混沌时间序列的2阶预测模型

为了克服传统预测方法对混沌时间序列预测精度不高的缺点,提出一种新的基于1阶预测模型(1-OP)和信息融合理论的混沌时间序列2阶预测模型(2-OP).首先根据相空间重构理论建立2个1阶预测模型,然后根据融合估计原理建立2阶预测模型.最后利用Lorenz和Mackey-Glass时间序列对该模型进行验证,结果表明,2阶预测模型对多变量和单变量混沌系统都是有效的.     

Sobolev方程的混合连续时空有限元解的误差估计

通过引入辅助变量构造Sobolev方程的混合连续时空有限元离散格式,使得该格式既利用混合法将方程降阶,又将时间和空间两个变量同时用有限元方法离散,从而获得时空形式高精度数值模型.证明了Sobolev方程混合时空有限元解的存在唯一性、稳定性,并利用时间和空间投影算子推导出时空数值解的误差估计.     

多输入多输出大规模动力系统模型简化的Frobenius范数最小二乘法

对多输入多输出大规模动力系统的模型简化提出了一种新的方法.它是一种投影方法,其投影依赖于奇异值分解(singular value decomposition,SVD)和Krylov子空间.该方法实际上等价于求解一个Frobenius范数最小二乘问题.通过该方法降阶后的模型能准确地匹配原模型的前r个模,剩余的高阶模以Frobenius范数最小二乘法的形式逼近原模型的模,其中,r是降阶系统的维数.还将该方法推广到任意插值点的模匹配,数值例子也证明了该方法的有效性.     

二维非稳态对流扩散边界控制问题的简化算法

针对二维非稳态对流扩散边界控制问题计算量大的问题,提出了基于降阶模型的最优实时控制方法.利用POD(the Proper Orthogonal Decomposition)和奇异值分解以及Galerkin投影方法得到了具有高精度离散形式的状态空间降阶模型.在所得的降阶状态空间模型中,利用离散时间线性二次调节器方法设计出了最优控制器.对流-扩散过程的控制模拟结果说明了所提方法的有效性和准确性.     

二阶系统基于奇异值的保结构模型降阶方法（英文）

本文提出了一种二阶系统基于奇异值的保结构模型降阶方法.该方法通过脉冲响应的移位勒让德多项式展开系数直接计算得到二阶系统的可控和可观格拉姆矩阵的低秩因子.然后基于二阶系统的奇异值结构,构造相应的平衡系统,进而通过截断较小奇异值对应的状态得到保结构的降阶系统.最后,通过两个数值实验展示了所提方法的有效性.     

矩阵构造法在动力模型物理参数识别中的应用

通过矩阵奇异值分解得到矩阵构造的表达式,并将其应用于动力模型物理参数识别问题.根据矩阵构造表达式的特点,可以使参数识别模型降阶,降阶后的模型与原模型之间的数学和物理性质有明确的对应关系,避免了为忽略高阶频率而采用缩聚方法造成的误差.最后,数值算例获得满意的结果.     

基于矩阵指数函数Laguerre多项式展开的模型降阶方法

在经典平衡截断模型降阶方法的基础上, 提出一种基于矩阵指数函数Laguerre多项式展开的模型降阶方法. 该方法首先利用矩阵指数函数的Laguerre多项式展开, 给出控制系统可控Gram矩阵和可观Gram矩阵的近似低秩分解, 然后构造正交投影变换得到近似平衡系统, 进而通过截断较小的Hankel奇异值对应的状态得到降阶系统. 该方法计算高效, 且具有一定的自适应性. 最后, 通过数值算例验证算法的有效性.     

ARIMA时间序列模型和BP神经网络组合预测在铁路客座率中的应用

首先利用python3.5对铁路客座率原始数据进行预处理,然后利用ARIMA时间序列和BP神经网络进行单一的模型预测,得出单一预测模型的均方误差.在组合预测求解时,先求出ARIMA时间序列模型的误差向量E_1和BP神经网络的预测误差为E_2,由于这两种预测方法是相互独立的,因此误差向量E_1和E_2线性无关且组合预测误差向量为E=(E_1,E_2),得出组合预测平方和的形式为J-W~TEW,然后根据组合预测误差平方和最小的原则来确定权值w_1,w_2,最后求解凸二次规划问题得到权值并求出组合预测模型和均方误差.通过比较单一模型预测和组合预测的均方误差,得出结论:组合预测模型的精确度高于单一预测模型的精确度.     

非线性抛物方程的EQ_1~(rot)非协调混合元方法的超收敛分析

基于EQ_1~(rot)非协调矩形元及零阶R-T元对非线性抛物方程构造了一个新的混合元格式.利用EQ_1~(rot)元所具有的两个特殊性质:(I)插值算子与其投影算子是一致的;(II)当所考虑问题的精确解属于H~3(ΩΩ)时,其相容误差可以达到O(h~2)(h是剖分参数),比插值误差高一阶.同时借助关于这两个单元的高精度分析、平均值技巧和插值后处理技术,得到了关于原始变量以及通量的超逼近和整体超收敛结果.     

隐式重新启动的Lanczos算法在模型降阶中的应用

主要研究了一种隐式重新启动的L anczos算法在模型降阶中的应用.分析了由这个算法得到的降价后的模型的一些性质,对于一个n阶稳定的线性时不变系统,模型降阶的思想是寻找一个m阶转换函数来近似原系统的n阶转换函数H(s),其中n m.传统的kry lov子空间方法仅仅产生一个不稳定的实现,并且在低频处的误差较大,本文所考虑的隐式重新启动的L anczos方法,能较好的解决上述两个问题.     

Integrodifferential approaches to frequency analysis and control design for compressible fluid flow in a pipeline element

In this study, modelling, frequency analysis, and optimization of control processes are considered for the fluid flow in pipeline systems. A mathematical model of controlled pipeline elements with distributed parameters is proposed to describe the dynamical behaviour of compressible fluid which is transported in a long rigid tube. By exploiting specific functions representing cross-sectional forces and effective displacements as well as linear approximations of fluidic resistances, the original problem with non-uniform parameters is reduced to a partial differential equation (PDE) system with constant coefficients and homogeneous initial and boundary conditions. Three numerical approaches are applied to an efficient analysis of natural vibrations and reliable control-oriented modelling of pipeline elements. The conventional Galerkin method is compared with the method of integrodifferential relations based on a weak formulation of the constitutive laws. In the latter approach, the original initial-boundary value problem is reduced to the minimization of an error functional which provides explicit energy estimates of the solution quality. A novel projection approach is implemented on the basis of the Petrov–Galerkin method combined with the method of integrodifferential relations. This technique benefits from the advantages of the above-mentioned projection and variational approaches, namely sufficient numerical stability, a lower differential order, and an explicit quality estimation. Numerical optimization procedures, making use of a modified finite element technique, are proposed to obtain a feedforward control strategy for changing the pressure and mass flow inside the pipeline system to a desired operating state. At this given finite point of time, residual elastic oscillations inside the pipeline are minimized. Numerical results, obtained for ideal as well as viscous fluid models, are analysed and discussed.     

Auxiliary model based parameter estimation for dual-rate output error systems with colored noise

The dual-rate sampled-data systems can offer better quality of control than the systems with single sampling rate in practice. However, the conventional identification methods run in the single-rate scheme. This paper focuses on the parameter estimation problems of the dual-rate output error systems with colored noises. Based on the dual-rate sampled and noise-contaminated data, two direct estimation algorithms are addressed: the auxiliary model based recursive extended least squares algorithm and the recursive prediction error method. The auxiliary model is employed to estimate the noise-free system output. An example is given to test and illustrate the proposed algorithms.     

Output Feedback Model Predictive Tracking Control Using a Slope Bounded Nonlinear Model

In this paper, an output feedback model predictive tracking control method is proposed for constrained nonlinear systems, which are described by a slope bounded model. In order to solve the problem, we consider the finite horizon cost function for an off-set free tracking control of the system. For reference tracking, the steady state is calculated by solving by quadratic programming and a nonlinear estimator is designed to predict the state from output measurements. The optimized control input sequences are obtained by minimizing the upper bound of the cost function with a terminal weighting matrix. The cost monotonicity guarantees that tracking and estimation errors go to zero. The proposed control law can easily be obtained by solving a convex optimization problem satisfying several linear matrix inequalities. In order to show the effectiveness of the proposed method, a novel slope bounded nonlinear model-based predictive control method is applied to the set-point tracking problem of solid oxide fuel cell systems. Simulations are also given to demonstrate the tracking performance of the proposed method.     

Empirical Gramian-based spatial basis functions for model reduction of nonlinear distributed parameter systems

Correct selection of spatial basis functions is crucial for model reduction for nonlinear distributed parameter systems in engineering applications. To construct appropriate reduced models, modelling accuracy and computational costs must be balanced. In this paper, empirical Gramian-based spatial basis functions were proposed for model reduction of nonlinear distributed parameter systems. Empirical Gramians can be computed by generalizing linear Gramians onto nonlinear systems, which results in calculations that only require standard matrix operations. Associated model reduction is described under the framework of Galerkin projection. In this study, two numerical examples were used to evaluate the efficacy of the proposed approach. Lower-order reduced models were achieved with the required modelling accuracy compared to linear Gramian-based combined spatial basis function- and spectral eigenfunction-based methods.     

A modified alternating projection based prediction–correction method for structured variational inequalities

In this paper, we propose a novel alternating projection based prediction–correction method for solving the monotone variational inequalities with separable structures. At each iteration, we adopt the weak requirements for the step sizes to derive the predictors, which affords fewer trial and error steps to accomplish the prediction phase. Moreover, we design a new descent direction for the merit function in correction phase. Under some mild assumptions, we prove the global convergence of the modified method. Some preliminary computational results are reported to demonstrate the promising and attractive performance of the modified method compared to some state-of-the-art prediction–contraction methods.     

Adaptive robust synchronization of Rossler systems in the presence of unknown matched time-varying parameters

This paper deals with the problem of adaptive robust synchronization of chaotic systems based on the Lyapunov theory. A controller is designed for a feedback linearizable error system with matched uncertainties. The proposed method shows that the drive and response systems are synchronized and states of the response system track the states of the drive system as time tends to infinity. Since this approach does not require any information about the bound of uncertainties, this information is not needed in advance. In order to prevent the frequent switching phenomenon in the control signal, the method is modified such that the norm of tracking error is bounded. Numerical simulations on two uncertain Rossler systems with matched uncertainties show fast responses of tracking error, while the errors are Uniformly Ultimately Bounded, and the control signal is reasonably smooth.     

基于修正的Magnus方法的高振荡动力系统的数值积分方法

基于建立于一般线性动力系统上的Magnus数值积分方法,针对随时间而高频率振荡的二阶动力系统,给出了有效的修正Magnus数值积分算法．首先,将二阶动力系统重新表示为一阶系统的形式,通过引进新变量进行参考坐标变换,使动力系统的高振荡性质保留在新形式内;进而基于局部线性化技术用修正的Magnus方法求解新形式下的系统方程;最后,通过一系列数值实验说明了文中方法的有效性．     

杆件轴向受迫振动的Galerkin有限元EEP法自适应求解

基于单元能量投影(element energy projection,EEP)法自适应分析在杆件静力问题以及离散系统运动方程组中所取得的成果,以直杆轴向受迫振动为例,研究并建立了一种在时间域和一维空间域同时实现自适应分析的方法.该方法在时间和空间两个维度都采用连续的Galerkin有限元法(finite element method,FEM)进行求解,根据半离散的思想,由空间有限元离散将模型问题的偏微分控制方程转化为离散系统运动方程组,对该方程组进行时域有限元自适应求解;然后再基于空间域超收敛计算的EEP解对空间域进行自适应,直至最终的时空网格下动位移解答的精度逐点均满足给定误差限要求.文中对其基本思想、关键技术和实施策略进行了阐述,并给出了包括地震波输入下的典型算例以展示该法有效可靠.     

Model reduction for large-scale dynamical systems via equality constrained least squares

In this paper, we present a new method of model reduction for large-scale dynamical systems, which belongs to the SVD-Krylov based method category. It is a two-sided projection where one side reflects the Krylov part and the other side reflects the SVD (observability gramian) part. The reduced model matches the first r+i Markov parameters of the full order model, and the remaining ones approximate in a least squares sense without being explicitly computed, where r is the order of the reduced system, and i is a nonnegative integer such that 1≤i<r. The reduced system minimizes a weighted ?₂ error. By the definition of a shift operator, the proposed approximation is also obtained by solving an equality constrained least squares problem. Moreover, the method is generalized for moment matching at arbitrary interpolation points. Several numerical examples verify the effectiveness of the approach.