is discussed in a way that is very close to the work of Bertotti. Classes of (moving) Preisach models are identified for which the anhysteretic magnetization curve is independent of the demagnetization factor. It is proven that the anhysteretic magnetization increases with N at fixed internal field, if the Preisach distribution decreases monotonically with increasing H_cent, the internal field value of a Preisach domain. It is shown that the Moving Preisach model may lead to a negative anhysteretic permeability.