FLP滤波算法在光纤陀螺信号预处理中的应用

在简要地介绍FLP（前向线性预测）滤波技术的基础上,采用该方法对某型光纤陀螺信号进行FLP 实时滤波,对滤波后的数据进行了功率谱密度和Allan方差分析,并把滤波效果与小波变换滤波和IIR数字滤波器的滤波效果进行了对比,得出了FLP滤波能有效的减少光纤陀螺的零偏不稳定性、角度随机游走误差和抑制高频噪声的结论.     

Computation of Fractional Order Derivative and Integral via Power Series Expansion and Signal Modelling

The three techniques of s-to-z transform, power series expansion (PSE) and signal modelling are combined to develop a new procedure for efficiently computing the fractional order derivatives and integrals of discrete-time signals. A mapping function between the s-plane and the z-plane is first chosen, and then a PSE of this mapping function raised to fractional order is performed to get the desired infinite impulse response of the ideal digital fractional operator. Finally, the desired impulse response is modelled as the impulse response of a linear invariant system whose rational transfer function is determined using deterministic signal modelling techniques. Three non-iterative techniques, namely Padé, Prony and Shanks’ methods have been considered in this paper. Using Al-Alaoui’s rule as s-to-z transform, computation examples show that both Prony and Shanks’ method can achieve more accurate fractional differentiation and integration than Padé method which is equivalent to continued fraction expansion technique.     

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m ₂) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m ₂ memory may be chosen for a particular application. Memory retentiveness (m ₂) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined.     

The Fractional Fourier Transform and Harmonic Oscillation

The ath-order fractional Fourier transform is a generalization ofthe ordinary Fourier transform such that the zeroth-order fractionalFourier transform operation is equal to the identity operation and thefirst-order fractional Fourier transform is equal to the ordinaryFourier transform. This paper discusses the relationship of thefractional Fourier transform to harmonic oscillation; both correspondto rotation in phase space. Various important properties of thetransform are discussed along with examples of commontransforms. Some of the applications of the transform are brieflyreviewed.     

Discrete and Continuous Random Walk Models for Space-Time Fractional Diffusion

A mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. A more general approach is however provided by the integral equation for the so-called continuous time random walk (CTRW), which can be understood as a random walk subordinated to a renewal process. We show how this integral equation reduces to our fractional diffusion equations by a properly scaled passage to the limit of compressed waiting times and jumps. The essential assumption is that the probabilities for waiting times and jumps behave asymptotically like powers with negative exponents related to the orders of the fractional derivatives. Illustrating examples are given, numerical results and plots of simulations are displayed.     

Numerical Simulations of Fractional Systems: An Overview of Existing Methods and Improvements

An overview of the main simulation methods of fractional systems is presented. Based on Oustaloups recursive poles and zeros approximation of a fractional integrator in a frequency band, some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters.     

基于小波变换及Wigner-Ville变换方法的超声导波信号分析

对结构中缺陷的检测和识别是无损检测中的一项重要研究课题,超声导波由于可在短时间内检测很远距离,故它的一个重要应用便是管材的检测。因而对导波检测信号的处理成为一重要研究内容,本文利用时-频分析方法中的小波变换和Wigner-Ville变换对管道和抽油杆缺陷的导波检测信号进行了分析处理。实验结果表明,进行小波变换后,缺陷回波信号的信噪比大大提高,直径仅1mm的小孔缺陷可容易地被识别出来,准确检测出其位置;通过对信号进行Wigner-Ville的相关变换,可同时在时频两域内对缺陷的回波信号进行分析,使缺陷辨别起来简单易行。两种信号处理方法的超声导波应用研究为以后导波信号的处理提供了新的实现依据。     

Fractional Calculus via Functional Calculus: Theory and Applications

This paper demonstrates the power of the functional-calculus definition oflinear fractional (pseudo-)differential operators via generalised Fouriertransforms.Firstly, we describe in detail how to get global causal solutions of linearfractional differential equations via this calculus. The solutions arerepresented as convolutions of the input functions with the related impulseresponses. The suggested method via residue calculus separates an impulseresponse automatically into an exponentially damped (possibly oscillatory)part and a `slow' relaxation. If an impulse response is stable it becomesautomatically causal, otherwise one has to add a homogeneous solution to getcausality.Secondly, we present examples and, moreover, verify the approach alongexperiments on viscolelastic rods. The quality of the method as an effectivefew-parameter model is impressively demonstrated: the chosen referenceexample PTFE (Teflon) shows that in contrast to standard classical modelsour model describes the behaviour in a wide frequency range within theaccuracy of the measurement. Even dispersion effects are included.Thirdly, we conclude the paper with a survey of the required theory. Therethe attention is directed to the extension from the L ₂-approachon the space of distributions .     

Models for Ground Water Flow: A Numerical Comparison Between Richards' Model and the Fractional Flow Model

In this paper we compare two models for flow in porous media. The first is the well known Richards' equation, which is based on the assumption that the air in the unsaturated zone has infinite mobility. This means that it models a single phase. In the second and more general full two-phase approach, the air is considered as a separate phase. Here, we use the fractional flow equation.We study the difference between the two models numerically by varying the relative contribution of the different physical terms (the gravity and the total velocity) in the fractional flow equation. Richards' equation is considered as the limit of the fractional flow approach when the mobility of the air-phase tends to infinity. In particular, we are interested in determining the parameter intervals where the two models differ significantly, and we will quantify the asymptotic behavior.The equations are studied in the two-dimensional (2D) case. The study is based on a relative permeability depending quadratically on the saturation, and a capillary pressure expressed by a cubic function of the saturation.