非线性Hammerstein系统辨识的动态分离方法

利用同幅值的M序列和逆M序列作为输入信号, 对Hammerstein模型中的线性动态部分进行分离处理, 通过辨识得到一个线性动态模型. 基于此线性模型, 依据系统的测量输出重构出系统的中间输入. 最后由系统的测试输入和中间输入估计出非线性部分的参数. 仿真结果表明本方法的有效性.     

基于人工神经网络的Hammerstein模型辨识

证明了Ｈａｍｍｅｒｓｔｅｉｎ模型在有色噪声情况下，可利用系统的稳态信息辨识模型的非线性增益，并提出了神经元网络的辨识方法。利用系统的动态信息，运用一般的辅助变量法可辨识Ｈ模型的线性子系统。仿真结果表明该方法辨识精度高，具有一定的实用性。     

一类多变量Hammerstein模型的参数辨识方法

通过对系统输入信号的设计,使Hammerstein系统输出只反映系统的线性动态,并将非线性部分的静态影响有效地分离掉.利用最小二乘辨识得到系统的线性动态模型.基于此模型并依据系统的测量输出重构系统的中间输入,进而可估计出非线性部分的参数,据此给出了多变量Hammerstein系统辨识的动态分离方法.仿真结果表明所提出的方法是有效的.     

基于数据滤波的随机梯度辨识方法

针对有色噪声干扰下的随机系统,利用数据滤波技术,对输入输出数据进行滤波,将具有滑动平均噪声的原始系统转换为白噪声干扰下的系统,提出有限脉冲响应滑动平均系统的滤波增广随机梯度算法,并对该算法进行收敛性分析.此外,为了提高参数估计的精度和加快算法的收敛速度,使用多新息辨识理论提出滤波多新息增广随机梯度算法,并分析其收敛性.与增广随机梯度算法相比,所提出的滤波增广随机梯度算法和滤波多新息增广随机梯度算法可以得到更高精度的参数估计.最后,通过仿真实例表明了所提出算法的有效性.     

一类双线性Hammerstein模型的集成辨识方法

对于一类静态非线性增益具有原点对称特性的双线性Ｈａｍｍｅｒｓｔｅｉｎ模型,提出了一种稳态与动态辨识相结合的集成辨识方法。该方法利用稳态信号获得稳态模型的强一致性估计,并通过稳态模型获得非线性增益的估计,再利用动态信息辨识获得双线性Ｈａｍｍｅｒｉｓｔｅｉｎ模型的双线性系统未知参数的一致性估计。仿真结果表明了该方法的有效性和实用性。     

基于Hammerstein型神经网络的非线性动态系统辨识

Hammerstein模型广泛应用于非线性系统的辨识中,其结构是由非线性静态增益部分和一个线性动态部分串联。提出一种Hammerstein型神经网络用来模拟传统的Hammerstein模型,并将其应用于非线性动态系统的辨识中。由Lipschitz熵来确定Hammerstein型神经网络的阶次,并利用反向传播算法对网络权值的进行训练。仿真结果表明,Hammerstein型神经网络具有较好的非线性动态系统辨识性能。     

基于Hammerstein模型描述的非线性系统辨识新方法

Hammerstein模型常用来描述pH值或具有幂函数、死区、开关等特性的过程,本文提出了一种辨识此类对象模型结构和参数的新方法,首先将非线性静态部分和线性动态部分分别用非线性基和Laguerre级数表示,然后通过最小二乘法、矩阵特征值分解和矩阵扩维,辨识出两部分参数．并证明了该方法在输出端存在白噪声情况下误差的收敛性．此方法仅需假设输入为持续激励,适用范围广,计算简单,辨识精度高．最后通过pH中和滴定实验验证了以上结论．     

一种多输入单输出Hammerstein系统的集成辨识方法

针对多输入单输出(MISO)Hammerstein系统提出了一种稳态与动态辨识相结合的集成辨识方法.该方法利用稳态信息获取稳态模型的强一致性估计,并通过稳态模型以神经网络获得其非线性逼近函数,再利用动态信息辨识获取多输入单输出(MISO)Hammerstein系统的线性子系统未知参数的一致性估计.仿真结果表明了该方法的有效性和实用性.     

基于滤波的伪线性回归系统递推最小二乘辨识方法

针对伪线性回归系统,提出了基于滤波的最小二乘辨识方法,基本思想是采用估计的噪声模型对系统观测数据和信息向量进行滤波,并用滤波后的数据进行辨识。仿真结果表明提出的算法能够估计伪线性回归系统的参数。     

损失数据线性参数系统的递推最小二乘辨识方法

针对损失数据线性参数系统的参数辨识问题, 借助辅助模型辨识思想推导出其变递推间隔辅助模型递 推最小二乘算法.为了提高该算法的计算效率, 利用分解技术得到变递推间隔分解递推最小二乘算法 估计系统参数.此外, 在变递推间隔分解递推最小二乘算法中引入遗忘因子, 从而提高参数估计精度和收敛速度.仿真结果表明, 所提出的算法能有效估计系统参数.     

Adaptive tracking and recursive identification for Hammerstein systems

A weighted least squares (WLS) based adaptive tracker is designed for a class of Hammerstein systems. It is proved that the tracking error is asymptotically minimized. Incorporating with the diminishing excitation technique, the minimality of the tracking error and strong consistency of the estimates for parameters of the system are simultaneously achieved. Numerical examples are given and the simulation results are consistent with the theoretical analysis.     

Subspace identification methods for Hammerstein systems: rank constraint and dimension problem

This article studies the subspace identification methods (SIMs) for Hammerstein systems with major focus on a rank constraint and the related dimension problem. We analyse the effects of the rank constraint on the three steps of a unifying framework for SIMs: the rank constraint has no effect on the first two steps, but does so on the third step. If the rank constraint is ignored, as in the existing over-parametrised method (OPM) for Hammerstein system identification, the optimality of the resulting estimate can still be established. Even so, the OPM may suffer from the dimension problem resulting in a low numerical efficiency. To resolve the dimension problem, we propose a new subspace-based method, named as the least-parametrised method (LPM), for identification of Hammerstein systems with non-coupling input nonlinearities. Simulation results are provided to demonstrate the effectiveness of the LPM, and show the necessity of considering the rank constraint to improve the numerical efficiency.     

Auxiliary model-based least-squares identification methods for Hammerstein output-error systems

The difficulty in identification of a Hammerstein (a linear dynamical block following a memoryless nonlinear block) nonlinear output-error model is that the information vector in the identification model contains unknown variables—the noise-free (true) outputs of the system. In this paper, an auxiliary model-based least-squares identification algorithm is developed. The basic idea is to replace the unknown variables by the output of an auxiliary model. Convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition. The simulation results show the effectiveness of the proposed algorithms.     

Iterative identification of Hammerstein systems

Convergences of iterative algorithms have been established for identification of Hammerstein systems in the case that the unknown nonlinearities are odd. Then, the results are further extended to nonsmooth nonlinearities.     

Identification of nonlinear systems using a piecewise-linear Hammerstein model

In the paper a method for nonlinear system identification is proposed. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The model and the identification algorithm are adapted to allow the parameter identification in the presence of a special form of the excitation signal. The identification method is derived from a recursive least-squares algorithm, which is properly adapted to take into account the proposed model structure and the properties of the identification signal. The applicability of the approach is illustrated by an example in which a discontinuous nonlinear static function is connected to a dynamic block.     

Blind maximum likelihood identification of Hammerstein systems

This paper is about the identification of discrete-time Hammerstein systems from output measurements only (blind identification). Assuming that the unobserved input is white Gaussian noise, that the static nonlinearity is invertible, and that the output is observed without errors, a Gaussian maximum likelihood estimator is constructed. Its asymptotic properties are analyzed and the Cramér–Rao lower bound is calculated. In practice, the latter can be computed accurately without using the strong law of large numbers. A two-step procedure is described that allows to find high quality initial estimates to start up the iterative Gauss–Newton based optimization scheme. The paper includes the illustration of the method on a simulation example. A theoretical analysis demonstrates that additive output measurement noise introduces a bias that is proportional to the variance of that additive, unmodeled noise source. The simulations support this result, and show that this bias is insignificant beyond a certain Signal-to-Noise Ratio (40 dB in the example).     

Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory

For Hammerstein output-error autoregressive systems, a decomposition based multi-innovation stochastic gradient (D-MISG) identification algorithm and a data filtering based multi-innovation stochastic gradient (F-MISG) identification algorithm are derived by means of the key-term separation principle and the multi-innovation identification theory. The D-MISG algorithm uses the decomposition technique to transform a Hammerstein system into two subsystems and requires less computational cost, and the F-MISG algorithm uses a linear filter to filter the input-output data and has a higher estimation accuracy for larger innovation lengths. The simulation results show that the proposed two algorithm can give satisfactory parameter estimates.     

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective.     

Strong consistency of recursive identification for Hammerstein systems with discontinuous piecewise-linear memoryless block

This note deals with identification of Hammerstein systems with discontinuous piecewise-linear memoryless block followed by a linear subsystem. Recursive algorithms are proposed for estimating coefficients of the linear subsystem and six unknown parameters contained in the nonlinear static block. By taking a sequence of iid random variables with uniform distribution to serve as the system input, strong consistency is proved for all estimates given in the note. The theoretical results are verified by computer simulation.     

Recursive identification of Hammerstein systems with application to electrically stimulated muscle

Modeling of electrically stimulated muscle is considered in this paper where a Hammerstein structure is selected to represent the isometric response. Motivated by the slowly time-varying properties of the muscle system, recursive identification of Hammerstein structures is investigated. A recursive algorithm is then developed to address limitations in the approaches currently available. The linear and nonlinear parameters are separated and estimated recursively in a parallel manner, with each updating algorithm using the most up-to-date estimation produced by the other algorithm at each time instant. Hence the procedure is termed the alternately recursive least square (ARLS) algorithm. When compared with the leading approach in this application area, ARLS exhibits superior performance in both numerical simulations and experimental tests with electrically stimulated muscle.