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.     

基于扩展卡尔曼滤波器的RBF神经网络学习算法

径向基函数（RBF）神经网络可广泛应用于解决信号处理与模式识别问题,目前存在一些学习算法用来确定RBF中心节点和训练网络,对于确定RBF中心节点向量值和网络权重值可以看作同一系统问题,因此该文提出把扩展卡尔曼滤波器（EKF）用于多输入多输出的径向基函数（RBF）神经网络作为其学习算法,当确定神经网络中网络节点的个数后,EKF可以同时确定中心节点向量值和网络权重矩阵,为提高收敛速度提出带有次优渐消因子的扩展卡尔曼滤波器（SFEKF）用于RBF神经网络学习算法,仿真结果说明了在学习过程中应用EKF比常规RBF神经网络有更好的效果,学习速度比梯度下降法明显加快,减少了计算负担。     

State of charge estimation for Li-ion battery based on model from extreme learning machine

Lithium-ion (Li-ion) battery state of charge (SOC) estimation is important for electric vehicles (EVs). The model-based state estimation method using the Kalman filter (KF) variants is studied and improved in this paper. To establish an accurate discrete model for Li-ion battery, the extreme learning machine (ELM) algorithm is proposed to train the model using experimental data. The estimation of SOC is then compared using four algorithms: extended Kalman filter (EKF), unscented Kalman filter (UKF), adaptive extended Kalman filter (AEKF) and adaptive unscented Kalman filter (AUKF). The comparison of the experimental results shows that AEKF and AUKF have better convergence rate, and AUKF has the best accuracy. The comparison from the radial basis function neural network (RBF NN) model also verifies that the ELM model has lighter computation load and smaller estimation error in SOC estimation process. In general, the performance of Li-ion battery SOC estimation is improved by the AUKF algorithm applied on the ELM model.     

A fast and accurate online self-organizing scheme for parsimonious fuzzy neural networks

In this paper, we present a fast and accurate online self-organizing scheme for parsimonious fuzzy neural networks (FAOS-PFNN), where a novel structure learning algorithm incorporating a pruning strategy into new growth criteria is developed. The proposed growing procedure without pruning not only speeds up the online learning process but also facilitates a more parsimonious fuzzy neural network while achieving comparable performance and accuracy by virtue of the growing and pruning strategy. The FAOS-PFNN starts with no hidden neurons and parsimoniously generates new hidden units according to the proposed growth criteria as learning proceeds. In the parameter learning phase, all the free parameters of hidden units, regardless of whether they are newly created or originally existing, are updated by the extended Kalman filter (EKF) method. The effectiveness and superiority of the FAOS-PFNN paradigm is compared with other popular approaches like resource allocation network (RAN), RAN via the extended Kalman filter (RANEKF), minimal resource allocation network (MRAN), adaptive-network-based fuzzy inference system (ANFIS), orthogonal least squares (OLS), RBF-AFS, dynamic fuzzy neural networks (DFNN), generalized DFNN (GDFNN), generalized GAP-RBF (GGAP-RBF), online sequential extreme learning machine (OS-ELM) and self-organizing fuzzy neural network (SOFNN) on various benchmark problems in the areas of function approximation, nonlinear dynamic system identification, chaotic time-series prediction and real-world regression problems. Simulation results demonstrate that the proposed FAOS-PFNN algorithm can achieve faster learning speed and more compact network structure with comparably high accuracy of approximation and generalization.     

Online State–Space Modeling Using Recurrent Multilayer Perceptrons with Unscented Kalman Filter

A nonlinear black-box modeling approach using a state–space recurrent multilayer perceptron (RMLP) is considered in this paper. The unscented Kalman filter (UKF), which was proposed recently and is appropriate for state–space representation, is employed to train the RMLP. The UKF offers a derivative-free computation and an easy implementation, compared to the extended Kalman filter (EKF) widely used for training neural networks. In addition, the UKF has a fast convergence rate and an excellent capability of parameter estimation which are appropriate for online learning. Through modeling experiments of nonlinear systems, the effectiveness of the RMLP trained with the UKF is demonstrated.     

地球卫星自主天文导航滤波方法性能分析

在系统硬件精度无法改进的条件下,滤波方法是影响地球卫星自主天文导航精度和实时性的最重要因素,本文针对地球卫星天文导航工程应用的需求,研究了目前导航系统中应用最为广泛的扩展卡尔曼滤波(EKF)、Unscented卡尔曼滤波(UKF)、Unscented粒子滤波(UPF)3种滤波方法,在滤波周期和噪声分布影响下的导航精度和实时性.半物理仿真结果表明,在相同仿真条件下,Unscented粒子滤波方法具有最高的导航精度,但计算量也最大,EKF方法计算量最小,导航精度最低.本文结果可为地球卫星自主导航系统中滤波方法的选择提供参考和依据.     

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.     

Variants of extended Kalman filtering approaches for Bayesian tracking

We provide a tutorial for a number of variants of the extended Kalman filter (EKF). In these methods, so called, sigma points are employed to tackle the nonlinearity of problems. The sigma points exactly represent the mean and the variance of the state distribution function in a dynamic state equation. The initially developed EKF variant, that is, unscented Kalman filter (UKF) (also called sigma point Kalman filter) shows enhanced performance compared with that of conventional EKF in the literature. Another variant, which is not well known, is central difference Kalman filter (CDKF) whose way to approximate the nonlinearity is based on the Sterling's polynomial interpolation formula instead of the Taylor series. Endeavor to reduce the computational load resulted in the development of square root versions of both UKF and CDKF, that is, square root unscented Kalman filter and square root central difference Kalman filter (SR‐CDKF). These SR‐versions are supposed to be numerically more stable than their original versions because the state covariance is guaranteed to be positive definite by avoiding the step of matrix decomposition. In this paper, we provide the step‐by‐step algorithms of above‐mentioned EKF variants with their pros and cons. We apply these filtering methods to a number of problems in various disciplines for performance assessment in terms of both mean squared error (MSE) and processing speed. Furthermore, we show how to optimize the filters in terms of MSE performance depending on diverse scenarios. According to simulation results, CDKF and SR‐CDKF show the best MSE performance in most scenarios; particularly, SR‐CDKF shows faster processing speed than that of CDKF. Therefore, we justify that SR‐CDKF is the most efficient and the best approach among the Kalman variants including the EKF for various nonlinear problems. The motivation of this paper targets at the contribution to the disseminative usage of the Kalman variants approaches, particularly, SR‐CDKF taking advantage of its estimating performance and high processing speed. Copyright © 2016 John Wiley & Sons, Ltd.     

基于EM-EKF算法的RBF-AR模型参数估计

为了利用EKF（extended Kalman filter）算法对RBF-AR（radial basis function network-based autoregressive）模型进行参数估计,重构了RBF-AR模型的网络结构,将其变换成一种新型的广义径向基函数（radial basis function,RBF）神经网络.与典型三层RBF网络结构相比,该广义RBF网络增加了线性输出加权层.为了克服基于EKF神经网络学习算法由于噪声统计特性未知导致滤波发散或者滤波精度不高的问题,利用EM（expectation maximization）算法对RBF-AR模型噪声协方差矩阵进行估计.同时,通过EKF滤波实时估计RBF-AR模型参数（系统状态）,EKF平滑过程得到了更加准确的期望估计.仿真结果显示,该方法用在此变形的RBF-AR模型结构中是有效的,特别在信噪比低的情况下,估计效果比SNPOM（structured nonlinear parameter optimization method）方法好,而且还能估计出噪声方差.F检验显示了两方法估计得到的标准偏差有显著性差异.     

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。     

Communication channel equalization using complex-valued minimalradial basis function neural networks

A complex radial basis function neural network is proposed for equalization of quadrature amplitude modulation (QAM) signals in communication channels. The network utilizes a sequential learning algorithm referred to as complex minimal resource allocation network (CMRAN) and is an extension of the MRAN algorithm originally developed for online learning in real-valued radial basis function (RBF) networks. CMRAN has the ability to grow and prune the (complex) RBF network's hidden neurons to ensure a parsimonious network structure. The performance of the CMRAN equalizer for nonlinear channel equalization problems has been evaluated by comparing it with the functional link artificial neural network (FLANN) equalizer of J.C. Patra et al. (1999) and the Gaussian stochastic gradient (SG) RBF equalizer of I. Cha and S. Kassam (1995). The results clearly show that CMRANs performance is superior in terms of symbol error rates and network complexity.     

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

Unscented Kalman filter (UKF) has been extensively used for state estimation of nonlinear stochastic systems, which suffers from performance degradation and even divergence when the noise distribution used in the UKF and the truth in a real system are mismatched. For state estimation of nonlinear stochastic systems with non-Gaussian measurement noise, the Masreliez–Martin extended Kalman filter (EKF) gives better state estimates in relation to the standard EKF. However, the process noise and the measurement noise covariance matrices should be known, which is impractical in applications. This paper presents a robust Masreliez–Martin UKF which can provide reliable state estimates in the presence of both unknown process noise and measurement noise covariance matrices. Two numerical examples involving relative navigation of spacecrafts demonstrate that the proposed filter can provide improved state estimation performance over existing robust filtering approaches. Vision-aided robot arm tracking experiments are also provided to show the effectiveness of the proposed approach.     

SSUKF-WNN算法及其在飞行器气动力建模中的应用

针对传统小波网络算法的不足,提出一种基于改进无迹Kalman滤波(UKF)的小波网络算法.该算法使用一种基于简化球形分布Sigma点的UKF(SSUKF)来训练小波网络的参数,以提高小波网络的学习性能和训练质量.飞行器气动力建模算例表明,相对于BP算法和EKF算法,SSUKF算法训练的小波网络收敛速度更快,估计精度更高,计算量更小.同时也为飞行器的气动力建模提供了一种有效可行的手段.     

基于EKF滤波的倒立摆神经网络控制研究

为解决一类带干扰的模型不确定倒立摆系统中存在的两类未知项——未知函数和外界干扰,采用了基于Lyapunov函数稳定性的神经网络控制方法设计控制器。控制器设计中利用扩展卡尔曼滤波(EKF)消除系统观测噪声,获取系统状态的估计值,进而利用径向基函数(RBF)神经网络良好的逼近性来近似设计的控制律中的未知项。最后在倒立摆系统中对设计的神经网络控制器进行了仿真研究,仿真结果表明所设计的控制器能有效抑制外界干扰,在精确控制倒立摆的同时可以保证控制系统的稳定性和快速性。     

基于UKF的两轮自平衡机器人姿态最优估计研究

针对扩展卡尔曼滤波器(EKF)设计困难并且容易发散的问题,提出基于采样卡尔曼滤波(UKF)的方法解决滤波器设计及收敛问题,并补偿低成本的惯性传感器陀螺仪和加速度计的误差,从而得到机器人姿态的最优估计．将滤波后的模型应用到两轮自平衡机器人系统,实验结果表明UKF参数设计简单,姿态估计误差小于EKF,方差估计优于EKF,估计精度、计算量基本与EKF相当．因此,UKF能够满足两轮自平衡机器人快速机动过程中的实时姿态估计要求．     

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.     

基于无迹卡尔曼滤波估算电池SOC

为了实现在线估计汽车动力电池的荷电状态（SOC）,提出了结合神经网络的无迹卡尔曼滤波算法。以Thevenin电路为等效电路模型,建立了状态空间表达式,采用最小二乘算法对模型参数进行辨识。在此基础上,利用神经网络算法拟合电池的荷电状态与模型各个参数之间的函数关系,经过多次实验,确定了神经网络算法的收敛曲线,此方法比传统的曲线拟合精度高。介绍了扩展卡尔曼滤波和无迹卡尔曼滤波的原理,并设计了等效电路模型验证实验、电池的SOC测试实验和算法的收敛性实验。实验结果表明,在不同的工况环境下,该方法估计SOC具有可在线估算、估算精度高和环境适应度高等优点,最大误差小于4%。最后验证了结合神经网络的无迹卡尔曼滤波的算法具有较好的收敛性和鲁棒性,可以有效解决初值估算不准确和累计误差的问题。     

一种基于改进型Logistic映射的混沌信号估算跟踪方法

虽然无先导卡尔曼滤波(UKF)技术在性能上要优于一阶线性化的扩展卡尔曼滤波(EKF)技术,但是对于改进型Logistic混沌映射的扩频通信系统,UKF运算时间长,算法复杂。针对上述缺点以及改进型Logistic映射的泰勒展开式最高项为二阶的特点,提出将二阶EKF运用到接收系统中,该接收系统能精确到泰勒展开式的二阶,达到与UKF相同的性能。相比UKF的复杂算法更加简单,运算速度也更快。仿真实验表明,虽然二阶EKF与UKF的误码率相同,但在运算速度与复杂度方面均优于UKF。     

Nonlinear model identification and adaptive control of CO2 sequestration process in saline aquifers using artificial neural networks

In recent years, storage of carbon dioxide (CO₂) in saline aquifers has gained intensive research interest. The implementation, however, requires further research studies to ensure it is safe and secure operation. The primary objective is to secure the CO₂ which relies on a leak-proof formation. Reservoir pressure is a key aspect for assessment of the cap rock integrity. This work presents a new pressure control methodology based on a nonlinear model predictive control (NMPC) scheme to diminishing risk of carbon dioxide (CO₂) back leakage to the atmosphere due to a fail in the integrity of the formation cap rock. The CO₂ sequestration process in saline aquifers is simulated using ECLIPSE-100 as black oil reservoir simulator while the proposed control scheme is realized in MATLAB software package to prevent over-pressurization. A modified form of growing and pruning radial basis function (MGAP-RBF) neural network model is identified online for prediction of reservoir pressure behaviors. MGAP-RBF is recursively trained via extended Kalman filter (EKF) and unscented Kalman filter (UKF) algorithms. A set of miscellaneous test scenarios has been conducted using an interface program to exchange ECLIPSE and MATLAB in order to demonstrate the capabilities of the proposed methodology in guiding saline aquifer to follow some desired time-dependent pressure profiles during the CO₂ injection process.