FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

On the robust control of stable minimum phase plants with large uncertainty in a time constant. A fractional-order control approach

This paper addresses the problem of designing controllers that are robust to a great uncertainty in a time constant of the plant. Plants must be represented by minimum phase rational transfer functions of an arbitrary order. The design specifications are: (1) a phase margin for the nominal plant, (2) a gain crossover frequency for the nominal plant, (3) zero steady state error to step commands, and (4) a constant phase margin for all the possible values of the time constant (T$T$): 0<T<∞$0<T<\infty$. We propose a theorem that defines the structure of the set of controllers that fulfil these specifications and show that it is necessary for these robust controllers to include a fractional-order PI$PI$ term. Examples are developed for both stable and unstable plants, and the results are compared with a standard PI$PI$ controller and a robust controller designed using the QFT$QFT$ methodology.     

LAG WINDOW ESTIMATION OF THE DEGREE OF DIFFERENCING IN FRACTIONALLY INTEGRATED TIME SERIES MODELS

Abstract. In this paper we consider the estimation of the degree of differencing d in the fractionally integrated autoregressive moving-average time series model ARFIMA ( p, d, q ). Using lag window spectral density estimators we develop a regression type estimator of d which is easy to calculate and does not require prior knowledge of p and q. Some large sample properties of the estimator are studied and the performance of the estimator for small samples is investigated using the simulation method for a range of commonly used lag windows. Some practical recommendations on the choice of lag windows and the choice of the window parameters are provided.     

电网电压不平衡且严重畸变时的软件锁相技术

针对传统软件锁相环（SPLL）在三相电压不平衡且严重畸变条件下不能准确跟踪电网电压的频率和相位的问题。本文提出了一种基于相序解耦（SDR）级联二阶广义积分（SOGI）的新型软件锁相模型,通过SDR和SOGI实现了正负序分离,电压基波提取,以及滤波功能,有效地消除了负序分量、谐波分量对准确获取频率和相位信息的影响。仿真结果表明在三相电压不平衡且严重畸变的条件下,该新型SPLL能够准确地锁定电网电压的频率和相位,从而有效性地验证了新方法的正确性。     

Persistence Heterogeneity Testing in Panels with Interactive Fixed Effects

We consider large N,T panel data models with fixed effects, a common factor allowing for cross‐section dependence, and persistent data and shocks, which are assumed fractionally integrated. In a basic setup, the main interest is on the fractional parameter of the idiosyncratic component, which is estimated in first differences after factor removal by projection on the cross‐section average. The pooled conditional‐sum‐of‐squares estimate is consistent but the normal asymptotic distribution might not be centred, requiring the time series dimension to grow faster than the cross‐section size for correction. We develop tests of homogeneity of dynamics, including the degree of integration, that have no trivial power under local departures from the null hypothesis of a non‐negligible fraction of cross‐section units. A simulation study shows that our estimates and tests have good performance even in moderately small panels.     

机车轨道平顺性滤波优化设计与仿真研究

研究机车轨道平顺性滤波优化问题,轨道不平顺作为机车车辆轨道耦合系统的激励源,对列车动态平稳性和舒适度影响很大.目前轨道不平顺信号处理系统中移变数字滤波器的设计多采用分级离线的方法,因而导致计算量大、设计效率低.针对上述问题,提出一种基于牛顿插值算法的有限长冲激响应(FIR)移变数字滤波器设计方法,通过改变原型滤波器分数延迟单元,可实现选择性的提取轨道不利波长不平顺信号.仿真结果表明,所设计的滤波器性能和理论一致,具有稳定的频响移变特性,对机车轨道不平顺信号实时提取准确有效,易于工程实现.     

面向限价指令簿趋势分析的网络集成模型

为了更好地分析限价指令簿(LOBs)的趋势,文中提出面向LOBs趋势分析的网络集成模型(NEM-LOB).模型融合2个长短期记忆(LSTM)子模型和1个卷积神经网络(CNN)子模型.一个LSTM子模型可通过LOBs的分布信息捕捉全局时间依赖性,另一个LSTM子模型可通过LOBs和订单流的动态信息捕捉全局动态性.CNN子模型通过LOBs的事实信息提取局部特征.最后,结合3个子模型,提取特征以获得预测结果.在FI-2010数据集上的实验表明NEM-LOB通过引入订单流信息,能对LOBs进行更好的趋势分析.     

Dynamic analysis of a novel time‐lag four‐dimensional fractional‐order financial system

In this paper, a novel four‐dimensional fractional‐order financial system (FFS) with time delay is presented. Unlike traditional bifurcation analysis of financial systems, the selection rules of two bifurcation points within the system are discussed. In addition, the motion state of the system in the vicinity of two bifurcation points are analyzed separately, such that the dynamic analysis of this novel nonlinear fourth‐dimensional FFS is more comprehensive. The detailed dynamical behaviors of this financial system, such as oscillation, stability, and bifurcation points, are deduced via rigorous mathematical analysis. Finally, some simulations are performed to verify the dynamic characteristics of the FFS around the two bifurcation points which satisfy the selection conditions of the bifurcation point.