Identification of Hammerstein Model Using Hybrid Neural Networks

The identification problem of Hammerstein model with extension to the multi input multi output (MIMO) case is studied. The proposed identification method uses a hybrid neural network (HNN) which consists of a multi layer feed forward neural network (MFNN) in cascade with a linear neural network (LNN). A unified back propagation (BP) algorithm is proposed to estimate the weights and the biases of the MFNN and the LNN simultaneously. Numerical examples are provided to show the efficiency of the proposed method.

Modelling of ultrasonic motor with dead-zone based on Hammerstein model structure

The ultrasonic motor (USM) possesses heavy nonlinearities which vary with driving conditions and load-dependent characteristics such as the dead-zone. In this paper, an identification method for the rotary travelling-wave type ultrasonic motor (RTWUSM) with dead-zone is proposed based on a modified Hammerstein model structure. The driving voltage contributing effect on the nonlinearities of the RTWUSM was transformed to the change of dynamic parameters against the driving voltage. The dead-zone of the RTWUSM is identified based upon the above transformation. Experiment results showed good agreement be- tween the output of the proposed model and actual measured output.

Digital Cancellation Scheme and Hardware Implementation for High-Order Passive Intermodulation Interference Based on Hammerstein Model

Passive intermodulation(PIM)interference urgently needs to be solved in the satellite communication system,owing to degrading the whole performance.Mainstream research contributions to the cancellation method for PIM were focused on the analog domain,however,the PIM distortion cannot be eliminated completely with the approaches.Meanwhile,some researchers attempt to tackle the problem through digital signal processing,nevertheless,the proposed methods were not suitable for the practical satellite communication scenario.In this paper,we present a general scheme for the adaptive feedforward PIM cancellation.High-order PIM signals at baseband are estimated by modeling the PIM distortion with Hammerstein model in the digital domain.Based on the reconstructed PIM signal,we adopt the least mean square algorithm to adaptively mitigate the PIM interference for tracking the variation of PIM.The time and frequency synchronization of PIM are based on the correlation of the peak of received signals with the corresponding reconstructed PIM signal.Practical experimental results show that the scheme can effectively cancel the PIM interference,and achieve an interference suppression gain more than 20dB.

Identification of Neuro-Fuzzy Hammerstein Model Based on Probability Density Function

A new identification method of neuro-uzzy Hammerstein model based on probability density function(PDF) is presented,which is different from the idea that mean squared error(MSE) is employed as the index function in traditional identification methods.Firstly,a neuro-fuzzy based Hammerstein model is constructed to describe the nonlinearity of Hammerstein process without any prior process knowledge.Secondly,a kind of special test signal is used to separate the link parts of the Hammerstein model.More specifically,the conception of PDF is introduced to solve the identification problem of the neuro-fuzzy Hammerstein model.The antecedent parameters are estimated by a clustering algorithm,while the consequent parameters of the model are identified by designing a virtual PDF control system in which the PDF of the modeling error is estimated and controlled to converge to the target.The proposed method not only guarantees the accuracy of the model but also dominates the spatial distribution of PDF of the model error to improve the generalization ability of the model.Simulated results show the effectiveness of the proposed method.

Identification of fractional order Hammerstein models based on mixed signals

An algorithm based on mixed signals is proposed,to solve the issues of low accuracy of identification algorithm,immeasurable intermediate variables of fractional order Hammerstein model,and how to determine the magnitude of fractional order.In this paper,a special mixed input signal is designed to separate the nonlinear and linear parts of the fractional order Hammerstein model so that each part can be identified independently.The nonlinear part is fitted by the neural fuzzy network model,which avoids the limitation of polynomial fitting and broadens the application range of nonlinear models.In addition,the multi-innovation Levenberg-Marquardt(MILM)algorithm and auxiliary recursive least square algorithm are innovatively integrated into the parameter identification algorithm of the fractional order Hammerstein model to obtain more accurate identification results.A simulation example is given to verify the accuracy and effectiveness of the proposed method.

Identification and nonlinear model predictive control of MIMO Hammerstein system with constraints

This work is concerned with identification and nonlinear predictive control method for MIMO Hammerstein systems with constraints. Firstly, an identification method based on steady-state responses and sub-model method is introduced to MIMO Hammerstein system. A modified version of artificial bee colony algorithm is proposed to improve the prediction ability of Hammerstein model. Next, a computationally efficient nonlinear model predictive control algorithm(MGPC) is developed to deal with constrained problem of MIMO system. The identification process and performance of MGPC are shown. Numerical results about a polymerization reactor validate the effectiveness of the proposed method and the comparisons show that MGPC has a better performance than QDMC and basic GPC.

Recursive least squares identification for piecewise affine Hammerstein models

Purpose-The purpose of this paper is to probe the recursive identification of piecewise affine Hammerstein models directly by using input-output data.To explain the identification process of a parametric piecewise affine nonlinear function,the authors prove that the inverse function corresponding to the given piecewise affine nonlinear function is also an equivalent piecewise affine form.Based on this equivalent property,during the detailed identification process with respect to piecewise affine function and linear dynamical system,three recursive least squares methods are proposed to identify those unknown parameters under the probabilistic description or bounded property of noise.Design/methodology/approach-First,the basic recursive least squares method is used to identify those unknown parameters under the probabilistic description of noise.Second,multi-innovation recursive least squares method is proposed to improve the efficiency lacked in basic recursive least squares method.Third,to relax the strict probabilistic description on noise,the authors provide a projection algorithm with a dead zone in the presence of bounded noise and analyze its two properties.Findings-Based on complex mathematical derivation,the inverse function of a given piecewise affine nonlinear function is also an equivalent piecewise affine form.As the least squares method is suited under one condition that the considered noise may be a zero mean random signal,a projection algorithm with a dead zone in the presence of bounded noise can enhance the robustness in the parameter update equation.Originality/value-To the best knowledge of the authors,this is the first attempt at identifying piecewise affine Hammerstein models,which combine a piecewise affine function and a linear dynamical system.In the presence of bounded noise,the modified recursive least squares methods are efficient in identifying two kinds of unknown parameters,so that the common set membership method can be replaced by the proposed methods.

Modeling of a distillation column based on NARMAX and Hammerstein models

The modeling of distillation column process is a very challenging problem because of the complex dynamic behavior.This paper investigates a Nonlinear Autoregressive Moving Average with eXogenous input(NARMAX)model,and a Hammerstein model to approximate the evolution of the overhead temperature in a separation system.The model development and validation are studied through experiments carried out on a distillation plant of laboratory scale.Three model order selection criteria such as Aikeke’s Information Criterion(AIC),Root Mean Square Error(RMSE)and Nash–Sutcliffe Efficiency(NSE)are used to evaluate the prediction performance of the process behavior.The results illustrate that both models produce acceptable predictions but the NARMAX model outperforms the Hammerstein model.

PEMFC Identification Based on a Fractional-Order Hammerstein State-Space Model with ADE-BH Optimization

Considering the fractional-order and nonlinear characteristics of proton exchange membrane fuel cells(PEMFC),a fractional-order subspace identification method based on the ADE-BH optimization algorithm is proposed to establish a fractional-order Hammerstein state-space model of PEMFCs.Herein,a Hammerstein model is constructed by connecting a linear module and a nonlinear module in series to precisely depict the nonlinear property of the PEMFC.During the modeling process,fractional-order theory is combined with subspace identification,and a Poisson filter is adopted to enable multi-order derivability of the data.A variable memory method is introduced to reduce computation time without losing precision.Additionally,to improve the optimization accuracy and avoid obtaining locally optimum solutions,a novel ADEBH algorithm is employed to optimize the unknown parameters in the identification method.In this algorithm,the Euclidean distance serves as the theoretical basis for updating the target vector in the absorption-generation operation of the black hole(BH)algorithm.Finally,simulations demonstrate that the proposed model has small output error and high accuracy,indicating that the model can accurately describe the electrical characteristics of the PEMFC process.

The Predictive Control Based on Hammerstein Model with NU=1

In acs paper,the generalized predictive control(GPC)law for Hammerstein model with control horizon NU=1 is presented and the algebraic equation satisfied by the GPC law is derived.Also,the simulation study shows tha tthe GPC based on Hammerstein system is such and algorithm which can be controlled by numerical computer with rather strong Robustness but without strict demand for the model.

基于Hammerstein模型的执行机构非线性参数辨识

针对火电机组中流过执行机构的介质流量难以测量,导致执行机构的非线性特性无法直接求取这一问题,提出用构建Hammerstein模型代替直接测量介质流量的间接测量法,进而求取执行机构的非线性特性,然后分别使用粒子群算法(PSO)和樽海鞘群算法(SSA),辨识所构建的Hammerstein模型的参数。另外,针对PSO算法和SSA算法辨识Hammerstein模型参数精度不高以及收敛速度慢的问题,提出了一种改进的粒子群-樽海鞘群的混合算法(IPS)。最后基于烟道挡板的指令数据与再热器出口温度数据对模型进行了仿真。仿真结果表明,提出的IPS算法能改善PSO算法的过早收敛问题,提高SSA算法的辨识速度。因此通过建立Hammerstein模型能够解决介质流量难以测量的执行机构非线性参数辨识问题,并且提出的IPS算法能准确且快速的辨识Hammerstein模型的各项参数。

基于改进最小角回归算法的Hammerstein模型辨识

针对一类未知时滞和阶次的Hammerstein模型的辨识问题,本文提出一种基于绝对角度停止准则最小角回归(AS-LAR)的稀疏辨识方法,该方法可以同时辨识出Hammerstein模型的时滞、阶次和参数.首先,通过引入最大非线性阶次和输入回归长度,将系统表示成具有稀疏参数向量的高维辨识模型;然后,提出一种绝对角度停止准则,对最小角回归算法进行改进,并基于改进的AS-LAR算法获得稀疏参数向量的估计;最后,基于参数向量稀疏结构,估计出系统的时滞和阶次,并从估计的参数向量中提取和分离出系统线性部分和非线性部分的参数估计值.数值仿真和水箱实例结果表明,提出的辨识方法有效,且与其它辨识方法相比,具有估计精度高、计算量小、速度快等特点.

超磁致伸缩材料迟滞特性的新Hammerstein建模

超磁致伸缩材料(Giant Magnetostrictive Material,GMM)作为一种新型功能材料,因其具有磁-机耦合系数大、响应速度快、频响特性好等优点而被广泛应用于能量采集、微位移驱动、精密定位控制等领域,但材料复杂的迟滞非线性影响了其致动器的定位精度,为了辨识超磁致伸缩材料中存在的迟滞非线性,本文提出一种新Hammerstein模型建模方法。此方法的优点在于模型可以更好地逼近迟滞非线性,提供更高的精度,减少了串联环节的参数辨识工作量。首先,构建一个基于双曲函数的迟滞算子扩展空间的极限学习机模型,用其表示新Hammerstein模型中的静态非线性部分。其次,提取极限学习机模型的全连接层的权重和偏置参数用于构建新模型中的动态线性部分的状态空间方程,减少了传统模型中串联环节的模型参数辨识的工作。最后,建立了可以描述超磁致伸缩材料迟滞特性的新Hammerstein模型。新Hammerstein模型的建模相对误差为0.86%~3.69%,平均绝对误差为2.63%,比传统Hammerstein模型均方根误差低0.8μm左右,平均绝对误差提高将近4%。仿真结果证明了新Hammerstein模型对超磁致伸缩材料复杂迟滞特性建模的有效性。

Auxiliary Model Based Multi-innovation Stochastic Gradient Identification Methods for Hammerstein Output-Error System

Special input signals identification method based on the auxiliary model based multi-innovation stochastic gradient algorithm for Hammerstein output-error system was proposed.The special input signals were used to realize the identification and separation of the Hammerstein model.As a result,the identification of the dynamic linear part can be separated from the static nonlinear elements without any redundant adjustable parameters.The auxiliary model based multi-innovation stochastic gradient algorithm was applied to identifying the serial link parameters of the Hammerstein model.The auxiliary model based multi-innovation stochastic gradient algorithm can avoid the influence of noise and improve the identification accuracy by changing the innovation length.The simulation results show the efficiency of the proposed method.

应用粒子群优化算法辨识Hammerstein模型

非线性系统的辨识一直是现代辨识领域中的一个主要课题。针对非线性系统中Hammerstein模型,文中提出了利用群集智能中的粒子群优化算法(PSO)对非线性模型进行辨识。讨论了PSO的基本算法与参数初值的设置与选择方法。通过仿真实验说明:与非线性最小二乘法相比PSO算法对于非线性辨识的有效性和鲁棒性。PSO算法是一种有效的解决优化问题的群集智能算法,它的突出特点是算法中需要选择的参数少,程序实现简单,并在种群数量、寻优速度等方面较其他进化算法具有一定的优势。尤其是在高噪信比情况下,也收到较满意的结果。

非线性Hammerstein模型预测控制策略及其在pH中和过程中的应用

所有实际工业过程都包含一定程度的非线性,如pH中和过程由于其本身的强非线性是工业过程控制中具有挑战性的难题,但至今为止仍缺乏有效的非线性控制方法。将基于差分方程模型的模型预测控制策略(model predictive control,MPC)推广到包含一个静态非线性多项式函数和一个线性差分方程动态环节的非线性Hammerstein系统,详细描述了基于静态非线性多项式函数的最优控制作用求解方法,提出了一套新的非线性Hammerstein MPC控制策略(nonlinear Hammerstein predictive control,NLHPC)。pH中和过程控制仿真和控制实验表明,NLHPC的控制结果好于工业上常用的非线性PID(nonlinear PID,NL-PID)控制器。

辨识Hammerstein模型的两步法

本文利用稳态和动态信息提出了一种辨识Ｈａｍｍｅｒｓｔｅｉｎ模型的新方法─—两步法．该方法利用稳态信息获取非线性增益的强一致性估计；利用动态信息获取线性子系统未知参数的强一致性估计．该方法具有计算简单和辨识精度高等优点．最后的仿真结果说明了该方法的有效性和实用性．

一种基于Hammerstein模型的数字预失真算法

记忆非线性放大器的预失真问题一直是预失真技术的难点.本文首先介绍了数字预失真器的几种模型结构和识别算法,它们虽然能够很好地实现功率放大器的线性化,却存在运算量较大的问题.结合LS算法和Hammerstein模型的优点,提出了一种基于Hammerstein模型的数字预失真算法,用几次简单的迭代运算代替一次复杂的直接运算,从而以较少的运算量,获得较好的线性化性能.通过计算机软件仿真验证了这种算法的有效性,它能以较少的参数,快捷、简便地实现记忆非线性功率放大器的预失真,显著提高了放大器的线性化性能.

辨识Hammerstein模型方法研究

提出了一种对单输入单输出Hammerstein模型的参数辨识方法。基本思想是:首先,将Hammerstein模型转换为一类中间模型。然后,提出利用一种改进的粒子群优化(improved particle swarm optimization,IPSO)算法获得中间模型的参数估计值。接着,通过相应的数学关系来达到对Hammerstein模型的辨识。最后,在数值仿真中,与使用其它辨识方法进行了比较,其结果表明了所给的参数辨识方法是切实可行的。

超磁致伸缩作动器的率相关Hammerstein模型与H∞鲁棒跟踪控制

利用Hammerstein模型对超磁致伸缩作动器(Giant magnetostrictive actuators,GMA)的率相关迟滞非线性进行建模,分别以改进的Prandtl-Ishlinskii(Modified Prandtl-Ishlinskii)模型和外因输入自回归模型(Autoregressive model with exogenous input,ARX)代表Hammerstein模型中的静态非线性部分和线性动态部分,并给出了模型的辨识方法.此模型能在1～100Hz频率范围内较好地描述GMA的率相关迟滞非线性.提出了带有逆补偿器和H∞鲁棒控制器的二自由度跟踪控制策略,实时跟踪控制实验结果证明了所提策略的有效性.