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。     

Volterra高阶核的新算法在航空涡轮转速控制上的应用

针对航空发动机的转速控制这个难题,提出了对非线性动态系统做建模研究的Volterra泛函方法的任意高阶核估计方法;该方法在核(kernel method)理论基础上,构造线性空间,将求解Volterra泛函各阶核的问题转化为求输出观测向量在希尔伯特空间(Hilbert space)子空间上的分量,利用线性空间中向量内积的求解而间接辨识出复杂的非线性动态系统;相对于其它在时域或频域估计Volterra核的理论,该方法数学基础牢固、计算量不随辨识精度增高而大量增加、理论上能够对任意高阶核进行估计,可对强非线性动态系统进行辨识。     

基于Volterra 级数并行递推AP 算法的陀螺漂移预测

为了预测某导弹陀螺漂移趋势,以该陀螺漂移角速度时间序列为对象,建立基于Volterra级数的非线性时间预测模型,提出了一种基于Volterra级数的并行递推放射投影AP自适应算法.以系统Volterra核向量增量的模与某约束总和为损失函数,按照最陡下降原理导出各阶Volterra核更新公式;再利用矩阵求逆引理递推求取各阶Volterra子系统自相关逆矩阵导出算法.某导弹实测的陀螺漂移数据预测应用研究表明,该算法运算速度快、预测精度高.     

Volterra 泛函级数在非线性系统辨识中的应用

利用Volterra泛函级数描述非线性系统，将非线性系统辨识问题转化为标准的最小二乘问题，并通过QR分解进行求解，在对输入矩阵P进行Householder变换过程中，提出利用输入向量对输出向量的影响因子进行P阵的列选择，同时完成模型辨识，有效地克服了Volterra泛函数辨识中维数灾难问题，数字仿真表明了该方法的有效性。     

基于Volterra频域核辨识的非线性模拟电路故障诊断

基于Volterra级数时域频域混合模型,提出了辨识非线性模拟电路频域核的故障诊断方法.利用混合模型辨识算法和范德蒙特法估计各种故障状态下电路响应的前3阶频域核,提取故障特征并与相应的故障模式一起构成特征样本集,借助于支持向量机多分类器进行分类识别,实现非线性模拟电路的故障诊断.阐述了诊断原理及诊断步骤,并给出了诊断实例.仿真结果表明,该方法的故障识别率较高,便于计算机计算.     

基于系统仿真的非线性Volterra核求解算法

提出了基于系统仿真的Volterra级数中三阶以内核的求解算法。根据各阶Volterra级数核对输出的响应特性,构造了各阶Volterra核输出分量的方法;然后根据核的对称特性,提出了各阶核求解的直接解法。它较一般的辨识算法,速度和简洁性有很大提高。     

Volterra核的测量及在非线性模拟电路测试中的应用

研究了Volterra频域核的测量方法。提出一种利用优化正弦谐波信号作为系统的激励信号测量Volterra频域核的方法．将其用于测量2阶Volterra核时，没有1，3，5等奇数阶和4阶Volterra核的干扰，测量精度高．利用2阶Volterra频域核作为故障特征对非线性模拟电路进行故障诊断，仿真结果表明，故障识别率高，时问开销小，通用性强．     

基于Volterra级数模型的非线性系统自适应控制稳定性研究

研究一类单输入单输出非线性系统的自适应控制问题, 这类系统能用有限阶离散Volterra级数模型表示. 采用递推最小二乘算法进行参数估计, 并通过解高次方程得到控制律. 结合反馈型Volterra级数系统的局部L稳定理论, 证明了算法的局部收敛性质. 通过对一个化工连续搅拌反应器 (CSTR)的过程控制进一步验证了该算法的有效性.     

基于双阶跃信号输入的Volterra模型辨识

Volterra模型作为非线性领域的一种非线性模型,由于其对工业过程可以以任意精度逼近,使得该模型有很广泛的应用研究意义。在将该模型运用到实际控制系统中之前,模型的高精度辨识显得尤为重要。在以往针对Volterra模型的辨识算法中,基本上主要是采用通用辨识算法识别模型参数,比如最小二乘法及各种改进的最小二乘法。这些通用的辨识算法在辨识Volterra模型时,不能充分考虑其非线性特点,同样不能在辨识过程中充分利用该特点。本文在充分考虑Volterra模型非线性的前提下,提出了一种基于双阶跃信号输入的Volterra模型辨识算法,该算法辨识原理简单,计算量较小,论文最后将该辨识算法应用到典型非线性CSTR系统的的辨识中,辨识结果证明了算法的有效性。     

一类非线性系统的在线建模新方法

为减少非线性系统的Volterra级数模型在线建模的计算量，根据多模型合成的思想。提出一种基于预设模型在线合成被测系统当前Volterra级数模型的新方法。建立了模型合成的公式和方法．仿真实验表明。该方法具有较高的建模精度。能有效减少Volterra模型在线建模的计算量。并且易于工程实现．     

交通流量VNNTF神经网络模型多步预测研究

研究了VNNTF 神经网络（Volterra neural network trafficflow model,VNNTF） 交通流量混沌时间序列多步预测问题. 通过分析比较交通流量混沌时间序列相空间重构的嵌入维数和Volterra 离散模型之间的关系,给出了确定交通流量Volterra 级数模型截断阶数和截断项数的方法,并在此基础上建立了VNNTF 神经网络交通流量时间序列模型;设计了交通流量Volterra 神经网络的快速学习算法;最后,利用交通流量混沌时间序列对VNNTF 网络模型,Volterra 预测滤波器和BP 网络进行了多步预测实验,比较了多步预测结果的仿真图、绝对误差的柱状图以及归一化后的方均根;实验结果表明VNNTF 神经网络的多步预测性能明显优于Volterra 预测滤波器和BP 神经网络.     

交通流序列的Volterra自适应预测

基于混沌动力系统的相空间重构和非线性系统的Volterra级数,构建交通流的Volterra自适应预测模型.在应用小数据量法判定交通流存在混沌特性的前提下,分别用平均互信息法和虚假邻点法选取延滞时间和嵌入维数以实现对交通流时间序列的相空间重构.通过Volterra级数展开式建立非线性预测模型,采用LMS自适应算法实时调...     

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。     

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.     

Volterra-series-based equivalent nonlinear system method for subharmonic vibration systems

Subharmonics generation in the nonlinear system, directly using the traditional finite Volterra series, cannot generally represent the aimed system. In this paper, a new approach is presented, which is an extension of single finite Volterra series for representation and analysis of the subharmonic vibration system based on equivalent nonlinear system. The equivalent nonlinear system, which is constructed by pre-compensating the subharmonic vibration system with the super-harmonic nonlinear model, yields the input–output relation between the virtual source and the response of the aimed nonlinear system. Orthogonal least square method is employed to identify the truncated order of Volterra series and predominant Volterra kernels of the equivalent nonlinear system. The MGFRFs (modified generalised frequency response functions) of the equivalent nonlinear system is obtained from the data of the virtual source and response, and verified by comparing the response estimated by the MGFRFs with its true value. Therefore, the aimed subharmonic vibration system can be analysed by taking advantage of a truncated Volterra series based on the equivalent nonlinear system. Numerical simulations were carried out, whose results have shown that the proposed method is valid and feasible, and suitable to apply on representation and analysis of subharmonic vibration systems.     

On Convergence of Volterra Series Expansion of a Class of Nonlinear Systems

A fundamental issue in conducting the analysis and design of a nonlinear system via Volterra series theory is how to ensure the excitation magnitude and/or model parameters will be in the appropriate range such that the nonlinear system has a convergent Volterra series expansion. To this aim, parametric convergence bounds of Volterra series expansion of nonlinear systems described by a NARX model, which can reveal under what excitation magnitude or within what parameter range a given NARX system is able to have a convergent Volterra series expansion subject to any given input signal, are investigated systematically in this paper. The existing bound results often are given as a function of the maximum input magnitude, which could be suitable for single‐tone harmonic inputs but very conservative for complicated inputs (e.g. multi‐tone or arbitrary inputs). In this study, the output response of nonlinear systems is expressed in a closed form, which is not only determined by the input magnitude but also related to the input energy or waveform. These new techniques result in more accurate bound criteria, which are not only functions of model parameters and the maximum input magnitude but also consider a factor reflecting the overall input energy or wave form. This is significant to practical applications, since the same nonlinear system could exhibit chaotic behavior subject to a simple single‐tone input but might not with respect to other different input signals (e.g. multi‐tone inputs) of the same input magnitude. The results provide useful guidance for the application of Volterra series‐based theory and methods from an engineering point of view. The Duffing equation is used as a benchmark example to show the effectiveness of the results.     

Structured Singular Valued based robust nonlinear model predictive controller using Volterra series models

A methodology is proposed for designing a robust nonlinear model predictive controller based on a Volterra series model with uncertain coefficients. A key benefit of using the Volterra series model is that it can be split into a nominal and an uncertainty model thus permitting the application of robust analysis tools. The controller is based on the on-line solution of a robust performance test based on a Structured Singular Value norm. The cost function of the controller can be formulated to account for manipulated variable movement weighting, manipulated variable constraints and a terminal condition. Finally, the proposed methodology is applied to a single-input–single-output continuous stirred tank reactor problem and to a multiple-input–multiple-output pH neutralization process.