基于相对贡献指标的自组织RBF神经网络的设计

针对RBF（radial basis function）神经网络的结构和参数设计问题,本文提出了一种基于相对贡献指标的自组织RBF神经网络的设计方法。首先,提出一种基于相对贡献指标（relative contribution,RC）的网络结构设计方法,利用隐含层输出对网络输出的相对贡献来判断是否增加或删减RBF网络相应的隐含层节点,并且对神经网络结构调整过程的收敛性进行证明。其次,采用改进的LM（Levenberg-Marquardt algorithm）算法对调整后的网络参数进行更新,使网络具有较少的训练时间和较快的收敛速度。最后,对提出的设计方法进行非线性函数仿真和污水处理出水参数氨氮建模,仿真结果表明,RBF神经网络能够根据研究对象自适应地动态调整RBF结构和参数,具有较好的逼近能力和更高的预测精度。     

基于快速密度聚类的RBF神经网络设计

针对径向基函数（radial basis function,RBF）神经网络隐含层结构难以确定的问题,提出一种基于快速密度聚类的网络结构设计算法。该算法将快速密度聚类算法良好的聚类特性用于RBF神经网络结构设计中,通过寻找密度最大的点并将其作为隐含层神经元,进而确定隐含层神经元个数和初始参数;同时,引入高斯函数的特性,保证了每个隐含层神经元的活性;最后,用一种改进的二阶算法对神经网络进行训练,提高了神经网络的收敛速度和泛化能力。利用典型非线性函数逼近和非线性动态系统辨识实验进行仿真验证,结果表明,基于快速密度聚类设计的RBF神经网络具有紧凑的网络结构、快速的学习能力和良好的泛化能力。     

RBF神经网络的结构动态优化设计

针对径向基函数(Radial basis function, RBF)神经网络的结构设计问题, 提出一种结构动态优化设计方法. 利用敏感度法(Sensitivity analysis, SA)分析隐含层神经元的输出加权值对神经网络输出的影响, 以此判断增加或删除RBF神经网络隐含层中的神经元, 解决了RBF神经网络结构过大或过小的问题, 并给出了神经网络结构动态变化过程中收敛性证明; 利用梯度下降的参数修正算法保证了最终RBF网络的精度, 实现了神经网络的结构和参数自校正. 通过对非线性函数的逼近与污水处理过程中关键参数的建模结果, 证明了该动态RBF具有良好的自适应能力和逼近能力, 尤其是在泛化能力、最终网络结构等方面较之最小资源神经网络(Minimal resource allocation networks, MRAN)与增长和修剪RBF 神经网络(Generalized growing and pruning radial basis function, GGAP-RBF) 有较大提高.     

RBF神经网络在惯导系统传递对准中的应用

针对系统阶次较高时卡尔曼滤波实时性较差的特点,将径向基（radial basis function,RBF）神经网络替代卡尔曼滤波应用于舰载机惯导系统的传递对准。利用卡尔曼滤波的输入、输出作为RBF神经网络滤波的样本值进行训练,得到了神经网络的输出值,实现了惯导传递对准中的滤波功能。仿真结果表明将RBF神经网络用于传递对准,既获得了与卡尔曼滤波相当的精度,又有效地降低了系统的解算时间,提高了系统的实时性。     

基于距离和密度聚类的RBF网络结构设计

为确定径向基函数RBF(radial basis function)神经网络隐含层结构,并针对基于距离或密度聚类的RBF神经网络的限制,提出一种基于距离和密度聚类(GDD)算法的RBF神经网络.GDD算法通过计算每个样本的密度,各样本间的距离及相似条件(密度标准、距离标准),相似条件是根据样本分布而改变的,进行样本空间...     

基于RBF-AR的船舶变形极短期预报

统一空间基准是海上作战平台实现精准探测打击的重要保证,而船体角变形的存在将严重影响空间基准的建立。针对这一问题,提出一种基于状态相依自回归（state-dependent auto-regressive, SD-AR）与径向基（radial basis function, RBF）神经网络的极短期变形预报方法,实现船体角形变的实时预报,为后续角变形的补偿提供依据。不同于传统的时间序列预报方法,该模型用一组RBF网络来逼近SD-AR模型中的函数系数,并采用一种结构化的非线性参数优化方法（structured nonlinear parameter optimization method, SNPOM）辨识该模型。基于该RBF-AR预报模型,给出了船舶变形预报算法设计并进行了仿真实验。实验结果表明,该方法在船体变形预测精度上优于传统时间序列预测方法,具有较好的应用前景。     

径向基函数神经网络的一种两级学习方法

建立RBF(radial basis function)神经网络模型关键在于确定网络隐中心向量、基宽度参数和隐节点数.为设计结构简单,且具有良好泛化性能径向基网络结构,本文提出了一种RBF网络的两级学习新设计方法.该方法在下级由正则化正交最小二乘法与D-最优试验设计结合算法自动构建结构节俭的RBF网络模型;在上级通过粒子群优化算法优选结合算法中影响网络泛化性能的3个学习参数,即基宽度参数、正则化系数和D-最优代价系数的最佳参数组合.仿真实例表明了该方法的有效性.     

多元时间序列的Web Service QoS预测方法

为准确并多步预测Web服务的服务质量（quality of service,简称QoS）,方便用户选择更好的Web服务,提出了一种基于多元时间序列的QoS预测方法MulA-LMRBF （multiple step forecasting with advertisement-levenberg marquardt radial basis function）.充分考虑多个QoS属性序列之间的关联,采用平均位移法（average dimension,简称AD）确定相空间重构的嵌入维数和延迟时间,将QoS属性历史数据映射到一个动力系统中,近似恢复多个QoS属性之间的多维非线性关系.将短期服务提供商QoS广告数据加入数据集中,采用列文伯格-马夸尔特法（Levenberg-Marquardt,简称LM）算法改进的径向基（radial basis function,简称RBF）神经网络预测模型,动态更新神经网络的权重,提高预测精度,实现QoS动态多步预测.通过网络开源数据和自测数据的实验结果表明,该方法与传统方法相比有较好预测效果,更适合动态多步预测.     

机械手的在线鲁棒自适应神经网络跟踪控制

考虑了一类具有外界干扰和不确定性的机械手臂轨迹跟踪鲁棒控制问题. 控制器由自适应RBF(radial basis function)神经网络控制器和PD控制器组成. 采用基于神经元灵敏度和获胜神经元概念的GP–RBF算法, 在线确定神经网络的初始结构和参数. 当误差满足一定要求时, 根据Lyapunov稳定性理论的自适应律进一步调整网络权值, 以保证机械手位置误差和速度跟踪误差渐近收敛于零. 所设计的控制器可保证闭环系统的稳定性和鲁棒性. 仿真结果证明了本文方法的有效性.     

二阶 Newton 法训练径向基函数神经网络的算法研究

提出了一种混合加权距离测量（weighted distance measure ,weighted DM ）参数的构建和训练RBF（radial basis function）神经网络的两步批处理算法。该算法在引进了 DM 系数参数的基础上,采用Newton 法分别对径向基函数的覆盖参数、均值向量参数、加权距离测度系数以及输出权值进行了优化,并在优化过程中利用 OLS（orthogonal least squares）法来求解 New ton 法的方程组。通过实验数据,不仅分析了 New ton 法优化的各个参数向量对 RBF 网络训练的影响,而且比较了混合优化加权 DM 与RLS‐RBF（recursive least square RBF neural network）网络训练算法的收敛性和计算成本。所得到的结论表明整合了优化参数的加权 DM‐RBF 网络训练算法收敛速度比 RLS‐RBF 网络训练算法更快,而且具有比 LM‐RBF （Levenberg‐Marquardt RBF ）训练算法更小的计算成本,从而说明 OLS 求解的Newton 法对优化 RBF 网络参数具有重要应用价值。     

A sequential learning algorithm based on adaptive particle filtering for RBF networks

To address the problem of low filtering accuracy and divergence caused by unknown process noise statistics and local linearization in neural network state-space model, this paper proposes an adaptive process noise covariance particle filter algorithm for the radial basis function (RBF) networks. Using the algorithm, the evolution of the weights and centers of RBF networks is achieved sequentially in time by use of the extended Kalman particle filter algorithm, and the process noise covariance matrices are also obtained simultaneously by maximizing the evidence density function with respect to the process noise covariance matrices. Performance of the presented approach is evaluated by two function approximation problems. Experimental results show that the proposed approach obtains better prediction accuracy than other well-known training algorithms.     

A comparison of simultaneous state and parameter estimation schemes for a continuous fermentor reactor

This article proposes a maximum likelihood algorithm for simultaneous estimation of state and parameter values in nonlinear stochastic state-space models. The proposed algorithm uses a combination of expectation maximization, nonlinear filtering and smoothing algorithms. The algorithm is tested with three popular techniques for filtering namely particle filter (PF), unscented Kalman filter (UKF) and extended Kalman filter (EKF). It is shown that the proposed algorithm when used in conjunction with UKF is computationally more efficient and provides better estimates. An online recursive algorithm based on nonlinear filtering theory is also derived and is shown to perform equally well with UKF and ensemble Kalman filter (EnKF) algorithms. A continuous fermentation reactor is used to illustrate the efficacy of batch and online versions of the proposed algorithms.     

基于SVD的推广卡尔曼滤波及其在飞行状态和参数估计中的应用

基于矩阵的奇异值分解技术，本文提出一种鲁棒推广卡尔曼波新算法，并将该算法应用于飞行状态和参数估计中，该算法不仅具有很好的数值稳定性，而且无需任何变换即可处理相关噪声，且适于并行计算。两种不同型号飞机飞行数据计算结果表明；与ＥＫＦ相比，本文算法对不同初始值的不同噪声均可获得更准确的估计结果，并且对飞机机动形式、噪声水平，数据长度等要求不高，收敛性好。     

基于自适应扩展卡尔曼滤波与神经网络的HPA预失真算法

针对强记忆功放的非线性问题,提出一种基于自适应扩展卡尔曼滤波与神经网络的高功放(High power amplifier, HPA)预失真算法.采用实数固定延时神经网络(Real-valued focused time-delay neural network, RVFTDNN)对间接学习结构预失真系统中的预失真器和逆估计器进行建模,扩展卡尔曼滤波(Extended Kalman filter, EKF)算法训练神经网络,从理论上指出Levenberg-Marquardt(LM)算法是EKF算法的特殊情况,并用李亚普诺夫稳定性理论分析EKF算法的稳定收敛条件,推导出测量误差矩阵的自适应迭代公式.结果表明:自适应EKF算法的训练误差和泛化误差均比LM算法更低,预失真后的邻道功率比(Adjacent channel power ratio, ACPR)比LM算法改善了2dB.     

基于RBF神经网络辅助的自适应UKF算法研究

卡尔曼滤波能在测量噪声干扰下对系统状态进行无偏估计。但无论是扩展卡尔曼滤波（EKF）算法,还是无轨迹卡尔曼滤波（UKF）算法,都无法避免滤波发散现象。给出利用径向基函数(RBF)神经网络的自适应调整能力来对卡尔曼滤波输出进行校正,从而避免输出发散的算法。计算机模拟和实际应用表明,基于RBFNN的卡尔曼滤波算法可以有效防止输出发散。     

基于RBF神经网络辅助的自适应UKF算法

卡尔曼滤波能在测量噪声干扰下对系统状态进行无偏估计.但无论是扩展卡尔曼滤波(EKF)算法,还是无轨迹卡尔曼滤波(UKF)算法,都无法避免滤波发散现象.给出利用径向基函数(RBF)神经网络的自适应调整能力来对卡尔曼滤波输出进行校正,从而避免输出发散的算法.计算机模拟和实际应用表明,基于RBFNN的卡尔曼滤波算法可以有效防止输出发散.     

Critical evaluation of non-linear filter configurations for the state estimation of Continuous Stirred Tank Reactor

A systematic approach has been attempted to design a non-linear observer to estimate the states of a non-linear system. The neural network based state filtering algorithm proposed by A.G. Parlos et al. has been used to estimate the state variables, concentration and temperature in the Continuous Stirred Tank Reactor (CSTR) process. (CSTR) is a typical chemical reactor system with complex nonlinear dynamics characteristics. The variables which characterize the quality of the final product in CSTR are often difficult to measure in real-time and cannot be directly measured using the feedback configuration. In this work, the comparison of the performances of an extended Kalman filter (EKF), unscented Kalman filter (UKF) and neural network (NN) based state filter for CSTR that rely solely on concentration estimation of CSTR via measured reactor temperature has been done. The performances of these three filters are analyzed in simulation with Gaussian noise source under various operating conditions and model uncertainties.     

Online identification of nonlinear multivariable processes using self‐generating RBF neural networks

This paper addresses the problem of online model identification for multivariable processes with nonlinear and time‐varying dynamic characteristics. For this purpose, two online multivariable identification approaches with self‐organizing neural network model structures will be presented. The two adaptive radial basis function (RBF) neural networks are called as the growing and pruning radial basis function (GAP‐RBF) and minimal resource allocation network (MRAN). The resulting identification algorithms start without a predefined model structure and the dynamic model is generated autonomously using the sequential input‐output data pairs in real‐time applications. The extended Kalman filter (EKF) learning algorithm has been extended for both of the adaptive RBF‐based neural network approaches to estimate the free parameters of the identified multivariable model. The unscented Kalman filter (UKF) has been proposed as an alternative learning algorithm to enhance the accuracy and robustness of nonlinear multivariable processes in both the GAP‐RBF and MRAN based approaches. In addition, this paper intends to study comparatively the general applicability of the particle filter (PF)‐based approaches for the case of non‐Gaussian noisy environments. For this purpose, the Unscented Particle Filter (UPF) is employed to be used as alternative to the EKF and UKF for online parameter estimation of self‐generating RBF neural networks. The performance of the proposed online identification approaches is evaluated on a highly nonlinear time‐varying multivariable non‐isothermal continuous stirred tank reactor (CSTR) benchmark problem. Simulation results demonstrate the good performances of all identification approaches, especially the GAP‐RBF approach incorporated with the UKF and UPF learning algorithms. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一种自适应滤波方法在捷联惯导系统大失准角初始对准中的应用

为了对静基座大失准角捷联惯导系统(SINS)进行初始对准,建立了在静基座下基于四元数的SINS非线性误差模型。该误差模型无需对姿态误差角进行小角度假设。为了在观测噪声方差未知的情况下估计SINS失准角,提出一种在线估计观测噪声方差矩阵的自适应扩展卡尔曼滤波方法。仿真结果表明,该自适应滤波方法能在观测噪声方差未知的情况下有效地对静基座大失准角SINS进行初始对准。     

Affine modeling of nonlinear multivariable processes using a new adaptive neural network-based approach

This paper presents a new method for on-line identification of exact affine model for multivariable processes with nonlinear and time-varying behaviors. A self-generating radial basis function (RBF) neural network trained by growing and pruning algorithm for RBF (GAP–RBF) is utilized for deriving the affine model. The extended Kalman filter (EKF) is used for parameter adaptation in the GAP–RBF neural network. The growing and pruning criteria of the original GAP–RBF have been modified with the objective to enhance its performance in on-line identification. Simulation results on two nonlinear multivariable CSTR benchmark problems show an excellent performance of the proposed approach, incorporated with the modified GAP–RBF (MGAP–RBF) neural network, for affine modeling.