FAST RECURSIVE LEAST SQUARES LEARNING ALGORITHM FOR PRINCIPAL COMPONENT ANALYSIS

Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the proposed algorithm providing the capability of the fast convergence and high accuracy for extracting all the principal components. It is shown that all the information needed for PCA can be completely represented by the unnormalized weight vector which is updated based only on the corresponding neuron input-output product. The convergence performance of the proposed algorithm is briefly analyzed.The relation between Oja’s rule and the least squares learning rule is also established. Finally, a simulation example is given to illustrate the effectiveness of this algorithm for PCA.

Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition

In this paper,a new recursive least squares(RLS)identification algorithm with variable-direction forgetting(VDF)is proposed for multi-output systems.The objective is to enhance parameter estimation performance under non-persistent excitation.The proposed algorithm performs oblique projection decomposition of the information matrix,such that forgetting is applied only to directions where new information is received.Theoretical proofs show that even without persistent excitation,the information matrix remains lower and upper bounded,and the estimation error variance converges to be within a finite bound.Moreover,detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition(VDF-ED).It is revealed that under non-persistent excitation,part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data,which could produce a more ill-conditioned information matrix than our proposed algorithm.Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

APPLICATION OF LEAST MEDIAN OF SQUARED ORTHOGONAL DISTANCE (LMD) AND LMD BASED REWEIGHTED LEAST SQUARES (RLS) METHODS ON THE STOCK RECRUITMENT RELATIONSHIP

Analysis of stock recruitment (SR) data is most often done by fitting various SR relationship curves to the data. Fish population dynamics data often have stochastic variations and measurement errors, which usually result in a biased regression analysis. This paper presents a robust regression method, least median of squared orthogonal distance (LMD), which is insensitive to abnormal values in the dependent and independent variables in a regression analysis. Outliers that have significantly different variance from the rest of the data can be identified in a residual analysis. Then, the least squares (LS) method is applied to the SR data with defined outliers being down weighted. The application of LMD and LMD based Reweighted Least Squares (RLS) method to simulated and real fisheries SR data is explored.

NEW EFFICIENT ORDER-RECURSIVE LEAST-SQUARES ALGORITHMS

Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.

An Effective Multiple Model Least Squares Method in Tracking of a Maneuvering Target

A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent.

基于WRLS-ARMAX系统辨识的新能源电力系统惯量评估

随着高比例新能源机组并入电网,电力系统低惯量特性愈加显著,严重影响了系统运行稳定性。为了准确估计新能源电网实际运行状态下的惯量大小,提出了一种基于加权递推最小二乘(WRLS)-受控自回归滑动平均(ARMAX)系统辨识的新能源电力系统等效惯量评估方法。首先,以发电机为对象,建立不同扰动情况下发电机功频响应特性的通用惯量解析模型;其次,以发电机并网母线有功功率和频率扰动作为输入和输出,建立ARMAX模型,考虑到实际电网运行过程中受大、小扰动共同影响,实际测量数据具有异方差性,采用WRLS求解模型中的待辨识参数;然后,提取辨识模型中包含惯量响应的传递函数模型,利用阶跃响应计算惯量源的惯性时间常数,进而计算得到系统等效惯量大小;最后,通过Matlab/Simulink仿真算例验证了所提方法的准确性和实用性。

Recursive Least Square Vehicle Mass Estimation Based on Acceleration Partition

Vehicle mass is an important parameter in vehicle dynamics control systems. Although many algorithms have been developed for the estimation of mass, none of them have yet taken into account the different types of resistance that occur under different conditions. This paper proposes a vehicle mass estimator. The estimator incorporates road gradient information in the longitudinal accelerometer signal, and it removes the road grade from the longitudinal dynamics of the vehicle. Then, two different recursive least square method （RLSM） schemes are proposed to estimate the driving resistance and the mass independently based on the acceleration partition under different conditions. A 6 DOF dynamic model of four In-wheel Motor Vehicle is built to assist in the design of the algorithm and in the setting of the parameters. The acceleration limits are determined to not only reduce the estimated error but also ensure enough data for the resistance estimation and mass estimation in some critical situations. The modification of the algorithm is also discussed to improve the result of the mass estimation. Experiment data on asphalt road, plastic runway, and gravel road and on sloping roads are used to validate the estimation algorithm. The adaptability of the algorithm is improved by using data collected under several critical operating conditions. The experimental results show the error of the estimation process to be within 2.6%, which indicates that the algorithm can estimate mass with great accuracy regardless of the road surface and gradient changes and that it may be valuable in engineering applications. This paper proposes a recursive least square vehicle mass estimation method based on acceleration partition.

基于FFRLS和ASR-UKF滤波算法的锂电池SOC估计

锂电池在工作过程中,其内部参数易受多种因素影响,为提高锂电池在复杂环境下荷电状态(SOC)估计精度,以二阶戴维宁(Thevenin)等效模型为基础,结合遗忘因子递推最小二乘法(FFRLS)对模型参数进行在线辨识。针对传统卡尔曼滤波算法高度非线性及系统噪声不确定性等缺点,提出了一种自适应平方根无迹卡尔曼滤波(ASR-UKF)算法,该算法利用平方根算法处理均值和协方差,确保了状态协方差的半正定性和稳定性,并引入自适应滤波算法对噪声进行实时修正,消除了系统时变噪声影响。结果表明,FFRLS能有效解决数据饱和及算法矩阵计算量大的问题,等效模型精度高达98%。在混合动力脉冲特性(HPPC)测试和北京公交动态测试工况(BBDST)下,ASR-UKF算法SOC估计最大误差分别为3.264%和0.572%,具备更好的跟踪效果,验证了改进算法良好的收敛性与自适应性。

CONVERGENCE AND STABILITY OF RECURSIVE DAMPED LEAST SQUARE ALGORITHM

The recursive least square is widely used in parameter identification. But if is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. rt is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.

基于DFFRLS-AUKF的单轨吊车动态倾角辨识方法研究

为保障单轨吊车在深部矿井复杂轨道工况环境下行驶的安全控制性能,需提高单轨吊车动态倾角辨识的精度及可靠性。因此,本文提出了基于DFFRLS-AUKF算法的单轨吊车动态倾角辨识方法。首先,利用自适应平滑滤波算法对实时采集的加速度和速度数据进行滤波处理,避免环境噪声的干扰,保证数据的完整性;其次,通过建立轨道曲率模型实现对轨道全工况的精准分析,在滤波处理后的数据基础上,再结合带有动态遗忘因子的递归最小二乘(DFFRLS)算法得到可靠地轨道曲率值;最终,在计算出的轨道曲率基础上,利用Sage-Husa噪声估计器对无迹卡尔曼滤波(UKF)进行改进,实现了对动态倾角辨识结果地自适应动态调整,提高了动态倾角辨识地精准度。实验表明,单轨吊车在单轨路段1和单轨路段2测试期间,所提的DFFRLS-AUKF算法与传统算法相比动态倾角辨识精度分别平均提升了25.25%和39.5%,表明了DFFRLS-AUKF算法在不同轨道工况下具有良好的精准性及可靠性,有效保障了单轨吊车在复杂轨道工况下行驶的安全性。

基于DFFRLS的PMSM自校正PI速度控制策略研究

基于惯量辨识的永磁同步电机自校正PI速度控制具有良好的抗负载扰动性能,但受到惯量辨识过程存在抖动的影响转速响应会产生高频振荡。为抑制高频振荡,提出一种基于动态遗忘因子递推最小二乘法惯量辨识的自校正PI控制策略。首先,构造指数函数形式的动态遗忘因子,分析其跟随辨识误差变化的规律并用于转动惯量辨识。然后,采用“振荡指标法”设计PI参数整定公式,并结合DFFRLS惯量辨识过程进行自校正PI控制。仿真和实验结果表明:改进的DFFRLS有效减小了辨识惯量的抖动幅度;所提ST-PIC调速控制策略在保证转速高性能响应的同时有效抑制了高频振荡。

MAFFRLS算法辨识锂离子电池模型参数

建模方法和模型参数辨识方法会影响锂离子电池状态的准确估计,特别是在动态工况下,因此在线辨识电池模型参数的方法很重要。提出一种改进的自适应遗忘因子递推最小二乘(MAFFRLS)法,优点是在不同误差范围内可以自适应地更新遗忘因子最优值。选用二阶RC等效电路模型,在动态工况下对该算法进行验证。将所提出的算法与递推最小二乘(RLS)法和遗忘因子递推最小二乘(FFRLS)法进行对比。在动态应力测试(DST)工况下,使用RLS、FFRLS和MAFFRLS算法估计电压,平均绝对误差分别为0.0102 V、0.0099 V和0.0046 V,均方根误差分别为0.0155 V、0.0150 V和0.0068 V。MAFFRLS算法的平均绝对误差和均方根误差更小,准确性更高。

基于FFRLS-SRUKF算法的锂电池SOC估计研究

传统无迹卡尔曼滤波在荷电状态(SOC)估计时主要面临两个问题:一是电池模型参数固定导致SOC估计精度低;二是协方差矩阵出现非正定时导致SOC估计失败。提出了遗忘因子递推最小二乘(FFRLS)算法结合平方根无迹卡尔曼滤波(SRUKF)的SOC估计算法。首先,建立二阶阻容(RC)等效电路模型。其次,利用FFRLS算法对电路模型参数在线辨识并实时修正电池等效电路模型,在此基础上使用SRUKF算法估计SOC。最后,通过间歇恒流脉冲放电和动态应力测试工况对所提算法进行验证。试验结果表明,该算法的平均绝对值误差低于0.0115、均方根误差低于0.012。与SRUKF算法相比,FFRLS-SRUKF算法具有更好的SOC估计性能,为电池管理系统解决锂电池的不一致性提供了可靠依据。

基于改进RLS算法的故障电流参数估计

由于故障电流中直流衰减分量的影响,快速准确地估计出故障电流参数并预测出可用的过零点成为故障电流相控开断的关键。将故障电流方程中指数项进行泰勒级数展开,保留前2项,并基于递推最小二乘法,估计电流参数。分析由泰勒级数展开引起的截断误差,提出时间常数补偿公式。利用Matlab软件对不含谐波和含有谐波两种情况下的故障进行仿真,结果表明:算法可在15 ms内得到足够精度的故障电流参数,电流过零点的预测精度在?0.2 ms以内。最后对故障录波数据的仿真结果证实了算法的效果。

一种改进RLS算法及其在SINS快速对准中的应用

在传统递推最小二乘算法(RLS)中,人为设置的递推初始值将导致状态估计的有偏性,也就丧失了最优性,当量测数据次数较小时尤为严重。摒弃了传统RLS算法"新估计值=旧估计值+修正值"的递推结构,提出了借助中间量进行递推,再由中间量直接作状态估计的改进算法。改进RLS算法状态估计结果与批处理LS算法完全一致,且无需初始状态的任何信息。将改进RLS算法应用于捷联惯导系统(SINS)初始对准。对于一定的初始对准精度要求,理论上改进RLS算法所需的初始对准时间是最短的。最后,SINS初始对准数值仿真结果验证了所提算法的正确性。

基于RLS的嵌入式永磁同步电机参数辨识技术

电机参数变化影响电机控制性能,因而需要对电机参数进行在线辨识,基于嵌入式永磁同步电机在两相坐标系里的动态状态方程,通过检测电机的定子电压、电流和转子转速信号,利用递推最小二乘法算法对嵌入式永磁同步电机参数进行辨识,由于该方法所用的信号均可检测到,从而减少了其他干扰对电机参数辨识的影响,提高了参数辨识的准确性。仿真结果和实验验证了辨识方案的有效性。

基于距离和DF-RLS的时间序列异常检测

为能同时检测时间序列中的附加异常和革新异常,改进自回归模型,提出距离因子递推最小二乘(DF-RLS)线性预测算法。在此基础上,给出一种基于距离和DF-RLS的联合异常检测方法——DDR-OD。实验结果表明,与当前其他时间序列异常检测方法相比,DDR-OD的检测效果较优。

一种具有快速跟踪能力的改进RLS算法研究

为了改善固定遗忘因子递推最小二乘(RLS)算法在时变系统中的跟踪性能,提出一种改进的RLS算法。改进的可变遗忘因子RLS算法,不仅克服了固定遗忘因子RLS算法中跟踪速度和参数失调的矛盾,而且避免了当参数估值趋于参数真值时,卡尔曼增益趋于零,RLS算法失去对时变系统的跟踪能力的问题。最后,在MATLAB仿真平台下,对改进的RLS算法性能进行仿真验证。仿真结果表明,改进的算法能够获得快速的跟踪能力,也具有较快的收敛速度和较小的稳态误差。

基于RLS算法的并联型APF全局积分滑模变结构控制

针对并联型有源电力滤波器(active power filter,APF)谐波检测环节的延时和谐波电流跟踪环节的鲁棒性差、跟踪精度不高的问题,建立了系统解耦后的数学模型,提出了基于递归最小二乘(recursive least squares,RLS)算法的并联型APF全局积分滑模变结构控制策略。谐波检测环节采用改进的瞬时无功功率理论的id-iq法,用RLS自适应滤波器替换传统的Butterworth低通滤波器,解决了传统的Butterworth低通滤波器因延时而导致的一个基波周期(20 ms)内检测盲区问题。谐波电流跟踪环节采用全局积分滑模变结构控制方法,引入了全局积分滑模面,运用Lyapunov稳定性理论导出的控制律兼顾了全局滑模的快速性和积分滑模的准确性。在解决了谐波检测环节延时的情况下,将全局积分滑模控制策略与传统的PI控制和滞环控制对比,仿真实验结果表明:全局积分滑模控制对指令电流具有更高的跟踪精度,且具有更低的电网侧电流总谐波畸变率(total harmonic distortion,THD)。