基于Volterra泛函级数的涡轮建模研究

给出了对非线性动态系统做任意精度逼近的Volterra级数高阶核的全新估算方法并将其应用在涡喷发动机的转速控制上。该方法在核函数理论基础上,构造线性空间,将求解Volterra级数各阶核的问题转化为求输出观测向量在希尔伯特空间中某一子空间上的投影的问题,使原本复杂的非线性系统的Volterra级数的逼近问题在线性空间中以向量内积的方式得到解决。与其他时域或频域估算Volterra核的方法相比较,该算法的优点在于理论体系严密、计算量不随阶数增高而成几何级数增加、辨识精度高。该方法理论上能够估算任意阶核,弥补了现有方法难以估算四阶以上核的缺点,可应用于动态系统和强非线性系统的建模。将发动机动态过程描述为四阶的Volterra级数模型。     

基于递推批量最小二乘的Volterra级数辨识方法

针对用批量最小二乘方法进行 Volterra级数在线辨识计算量大 ,所需数据存储空间多 ,以及实际应用时自相关矩阵易出现病态的不足 ,提出了一种基于递推批量最小二乘的 Volterral级数辨识方法 .该方法利用观测矩阵维数固定的批量最小二乘辨识 ,形式简单 ,所需数据存储空间小 ;同时利用递推辨识的思想 ,避免了对矩阵直接求逆 ,减小了计算量 .另外 ,为了防止自相关矩阵出现病态 ,文中引入影响因子的概念对观测数据进行取舍 ,一定程度上增强辨识的数值稳定性 .最后通过一个工程实例验证了该方法的有效性 .该方法为 Volterra级数的在线辨识提供了一个重要方法     

非线性系统的参数空间分割辨识方法

本文提出了一种新的非线性系统Volterra级数模型辨识方法,为非线性系统辨识中 的“维数灾难”问题提供了一种满意的解决．算法中参数空间分割和模型辨识同时完成,降 维依据采用输出拟合结果的均方误差,最终得到输出拟合均方误差意义上的准最优解．本算 法也可以作为非线性系统模型的结构辨识算法,并可以直接推广应用于其它很大一类非线性 系统模型．仿真试验结果表明,算法计算量小,精度高,并具有较好的稳定性,可以应用于 在线实时辨识．     

基于谐波探测理论功率放大器线性化仿真研究

Volterra级数是一种用于解决非线性问题数学模型,在功率放大器线性化领域中,其庞大的计算难度限制了实际线性化处理的效果。为了解决Volterra级数计算量过大的问题,使用谐波探测方法替代Volterra级数,使用多个简单多项式对功率放大器复杂的记忆非线性特性进行建模,结合该模型与前馈线性化结构,提出了一个基于谐波检测的数字前馈结构。该数字前馈方法避免了前馈方法中时延因素对于功率放大器线性化效果的影响。仿真中,上述方法提供了平均20dB的抑制效果,验证了谐波探测理论应用于功率放大器线性化领域的可行性。     

基于线性空间投影的计算Volterra级数高阶核的方法

研究了对非线性动态系统作任意精度逼近的Volterra级数高阶核的全新估计方法。该方法在核函数理论基础上构造特殊线性空间,将求解Volterra级数的各阶核的问题转换为求用输出观测向量在希尔伯特空间中某一子空间上的投影问题,使原本复杂、难以计算的非线性系统的Volterra级数的逼近问题在所构建的线性空间中巧妙地以向量内积的方式解决,并给出了具体算法。相比于其他时域或频域估计Volterra核的方法,该算法的优点在于理论体系严密、计算量不会随着阶数增高而呈几何级数增加,辨识精度高,理论上能够辨识出任意阶的核,弥补了迄今现有的各种估计Volterra核的方法难以估计超过四阶或更高阶核的缺点,特别能够应用在对动态系统和强非线性系统的建模上。仿真研究的结果证明了该方法的有效性。     

一种泛函级数建模的新方法及其应用

针对非线性动态系统较难做任意精度逼近的这一问题,提出了使用Volterra级数高阶核估算的全新估计方法。该方法在核函数理论基础上,构造特殊线性空间,将求解Volterra级数的各阶核的问题转化为求用输出观测向量在希尔伯特空间中某一子空间上的投影的问题,使原本复杂、难于计算的非线性系统的Volterra级数的逼近问题在所构建的线性空间中巧妙地以向量内积的方式解决。给出了具体计算方法。相比于其他时域或频域估计Volterra核的方法,该算法的优点在于理论体系严密、计算量不会随着阶数增高而成几何级数增加,辨识精度高,理论上能够辨识出任意阶的核,改善了现有的估计Volterra核的方法难以估计超过4阶或更高阶核的缺点,特别能够应用在对动态系统和强非线性系统的建模上。通过对电厂汽轮机轴系统的辨识和仿真,证明了该方法的有效性。     

非线性系统广义脉冲响应函数的盲辨识

探讨减少非线性系统广义脉冲响应函数（GIRF）盲辨识所需计算量问题。 基于线性MIMO模型，应用多项式矩阵理论和子空间盲辨识技术，研究使用部分噪声向量对非线性Volterra系统的GIRF盲辨识方法。该方法的优点是能有效减少GIRF盲辨识所需的计算量。这对GIRF盲辩识方法的在线应用是有利的。仿真结果说明了这一方法的有效性。     

基于自适应模糊聚类的神经网络软测量建模方法

提出一种基于模糊聚类的神经网络软测量建模方法．该方法采用数据分组训练、自动确定模糊分类数、在线测量时分类中心自适应修正，降低了计算量，提高了建模精度．将该算法用于步进式加热炉钢坯温度预报的仿真结果表明，它能够解决钢坯温度难以在线测量的问题。     

现代温室温度系统在线建模

在分析温室温度系统机理模型的基础上,分别采用ARMAX 模型和ARIMAX 模型描述温度系统． 选择温室外温度、相对湿度、太阳辐射强度和风速作为系统扰动输入变量,选择温室内温度作为系统输出变 量．采用统计假设检验和模型拟合度分析相结合的方法确定模型结构,采用渐消记忆递推增广最小二乘法在 线辨识模型参数,并构造智能监督级监控在线建模过程．最后对4 输入或3 输入（忽略风速）的ARMAX 模型 或ARIMAX 模型相互组合,总计4 种模型的在线建模及仿真结果进行了对比分析．仿真试验结果表明,带智 能监督级的渐消记忆递推增广最小二乘在线建模能够较好地描述现代温室温度系统的动力学特性．     

大型装备传动系统非线性频谱特征提取与故障诊断

基于Volterra级数的非线性频谱分析方法,建立了大型数控装备传动系统伺服电机的非线性频谱模型,对传动系统两类参数型故障的频谱特征进行了分析.在此基础上,提出一种实用的在线频谱特征提取与故障识别方法,采用自适应辨识算法求解时域Volterra核,用快速多维傅立叶变换获得非线性频谱特征.实验结果表明,该方法实时性好,故障识别率高.     

Nonlinear thermal system identification using fractional Volterra series

Linear fractional differentiation models have already proven their efficacy in modeling thermal diffusive phenomena for small temperature variations involving constant thermal parameters such as thermal diffusivity and thermal conductivity. However, for large temperature variations, encountered in plasma torch or in machining in severe conditions, the thermal parameters are no longer constant, but vary along with the temperature. In such a context, thermal diffusive phenomena can no longer be modeled by linear fractional models. In this paper, a new class of nonlinear fractional models based on the Volterra series is proposed for modeling such nonlinear diffusive phenomena. More specifically, Volterra series are extended to fractional derivatives, and fractional orthogonal generating functions are used as Volterra kernels. The linear coefficients are estimated along with nonlinear fractional parameters of the Volterra kernels by nonlinear programming techniques. The fractional Volterra series are first used to identify thermal diffusion in an iron sample with data generated using the finite element method and temperature variations up to 700 K. For that purpose, the thermal properties of the iron sample have been characterized. Then, the fractional Volterra series are used to identify the thermal diffusion with experimental data obtained by injecting a heat flux generated by a 200 W laser beam in the iron sample with temperature variations of 150 K. It is shown that the identified model is always more accurate than the finite element model because it allows, in a single experiment, to take into account system uncertainties.     

Choice of free parameters in expansions of discrete-time Volterra models using Kautz functions

This work tackles the problem of modeling nonlinear systems using Volterra models based on Kautz functions. The drawback of requiring a large number of parameters in the representation of these models can be circumvented by describing every kernel using an orthonormal basis of functions, such as the Kautz basis. The resulting model, so-called Wiener/Volterra model, can be truncated into a few terms if the Kautz functions are properly designed. The underlying problem is how to select the free-design complex poles that fully parameterize these functions. A solution to this problem has been provided in the literature for linear systems, which can be represented by first-order Volterra models. A generalization of such strategy focusing on Volterra models of any order is presented in this paper. This problem is solved by minimizing an upper bound for the error resulting from the truncation of the kernel expansion into a finite number of functions. The aim is to minimize the number of two-parameter Kautz functions associated with a given series truncation error, thus reducing the complexity of the resulting finite-dimensional representation. The main result is the derivation of an analytical solution for a sub-optimal expansion of the Volterra kernels using a set of Kautz functions.     

A methodology for control-relevant nonlinear system identification using restricted complexity models

A broadly-applicable, control-relevant system identification methodology for nonlinear restricted complexity models (RCMs) is presented. Control design based on RCMs often leads to controllers which are easy to interpret and implement in real-time. A control-relevant identification method is developed to minimize the degradation in closed-loop performance as a result of RCM approximation error. A two-stage identification procedure is presented. First, a nonlinear ARX model is estimated from plant data using an orthogonal least squares algorithm; a Volterra series model is then generated from the nonlinear ARX model. In the second stage, a RCM with the desired structure is estimated from the Volterra series model through a model reduction algorithm that takes into account closed-loop performance requirements. The effectiveness of the proposed method is illustrated using two chemical reactor examples.     

基于Volterra模型的预测控制及应用

由于工业实践的需要,非线性预测控制近年来受到广泛地关注.Volterra模型是一类特殊的非线性模型,非常适合描述工业过程中的无记忆非线性对象.传统的基于Volterra模型的控制器合成法及迭代计算预测控制器法计算量大,且不便于处理控制约束.非线性模型预测控制求解是典型的非线性规划问题,序列二次规划(sequential quadratic program,SQP)算法是求解非线性规划问题常用方法之一.针对Volterra非线性模型预测控制求解问题,本文将滤子法与一种信赖域SQP算法相结合,提出一种改进SQP算法用于基于非线性Volterra模型的带控制约束的多步预测控制求解,并分析了所提方法的收敛性.工业实例仿真结果证实了所提方法的可行性与有效性.     

Shape description by time series

Time series modeling techniques are adapted to represent or describe two-dimensional closed contours. Both linear and nonlinear models are fitted. It is found that to detect small changes in shape nonlinear modeling is necessary, even though linear models may be sufficient to differentiate between shapes which differ widely. A nonlinear model called the noncausal quadratic Volterra model is developed for the purpose. Implementation is illustrated with shapes of aircraft     

稀疏的归一化功放模型及预失真应用*

针对射频功放的非线性特性进行了研究,提出一种新的稀疏化的Volterra级数模型。该模型基于压缩感知算法,将稀疏系统的辨识等效为信号的重构问题,利用正则正交匹配（ROMP）算法对核系数进行稀疏化并选择出活跃的核系数。将提出的模型与记忆多项式（MP）模型、通用记忆多项式（GMP）模型进行比较,较MP模型的建模精度提升10.7dB,模型系数减少25%,较GMP模型的建模精度提升3.9dB,但模型系数减少84.58%。仿真结果表明：提出的方法实现良好的预失真线性化性能,极大地降低模型系数,优于传统的功放行为模型。由此验证对功放的线性化技术发展具有参考价值。     

基于Volterra泛函级数的非线性系统的鲁棒辨识

针对弱非线性系统的鲁棒建模问题, 基于Volterra泛函级数, 结合集员辨识理论, 提出了广义频率响应函数的鲁棒辨识方法, 形成了一套较完整的弱非线性系统的鲁棒建模方法, 仿真结果表明该方法是行之有效的.     

Comparative nonlinear modeling of renal autoregulation in rats:Volterra approach versus artificial neural networks

In this paper, feedforward neural networks with two types of activation functions (sigmoidal and polynomial) are utilized for modeling the nonlinear dynamic relation between renal blood pressure and flow data, and their performance is compared to Volterra models obtained by use of the leading kernel estimation method based on Laguerre expansions. The results for the two types of artificial neural networks and the Volterra models are comparable in terms of normalized mean square error (NMSE) of the respective output prediction for independent testing data. However, the Volterra models obtained via the Laguerre expansion technique achieve this prediction NMSE with approximately half the number of free parameters relative to either neural-network model. However, both approaches are deemed effective in modeling nonlinear dynamic systems and their cooperative use is recommended in general