Variable knot-based spline approximation recursive Bayesian algorithm for the identification of Wiener systems with process noise

Wiener systems consist of a linear dynamic block in cascade with static nonlinearity. One of the challenging issues in the identification of a process noise disturbed Wiener system is that the influence of noise is difficult to eliminate. For Wiener systems with process noise, traditional algorithms will result in biased estimates. To solve this problem, a novel recursive Bayesian algorithm based on variable knot spline approximation is proposed in this paper. First, a spline function is taken to approximate the inverse function of the nonlinear part, which can achieve excellent extrapolation and eliminate oscillatory behaviors. A knot selection method is then presented to achieve accurate estimates. Furthermore, a knot variation strategy to improve the accuracy of the spline approximation is described. Finally, the proposed algorithm is validated through a numerical simulation.     

Instrumental variables approach to identification of a class of MIMO Wiener systems

A new approach to identification of multi-input multi-output (MIMO) Wiener systems using the instrumental variables method is presented. It is assumed that static nonlinear elements are invertible and their inverse characteristics can be expressed or approximated by polynomials of known orders. It is also assumed that the linear part of the Wiener system can be represented by a matrix polynomial form. Based on these assumptions, the Wiener system is transformed introducing a new parameterization and its parameters are estimated using a linear-in-parameters model. To solve the problem of non-consistency of least squares parameter estimates, an instrumental variables method is employed. A numerical example is included to show the effectiveness and the practical feasibility of the presented approach.     

Gradient-based iterative identification for Wiener nonlinear systems with non-uniform sampling

This paper focuses on the identification problem of Wiener nonlinear systems with non-uniform sampling. The mathematical model for the Wiener nonlinear system is established from the non-uniformly sampled input–output data. In order to solve the identification problem of the Wiener nonlinear system with the unmeasurable variables in the information vector, the gradient-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. Finally, the simulation results indicate that the proposed algorithm is effective.     

Highly computationally efficient parameter estimation algorithms for a class of nonlinear multivariable systems by utilizing the state estimates

This paper investigates the parameter estimation issue for an input nonlinear multivariable state-space system. First, the canonical form of the input nonlinear multivariable state-space system is obtained through the linear transformation and the over-parameterization identification model of the considered system is derived. Second, by cutting down the redundant parameter estimates and extracting the unique parameter estimates from the parameter estimation vector in the least-squares identification method, we present an over-parameterization-based partially coupled average recursive extended least-squares parameter estimation algorithm to estimate the parameters. As for the unknown states in the parameter estimation algorithm, a new state estimator is designed to generate the state estimates. Third, in order to improve the computational efficiency of the parameter estimation algorithm, an over-parameterization-based multi-stage partially coupled average recursive extended least-squares algorithm is proposed. Finally, the computational efficiency analysis and the simulation examples are given to verify the effectiveness of the proposed algorithms.

     

一种辩识多输入多输出振动系统参数的方法

本文讨论的是多输入、多输出串联振动系统传递函数的辩识问题.本文表明:从系统结构来看,多输入、多输出串联振动系统可以化成为多重交叉闭环系统.本文将这类振动系统的传递函数分解成多个二阶子系统.从系统辩识的角度出发,提出了一种通过辩识子系统传递函数,实现对整个系统传递函数辩识的新方法.仿真结果及模型实验结果表明:这种方法是可行的,且具有较高的精度.     

大长细比导弹的气动弹性降阶模型

对于大长细比导弹,需要在设计阶段准确计算气动弹性/气动伺服弹性,但其复杂的气动力给计算带来困难,因此气动力降阶模型是突破大长细比导弹跨音速气动弹性分析与控制瓶颈的关键技术.虽然气动力模型降阶方法已在预测二维机翼结构的气动弹性方面取得重要进展,但几乎未见关于全机模型的气动力降阶模型研究报道.本文基于递归Wiener模型的气动力降阶方法,利用CFD计算的气动力作为模型辨识数据,用鲁棒子空间和Levenberg-Marquardt算法辨识降阶模型参数,建立了大长细比导弹气动力降阶模型.在此基础上与大长细比导弹有限元模型相结合,构造出气动弹性降阶模型,并在数值仿真中测试气动弹性降阶模型在不同马赫数下的适用性.数值仿真结果表明,该气动弹性降阶模型能够精确预测导弹模型在不同飞行条件下的非定常气动力和导弹模型的气动弹性频率响应特性.     

Recursive identification of discrete-time nonlinear cascade systems with time-varying output hysteresis

Nonlinear Dynamics - A recursive identification method for discrete-time nonlinear cascade systems with a linear dynamic system followed by a time-varying output hysteresis is presented. The...     

Long-memory recursive prediction error method for identification of continuous-time fractional models

This paper deals with recursive continuous-time system identification using fractional-order models. Long-memory recursive prediction error method is proposed for recursive estimation of all parameters of fractional-order models. When differentiation orders are assumed known, least squares and prediction error methods, being direct extensions to fractional-order models of the classic methods used for integer-order models, are compared to our new method, the long-memory recursive prediction error method. Given the long-memory property of fractional models, Monte Carlo simulations prove the efficiency of our proposed algorithm. Then, when the differentiation orders are unknown, two-stage algorithms are necessary for both parameter and differentiation-order estimation. The performances of the new proposed recursive algorithm are studied through Monte Carlo simulations. Finally, the proposed algorithm is validated on a biological example where heat transfers in lungs are modeled by using thermal two-port network formalism with fractional models.

     

Gradient-Based Identification Methods for Hammerstein Nonlinear ARMAX Models

Two identification algorithms, an iterative gradient and a recursive stochastic gradient based, are developed for a Hammerstein nonlinear ARMAX model, a linear dynamical block following a memoryless nonlinear block. The basic idea is to use the gradient search principle, to replace unmeasurable noise terms in the information vectors by their estimates, and to compute iteratively or recursively the noise estimates based on the obtained parameter estimates. Convergence analysis of the recursive stochastic gradient algorithm indicates that the parameter estimation error consistently converges to zero under certain conditions. The simulation results show the effectiveness of the proposed algorithms. An erratum to this article is available at .     

Online system identification using fractional-order Hammerstein model with noise cancellation

Slow convergence and low accuracy are two main drawbacks in nonlinear system identification methods. It becomes more complicated when time delay and noises are considered. In this paper, considering a fractional-order Hammerstein model, an online identification method is proposed. A combination of an evolutionary optimization method and recursive least square algorithm is used to estimate the system parameters and orders in the presence of unknown noises. Finally, simulation results are taken to prove the effectiveness of the proposed algorithm.

     

哈密顿系统正则变换在时变最优控制中的应用

利用哈密顿系统正则变换和生成函数理论求解线性时变最优控制问题,构造了新的最优控制律形式并提出了控制增益计算的保结构算法. 利用生成函数求解最优控制导出的哈密顿系统两端边值问题,并构造线性时变系统的最优控制律,由第2类生成函数所构造的最优控制律避免了末端时刻出现无穷大反馈增益. 控制系统设计中需求解生成函数满足的时变矩阵微分方程组. 根据生成函数与哈密顿系统状态转移矩阵之间的关系,从正则变换的辛矩阵描述出发,导出了求解这组微分方程组的保结构递推算法.为了保持递推计算中的辛矩阵结构,哈密顿系统状态转移矩阵的计算中利用了Magnus级数.      

基于非线性状态空间辨识的气动弹性模型降阶

高维、非线性气动弹性系统的模型降阶是当前气动弹性力学与控制领域的研究热点之一.然而国内外现有的非线性模型降阶方法仍存在辨识算法复杂、精度有待提高等问题.本研究提出了一种基于非线性状态空间辨识的跨音速气动弹性模型降阶方法. 首先,该方法基于非定常空气动力的单位脉冲响应数据,采用特征系统实现算法对非线性状态空间模型的线性动力学部分进行系统辨识. 其次,引入状态和控制输入的非线性函数, 采用优化算法对非线性函数的系数矩阵进行优化,进而得到考虑非线性效应的空气动力降阶模型.为了验证该降阶模型在预测跨音速气动弹性力学行为的精确性,本文以三维机翼为研究对象,分别从基于非线性降阶模型的气动力辨识、跨声速颤振边界计算和极限环振荡预测三方面进行了算例验证,并与现有的模型降阶方法进行了对比, 进一步说明本文所提出方法的有效性.研究结果表明, 该降阶模型对上述三类问题的计算精度与直接流-固耦合方法相吻合,可用于高效预测飞行器跨声速气动弹性力学行为.      

Least squares algorithm for an input nonlinear system with a dynamic subspace state space model

For a Hammerstein input nonlinear system with a subspace state space linear element, this paper transforms the system into a bilinear identification model by using the property of the shift operator to the state space model and presents a recursive and an iterative least squares algorithms to generate parameter estimates and state estimates by using the hierarchical identification principle and by replacing the unknown state variables with their estimates. The proposed approaches are computationally more efficient than the over-parameterization model based least squares method.     

Filtering based recursive least squares algorithm for Hammerstein FIR-MA systems

We consider the parameter estimation problem for Hammerstein finite impulse response (FIR) systems. An estimated noise transfer function is used to filter the input–output data of the Hammerstein system. By combining the key-term separation principle and the filtering theory, a recursive least squares algorithm and a filtering-based recursive least squares algorithm are presented. The proposed filtering-based recursive least squares algorithm can estimate the noise and system models. The given examples confirm that the proposed algorithm can generate more accurate parameter estimates and has a higher computational efficiency than the recursive least squares algorithm.     

Iterative estimation methods for Hammerstein controlled autoregressive moving average systems based on the key-term separation principle

This paper considers iterative identification problems for a Hammerstein nonlinear system which consists of a memoryless nonlinear block followed by a linear dynamical block. The difficulty of identification is that the Hammerstein nonlinear system contains the products of the parameters of the nonlinear part and the linear part, which leads to the unidentifiability of the parameters. In order to obtain unique parameter estimates, we express the output of the system as a linear combination of all the system parameters by means of the key-term separation principle and derive a gradient based iterative identification algorithm by replacing the unknown variables in the information vectors with their estimates. The simulation results indicate that the proposed algorithm can work well.     

Recursive parameter identification of the dynamical models for bilinear state space systems

This paper investigates the recursive parameter and state estimation algorithms for a special class of nonlinear systems (i.e., bilinear state space systems). A state observer-based stochastic gradient (O-SG) algorithm is presented for the bilinear state space systems by using the gradient search. In order to improve the parameter estimation accuracy and the convergence rate of the O-SG algorithm, a state observer-based multi-innovation stochastic gradient algorithm and a state observer-based recursive least squares identification algorithm are derived by means of the multi-innovation theory. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed algorithms.     

线性时不变系统集员辨识的区间算法

在不确定但有界(UBB)噪声假设下，提出一种针对线性时不变系统参数集员辨识的区间算法. 借助区间数学，寻求与观测数据和噪声相容的参数的最小超长方体(或区间向量)，推导了递 推列式，并分析了算法的收敛性. 此算法不仅可以给出参数估计值，还可以给出参数的不确 定性界限. 通过数值算例，将此算法与Fogel椭球算法和最小二乘算法进行了比较，显示 了其计算量小和精度高的优点。     

Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium

The differential equations governing transfer and stiffness matrices and acoustic impedance for a functionally graded generally anisotropic magneto-electro-elastic medium have been obtained. It is shown that the transfer matrix satisfies a linear 1st order matrix differential equation, while the stiffness matrix satisfies a nonlinear Riccati equation. For a thin nonhomogeneous layer, approximate solutions with different levels of accuracy have been formulated in the form of a transfer matrix using a geometrical integration in the form of a Magnus expansion. This integration method preserves qualitative features of the exact solution of the differential equation, in particular energy conservation. The wave propagation solution for a thick layer or a multilayered structure of inhomogeneous layers is obtained recursively from the thin layer solutions. Since the transfer matrix solution becomes computationally unstable with increase of frequency or layer thickness, we reformulate the solution in the form of a stable stiffness-matrix solution which is obtained from the relation of the stiffness matrices to the transfer matrices. Using an efficient recursive algorithm, the stiffness matrices of the thin nonhomogeneous layer are combined to obtain the total stiffness matrix for an arbitrary functionally graded multilayered system. It is shown that the round-off error for the stiffness-matrix recursive algorithm is higher than that for the transfer matrices. To optimize the recursive procedure, a computationally stable hybrid method is proposed which first starts the recursive computation with the transfer matrices and then, as the thickness increases, transits to the stiffness matrix recursive algorithm. Numerical results show this solution to be stable and efficient. As an application example, we calculate the surface wave velocity dispersion for a functionally graded coating on a semispace.     

Recursive least squares parameter estimation algorithm for dual-rate sampled-data nonlinear systems

This paper focuses on the identification problem of Hammerstein systems with dual-rate sampling. Using the key-term separation principle, we derive a regression identification model with different input updating and output sampling rates. To solve the identification problem of the dual-rate Hammerstein systems with the unmeasurable variables in the information vector, an auxiliary model-based recursive least squares algorithm is presented by replacing the unmeasurable variables with their corresponding recursive estimates. Convergence properties of the algorithm are analyzed. Simulation results show that the proposed algorithm can estimate the parameters of a class of nonlinear systems.     

基于黎曼几何的非线性振子动力学分析递推解析算法

基于黎曼几何和变分原理，推导了黎曼流形上非线性耗散动力系统的二阶微分动力学方程，并运用流形收缩的概念将动力学方程离散化，进而建立了相应的递推求解格式。选取3个自治非线性阻尼振子系统，分别采用递推解析算法和龙格库塔法求解微分动力学方程，并比较分析了不同的时间步长下两种算法的计算耗时。结果表明，与龙格库塔法相比，基于黎曼几何的递推算法不仅能得到每一时步的解析表达式，而且计算耗时短，计算效率高。基于黎曼流形的动力学方程递推算法为非线性动力学系统的解析求解提供了新思路。