基于SVR的非线性动态系统建模方法研究

提出一种基于支持向量回归机(SVR)的非线性动态系统建模方法。用非线性静态子环节和线性动态子环节串联——Hammerstein模型来描述非线性动态系统。然后,通过函数展开将Hammerstein模型的非线性传递函数转换为等价的线性形式,从而建立起线性中间模型。再由SVR算法辨识出中间模型参数。最后,通过中间模型参数与Hammerstein模型参数之间的关系,实现原系统的非线性静态环节和线性动态环节的同时辨识。用非线性动态系统标定实验数据进行测试,建模结果表明所提方法具有如下优点：1)只需进行一次动态标定实验; 2)能给出非线性动态模型的数学解析表达式;3)充分利用SVR的优点,使所建模型具有更好的鲁棒性。该研究为非线性动态系统建模又提供了一种新方法。     

应用遗传算法辨识Hammerstein模型

基于遗传算法,提出了一种辨识Hammerstein模型的方法,该方法能够克服有色观测噪声的污染,获得非线性静态环节参数和线性动态环节参数的无偏估计,并与Hammerstein模型的MSLS辨识方法进行了比较,仿真结果说明了该方法的有效性。     

非线性动态系统建模方法研究

讨论了一类非线性动态系统建模的新方法。首先,假设原非线性动态系统可以用Hammerstein模型来表示。然后,将Hammerstein模型的非线性传递函数转换为等价的线性形式,从而建立起中间模型。接下来,利用粒子群优化（Particle Swarm Optimization,PSO）算法辨识出中间模型参数。最后,通过中间模型参数与Hammerstein模型参数之间的关系,推出非线性静态环节和线性动态环节的参数,从而实现原非线性动态系统建模。为了进一步增强建模的性能,提出了利用一种改进的粒子群优化（Improved Particle Swarm Optimization,IPSO）算法。仿真结果说明了该方法的合理性和有效性。     

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.     

非线性动态传感器系统的H模型神经网络辨识

针对非线性动态传感器模型辨识问题,提出一种新的Hammerstein模型神经网络结构辨识法。非线性动态传感器系统采用Hammerstein模型描述,将系统分解为非线性静态增益串接线性动态环节。再设计一种网络权系数对应于相应的Hammerstein模型参数的新型神经网络结构,推导了基于反向传播的网络权系数调整方法。通过网络迭代训练同时得到静态与动态两个环节的模型参数。最后通过一个H模型的数值仿真来验证方法的有效性,仿真结果表明所提辨识方法是有效的。     

Hammerstein模型辨识的回顾及展望

Hammerstein模型是一类具有特定结构的典型非线性模型,由静态非线性环节和动态线性环节串联而成,能较好地反映过程特征的特点,可以描述一大类非线性过程.本文结合Hammerstein模型辨识的基本过程和特点,从Hammerstein模型中间变量不可测量的角度出发,首先按静态非线性环节与动态线性环节同步辨识法和分步辨识法综述了Hammerstein模型的相关理论和方法;然后,分析了现有的基于Hammerstein模型的控制系统设计方案;最后对Hammerstein系统未来可能的研究提出若干看法.     

质子交换膜燃料电池的分数阶非线性状态空间模型研究

针对质子交换膜燃料电池(PEMFC)发电过程中的分数阶和非线性特性,本文提出了一种分数阶子空间辨识方法建立了PEMFC非线性状态空间模型.首先,为了降低建模复杂度,采用典型相关分析法和相关分析法确定了模型输入变量;其次,将分数阶微分理论与Hammerstein模型子空间辨识方法相结合,采用Poisson矩函数对输入输出数据进行预处理,构造了子空间辨识方法的输入输出矩阵,并引入分数阶短时记忆法减少辨识算法计算量;最后,选取多项式作为Hammerstein模型前端静态非线性环节,采用模糊遗传算法优化系统分数阶阶次和系数矩阵.仿真结果验证了算法的有效性,改进的辨识算法可以明显减小计算时间,所得PEMFC辨识模型能够准确地描述PEMFC的动态过程.     

废气氧传感器Hammerstein模型结构的确定

研究了废气氧(EGO)传感器Hammerstein模型结构辨识方法。静态非线性函数选用双曲正切与多项式组合形式,动态线性环节分别选用带外生变量的自回归(ARX)模型、输出误差(OE)模型和Box-Jenkins(BJ)模型结构。采用交叉准则法进行参数估计和阶次选择,通过仿真比较对模型进行检验。结果表明:最终输出误差(FOE)准则和最终预报误差(FPE)准则均适用于用估计数据选择阶次,但前者比后者更可靠。基于预测误差法的3阶OE模型和BJ模型均可用于EGO传感器Hammerstein模型动态线性环节的建模。     

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。     

利用SVR的非线性动态系统Wiener模型补偿

提出一种新的利用支持向量回归机(SVR)的非线性动态系统维纳(Wiener)模型补偿方法.首先,将非线性动态系统用Wiener模型描述成线性动态子环节和非线性静态增益;再设计结构上与之对应的Wiener补偿器,并进一步将其变换为可用SVR辨识的线性中间模型;最后,通过关系矩阵将中间模型的估计值转换为Wiener补偿器的实际参数.用实际压力响应系统的动态标定实验数据进行测试,结果表明,与最小二乘方法比较,所提方法建立的Wiener补偿器具有更强的抗干扰能力.因此,该研究为非线性动态系统补偿又提供了一种可选方法.     

传感器动态非线性补偿方法及DSP实现

利用Hammerstein模型描述传感器的动态非线性。动态非线性环节表示为静态非线性子环节和动态线性子环节的串联,相应的动态非线性补偿分为两个阶段：动态线性补偿和静态非线性校正。通过仿真和对腕力传感器响应的补偿验证了两阶段补偿方法的可行性。研制了基于DSP的动态非线性实时补偿系统,通过实验验证了动态非线性补偿方法的有效性。     

含有色噪声的神经模糊Hammerstein模型分离辨识

针对实际工业过程中普遍存在的有色噪声,本文提出一种基于递推增广最小二乘算法的神经模糊Hammerstein模型辨识方法,突破了传统的Hammerstein模型迭代分离算法.首先,利用多信号源实现Hammerstein模型中静态非线性环节和动态线性环节的分离,大大简化了辨识过程,提高了串联环节参数的分离精度.其次,利用长除法将噪声模型用有限脉冲响应模型逼近,采用增广递推最小二乘法进行线性环节的参数估计.最后,采用神经模糊模型拟合静态非线性环节,同时设计了神经模糊模型参数的非迭代优化算法,改善了模型的使用范围.该方法保证了模型的预测精度,对含有色噪声的非线性系统具有较好的拟合效果.仿真结果验证了上述方法的有效性.     

Correlation analysis based MIMO neuro-fuzzy Hammerstein model with noises

A novel identification algorithm for neuro-fuzzy based MIMO Hammerstein system with noises by using the correlation analysis method is presented in this paper. A special test signal that contains independent separable signals and uniformly random multi-step signal is adopted to identify the MIMO Hammerstein system, resulting in the identification problem of the linear model separated from that of nonlinear part. As a result, it can circumvent the problem of initialization and convergence of the model parameters encountered by the existing iterative algorithms used for identification of MIMO Hammerstein model. Moreover, least square method based parameter identification algorithms of dynamic linear part and static nonlinear part are proposed to avoid the influence of noise. Examples are used to illustrate the effectiveness of the proposed method.     

Subspace identification of Hammerstein systems using least squares support vector machines

This paper presents a method for the identification of multiple-input-multiple-output (MIMO) Hammerstein systems for the goal of prediction. The method extends the numerical algorithms for subspace state space system identification (N4SID), mainly by rewriting the oblique projection in the N4SID algorithm as a set of componentwise least squares support vector machines (LS-SVMs) regression problems. The linear model and static nonlinearities follow from a low-rank approximation of a matrix obtained from this regression problem.     

Non-parametric identification of continuous-time Hammerstein systems using Gaussian process model and particle swarm optimization

This paper deals with a non-parametric identification of continuous-time Hammerstein systems using Gaussian process (GP) models. A Hammerstein system consists of a memoryless non-linear static part followed by a linear dynamic part. The identification model is derived using the GP prior model which is described by the mean function vector and the covariance matrix. This prior model is trained by the separable least-squares (LS) approach combining the linear LS method with particle swarm optimization to minimize the negative log marginal likelihood of the identification data. Then the non-linear static part is estimated by the predictive mean function of the GP, and the confidence measure of the estimated non-linear static part is evaluated by the predictive covariance function of the GP. Simulation results are shown to illustrate the proposed method.     

Hammerstein system identification through best linear approximation inversion and regularisation

Hammerstein systems are composed by the cascading of a static nonlinearity and a linear system. In this paper, a methodology for identifying such systems using a combination of least squares support vector machines (LS-SVM) and best linear approximation (BLA) techniques is proposed. To do this, a novel method for estimating the intermediate variable is presented allowing a clear separation of the identification steps. First, an approximation to the linear block is obtained through the BLA of the system. Then, an approximation to the intermediate variable is obtained using the inversion of the estimated linear block and the known output. Afterwards, a nonlinear model is calculated through LS-SVM using the estimated intermediate variable and the known input. To do this, the regularisation capabilities of LS-SVM play a crucial role. Finally, a parametric re-estimation of the linear block is made. The method was tested in three examples, two of them with hard nonlinearities, and was compared with four other methods showing very good performance in all cases. The obtained results demonstrate that also in the presence of noise, the method can effectively identify Hammerstein systems. The relevance of these findings lies in the fact that it is shown how the regularisation allows to bypass the usual problems associated with the noise backpropagation when the inversion of the estimated linear block is used to compute the intermediate variable.