非平稳时序数据的分段辨识及其递推算法

在实际生活中,广泛地存在着一类在整体上属于非平稳但又可转化为数段局部平稳的时序数据,对该类非平稳时序数据的辨识问题进行了研究,并提出了一种具有递推机制的分段辨识算法.该算法从平稳时序数据的定义出发,以均值、方差及自相关函数等数字统计特征为校验统计量,构造了具有递推机制的均值突变点、方差突变点及自相关函数突变点的析出算法,在此基础上,从被辨识的非平稳序列中划分出数段局部平稳的子序列,进一步,应用Burg算法对各局部平稳子序列进行了自回归的递推辨识.实验表明,新设计的算法能以较小的位置偏差析出各局部平稳子序列的分界点,同时,在保证较高精度的辨识条件下,计算效能获得了显著的提升.     

一种回归神经网络的快速在线学习算法

针对回归神经网络BP学习算法收敛慢的缺陷,提出了一种新的快速在线递推学 习算法.本算法在目标函数中引入了遗忘因子,并借助于非线性系统的最大似然估计原理成 功地解决了动态非线性系统回归神经网络模型权系数学习的实时性和快速性问题.仿真结果 表明,该算法比传统的回归BP学习算法具有更快的收敛速度.     

Wiener系统的变聚点样条逼近递推贝叶斯算法

为了辨识过程噪声干扰的Wiener非线性系统,提出了一种基于三样条函数逼近的递推贝叶斯算法.众所周知,传统的多项式逼近具有不能外推、高阶易震荡等缺点.为了克服这些缺点,首先利用三样条函数对Wiener系统的非线性反函数进行逼近,在此基础上将待辨识系统参数化为伪线性回归系统.然后把估计到的噪声方差融入算法,接着使用递推贝叶斯算法对参数进行了估计.为了提高三样条函数对非线性反函数的逼近能力,一种基于均值的变聚点选择方法被应用于算法.文中还对算法的收敛性进行了分析,并用数值仿真和案例建模验证了算法的有效性.     

基于KRLS的非均匀采样非线性系统辨识

利用提升技术可将非均匀采样非线性系统离散化为一个多输入单输出传递函数模型,从而将系统输出表示为非均匀刷新非线性输入和输出回归项的线性参数模型,进一步基于非线性输入的估计或过参数化方法进行辨识.然而,当非线性环节结构未知或不能被可测非均匀输入参数化表示时,上述辨识方法将不再适用.为了解决这个问题,利用核方法将原始非线性数据投影到高维特征空间中使其线性可分,再对投影后的数据应用递推最小二乘算法进行辨识,提出基于核递推最小二乘的非均匀采样非线性系统辨识方法.此外,针对系统含有有色噪声干扰的情况,参考递推增广最小二乘算法的思想,利用估计残差代替不可测噪声,提出核递推增广最小二乘算法.最后,通过仿真例子验证所提算法的有效性.     

随机系统的递推辨识: 从个例到一般框架

本文考察Hammerstein系统、Wiener系统和非线性带外源输入的自回归系统(autoregressive system with exogenous input,ARX)等常见的随机非线性系统的递推辨识和因特网PageRank的分布式、随机化算法.对非线性系统分别构造递推辨识算法,证明了估计的强一致性;对因特网PageRank的分布式、随机化算法,给出估计的强一致性和收敛速度;在此基础上,总结了这类问题的统一处理框架–将辨识(估计)问题转化为函数求根、进而基于随机逼近构造算法得到强一致的递推辨识;最后,通过数值例子来验证算法的有效性.     

应用非单调线搜索求解一类互补问题

考虑一类含非Lipschtizian连续函数的非线性互补问题。引入plus函数的一类广义光滑函数,讨论其性质。应用所引入函数将互补问题重构为一系列光滑方程组,提出一个具有非单调线搜索的Newton算法求解重构的方程组以得到原问题的解。在很弱的条件下,该算法具有全局收敛性和局部二次收敛性。利用该算法求解一自由边界问题,其数值结果显示该算法是有效的。     

递推更新高斯粒子滤波器

传统高斯粒子滤波算法(Gaussian particle Filter,GPF)中,粒子的重要性密度函数是由高斯滤波器结合当前最新量测来构建的.由于传统高斯滤波器在量测更新阶段直接利用量测对状态进行线性更新,在某些条件下会导致所构建的重要性密度函数并不能很好地近似状态真实分布.为了解决这一问题,结合递推更新的思想,本文推导出了递推更新高斯滤波器(recursive update Gaussian filter,RUGF)的一般结构.并在此基础上,选用RUGF来构建粒子滤波的重要性密度函数,从而提出了基于递推更新的高斯粒子滤波算法(recursive update gaussian particle filter,RUGPF).仿真表明,在非线性系统状态估计问题中,递推更新可以很好的利用量测信息,相比于传统的GPF,本文所提出的RUGPF滤波算法可以提供更高精度的估计结果.     

一类非线性系统的结构辨识

本文研究了加性噪声指数模型描述的一类非线性系统的结构辨识问题，在文献[3]的参数估计算法基础上，通过使CIC准则函数的数最小化，给出了一种递推结构辨识算法，数字仿真表明该算法的收敛性，便于实际应用。     

基于改进灰狼算法优化多核支持向量回归机及其应用

为更好发现数据中的复杂规律,避免核函数选择的盲目性和局部最优等非线性优化问题,本文提出一种基于改进灰狼算法优化多核支持向量回归机算法.首先,基于全局核函数和局部核函数构建多核支持向量机采油速度预测模型;其次,利用基于云模型和二次插值算法改进灰狼优化算法对核函数权值和参数的选取进行优化;最后,应用灰色关联分析理论确定采油速度影响因素集,并作为多核支持向量回归机预测模型的输入.与6种采油速度预测方法进行对比,所提方法具有较好的全局寻优能力和较高的预测率的优点.     

非匹配不确定系统的显式反步变结构控制

研究非线性多输入多输出不确定系统在非匹配条件下的鲁棒输出跟踪问题.基于相对阶的假设,给出了多输入多输出不确定系统的标准型;进而结合反步设计方法和变结构控制方法,提出一种非匹配条件下非线性不确定系统鲁棒输出跟踪问题的显式反步变结构控制器设计方法.所给跟踪算法不仅只由不确定性的变化范围直接确定,而且有效地克服了现有反步设计算法因隐式递推关系和复杂偏导数计算给实时控制带来的困难.     

Using wavelet network in nonparametric estimation

Wavelet networks are a class of neural networks consisting of wavelets. In this paper, algorithms for wavelet network construction are proposed for the purpose of nonparametric regression estimation. Particular attentions are paid to sparse training data so that problems of large dimension can be better handled. A numerical example on nonlinear system identification is presented for illustration.     

&thetas;-adaptive neural networks: a new approach to parameterestimation

A novel use of neural networks for parameter estimation in nonlinear systems is proposed. The approximating ability of the neural network is used to identify the relation between system variables and parameters of a dynamic system. Two different algorithms, a block estimation method and a recursive estimation method, are proposed. The block estimation method consists of the training of a neural network to approximate the mapping between the system response and the system parameters which in turn is used to identify the parameters of the nonlinear system. In the second method, the neural network is used to determine a recursive algorithm to update the parameter estimate. Both methods are useful for parameter estimation in systems where either the structure of the nonlinearities present are unknown or when the parameters occur nonlinearly. Analytical conditions under which successful estimation can be carried but and several illustrative examples verifying the behavior of the algorithms through simulations are presented.     

Identification of Hammerstein nonlinear ARMAX systems

Two identification algorithms, an iterative least-squares and a recursive least-squares, are developed for Hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by ARMAX/CARMA models. The basic idea is to replace unmeasurable noise terms in the information vectors by their estimates, and to compute the noise estimates based on the obtained parameter estimates. Convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition. The simulation results validate the algorithms proposed.     

Stochastic approximation in nonparametric identification of Hammerstein systems

Derived from the idea of stochastic approximation, recursive algorithms to identify a Hammerstein system are presented. Two of them recover the characteristic of the nonlinear memoryless subsystem, while the third one estimates the impulse response of the linear dynamic part. The a priori information about both subsystems is nonparametric. Consistency in quadratic mean is shown, and the convergence rate is examined. Results of numerical simulation are also presented.     

带相关噪声异步采样系统的分布式最优线性递推融合估计

对带相关噪声的异步均匀采样线性离散系统, 研究了分布式最优线性递推融合预报和滤波问题. 通过引入 满足伯努利分布的随机变量将系统同步化, 给出了局部Kalman预报器和滤波器. 分别推导了局部估值间的互协方 差阵、分布式最优线性融合估值与局部估值间的互协方差阵. 提出了分布式最优线性递推融合预报器和滤波器. 与 局部估值按矩阵加权的分布式融合估计算法相比, 所提出的算法具有更高的估计精度, 但与集中式融合相比有精度 损失. 为了进一步提高估计精度, 又提出了带反馈的分布式最优线性递推融合预报器和滤波器, 证明了带反馈的融 合估计与集中式融合估计具有相同的精度. 仿真例子验证了所提算法的有效性.     

非参数模型控制在液位控制系统中的应用研究

针对工业控制过程中液位系统的时变和明显的滞后特征,研究了非参数模型控制方法在液位控制系统中的设计方案,讨论了控制算法中引入的伪偏导数的在线估计问题,实现了通过液位系统的输入输出信息并利用递归最小二乘法对伪偏导数进行在线估计的过程,仿真实验验证了非参数模型算法对液位控制的鲁棒性、快速性及抗干扰性,通过仿真比较,展示了该算法性能优于PID算法和模糊控制的结果.     

Quantile regression neural networks: Implementation in R and application to precipitation downscaling

The qrnn package for R implements the quantile regression neural network, which is an artificial neural network extension of linear quantile regression. The model formulation follows from previous work on the estimation of censored regression quantiles. The result is a nonparametric, nonlinear model suitable for making probabilistic predictions of mixed discrete-continuous variables like precipitation amounts, wind speeds, or pollutant concentrations, as well as continuous variables. A differentiable approximation to the quantile regression error function is adopted so that gradient-based optimization algorithms can be used to estimate model parameters. Weight penalty and bootstrap aggregation methods are used to avoid overfitting. For convenience, functions for quantile-based probability density, cumulative distribution, and inverse cumulative distribution functions are also provided. Package functions are demonstrated on a simple precipitation downscaling task.     

Recursive algorithms for inner ellipsoidal approximation of convex polytopes

In this paper, fast recursive algorithms for the approximation of an n-dimensional convex polytope by means of an inscribed ellipsoid are presented. These algorithms consider at each step a single inequality describing the polytope and, under mild assumptions, they are guaranteed to converge in a finite number of steps. For their recursive nature, the proposed algorithms are better suited to treat a quite large number of constraints than standard off-line solutions, and have their natural application to problems where the set of constraints is iteratively updated, as on-line estimation problems, nonlinear convex optimization procedures and set membership identification.     

Modified unscented recursive nonlinear dynamic data reconciliation for constrained state estimation

In state estimation problems, often, the true states satisfy certain constraints resulting from the physics of the problem, that need to be incorporated and satisfied during the estimation procedure. Amongst various constrained nonlinear state estimation algorithms proposed in the literature, the unscented recursive nonlinear dynamic data reconciliation (URNDDR) presented in [1] seems to be promising since it is able to incorporate constraints while maintaining the recursive nature of estimation. In this article, we propose a modified URNDDR algorithm that gives superior performance when compared with the basic URNDDR. The improvements are obtained via better constraint handling and are demonstrated on representative case studies [2], [3]. In addition to this modification, an efficient strategy combining basic unscented Kalman filter (UKF), URNDDR and modified URNDDR is also proposed in this article for solving large scale state estimation problems at relatively low computational cost. The utility of the proposed strategy is demonstrated by applying it to the Tennessee Eastman challenge process [4].     

Simulation-based two-stage estimation for multiple nonparametric regression

To reduce the curse of dimensionality arising from nonparametric estimation procedures for multiple nonparametric regression, in this paper we suggest a simulation-based two-stage estimation. We first introduce a simulation-based method to decompose the multiple nonparametric regression into two parts. The first part can be estimated with the parametric convergence rate and the second part is small enough so that it can be approximated by orthogonal basis functions with a small trade-off parameter. Then the linear combination of the first and second step estimators results in a two-stage estimator for the multiple regression function. Our method does not need any specified structural assumption on the regression function and it is proved that the newly proposed estimation is always consistent even if the trade-off parameter is designed to be small. Thus when the common nonparametric estimator such as local linear smoothing collapses because of the curse of dimensionality, our estimator still works well.