Parameter identification of linear multi-delay systems via a hybrid of block-pulse functions and Taylor’s polynomials

In this paper, an efficient and effective procedure is successfully developed for parameter identification of linear time-invariant multi-delay systems. The proposed framework is based on a hybrid of block-pulse functions and Taylor’s polynomials. Two upper error bounds corresponding to hybrid functions are established. The excellent properties of these functions together with the associated operational matrices of integration and delay are utilised to transform the original problem into a system of linear algebraic equations. The least squares method is then implemented for estimation of the unknown parameters. Several numerical experiments are investigated to demonstrate the usefulness and effectiveness of the proposed procedure. Easy implementation, simple operations and accurate solutions are the main features of the suggested approximation scheme.     

A hybrid analysis direct method in the calculus of variations

This paper presents a direct method for finding the solution of variational problems using a hybrid function. The properties of hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. An operational matrix of integration and the cross product of two hybrid function vectors are used to reduce a variational problem to the solution of algebraic equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.     

飞机颤振模态参数辨识的频域广义整体最小二乘算法

采用一种适用于噪声环境的广义整体最小二乘算法,准确地辨识飞机的颠振模态参数．该算法结合有理传递函数模型,将带噪系统的辨识问题转化为广义整体最小二乘问题．利用线性的广义奇异值分解求解模型系数,避免了非线性优化的复杂计算．通过迭代法更新加权项,获得了接近于极大似然估计的辨识效果．最后利用试飞试验数据辨识飞机的模态参数,验证了该方法的有效性．     

Analysis of time-varying delay systems by hybrid of block-pulse functions and biorthogonal multiscaling functions

This paper proposes new effective methods for analysis of time-varying delay systems using new hybrid functions. The excellent properties of the hybrid functions which consist of block pulse functions and biorthogonal multiscaling functions are presented. We utilise operational matrices of product, delay and integration to reduce the solution of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.     

方块脉冲函数用于连续分布时滞系统的最优控制

本文应用方块脉冲函数推出了连续分布时滞系统的分段恒定解答,给出了最优控制的综合表达式及泛函目标的最优值。     

非整数阶系统的频域辨识法

提出了一类非整数阶系统的频域辨识最小二乘方法, 给出了算法的详细推导过程. 通过对已知系统仿真, 结果表明该方法有如下优点: 对于非整数阶对象, 能够用更简单的模型获得更好的频域响应拟合; 对于整数阶对象, 采用阶数扫描的方法仍然能找到拟合其频域响应的最好的整数阶模型; 与整数阶系统辨识算法相比, 该算法更稳定.     

基于Legendre多项式微分变换的随机连续系统无偏一致参数估计

基于Legendre多项式微分变换,导出随机连续线性系统的统计无关逼近模型,然后由最小二乘原理给出参数估计算法。理论分析和仿真结果表明该估计是无偏一致的。     

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective.     

Accuracy analysis of bias-eliminating least squares estimates for errors-in-variables systems

The bias-eliminating least squares (BELS) method is one of the consistent estimators for identifying dynamic errors-in-variables systems. In this paper, we investigate the accuracy properties of the BELS estimates. An explicit expression for the normalized asymptotic covariance matrix of the estimated parameters is derived and supported by some numerical examples.     

基于递推最小二乘的荧光补偿参数辨识方法

研究流式细胞仪样本检测数据的荧光光谱重叠补偿问题.针对全矩阵补偿算法中补偿矩阵参数的获取,提出了一种使用多变量系统的递推最小二乘算法辨识补偿矩阵参数的方法.在全矩阵补偿方法的基础上,用单染色荧光光谱线性和对多染色荧光实际测量光谱进行近似,并使用多变量系统的递推最小二乘算法辨识系统参数获得补偿矩阵的元素.仿真结果表明,利用多变量系统的递推最小二乘算法进行荧光补偿与一般最小二乘算法相比,补偿结果的CV值相对误差在2％以内,进而验证了所采用的算法的有效性与可行性.     

Identification of nonlinear systems using a piecewise-linear Hammerstein model

In the paper a method for nonlinear system identification is proposed. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The model and the identification algorithm are adapted to allow the parameter identification in the presence of a special form of the excitation signal. The identification method is derived from a recursive least-squares algorithm, which is properly adapted to take into account the proposed model structure and the properties of the identification signal. The applicability of the approach is illustrated by an example in which a discontinuous nonlinear static function is connected to a dynamic block.     

基于动态遗忘因子递推最小二乘法的永磁同步电机参数辨识算法

针对固定遗忘因子递推最小二乘法(RLS)在永磁同步电机参数识别中难以同时保证快速性和鲁棒性的问题,提出一种动态调节遗忘因子大小的递推最小二乘参数识别算法.分析了遗忘因子对RLS算法的影响特性,以理论模型与实际模型输出的差值为变量构建遗忘因子调节函数,实现遗忘因子动态调整.仿真结果表明,相比于固定遗忘因子RLS算法,改进...     

学习辨识:最小二乘算法及其重复一致性

针对重复时变系统, 提出学习辨识方法用于估计系统的时变参数. 讨论了有限时间作业区间上重复运行的时变系统以及周期时变系统两种情形. 文中给出最小二乘学习算法的推导过程, 并分析了所提算法的收敛性. 结果表明, 当重复持续激励条件成立时, 提出的学习算法具有重复一致性, 能够给出时变参数的完全估计. 通过数值算例进一步验证了学习算法的有效性.     

多变量系统高效耦合递推最小二乘辨识算法及计算量分析

针对多变量系统维数大、参数数目多,导致辨识算法计算量大的问题,基于耦合辨识概念,推导了多变量系统的高效耦合递推最小二乘算法.算法的主要思想是根据各子系统辨识模型的特点,通过耦合辨识概念将子系统间相同的参数向量耦合起来,避免子系统参数向量的冗余估计.通过算法计算量分析表明,与递推最小二乘算法相比,所提出算法具有较少的计算量.仿真实例验证了算法的有效性.     

Least squares based iterative identification for a class of multirate systems

This paper studies modeling and identification problems for multi-input multirate systems with colored noises. The state-space models are derived for the systems with different input updating periods and furthermore the corresponding transfer functions are obtained. To solve the difficulty of identification models with unmeasurable noises terms, the least squares based iterative algorithm is presented by replacing the unmeasurable variables with their iterative estimates. Finally, the simulation results indicate that the proposed iterative algorithm has advantages over the recursive algorithms.     

Recursive identification of switched ARX systems

We consider the problem of recursively identifying the parameters of a deterministic discrete-time Switched Auto-Regressive eXogenous (SARX) model, under the assumption that the number of models, the model orders and the mode sequence are unknown. The key to our approach is to view the identification of multiple ARX models as the identification of a single, though more complex, lifted dynamical model built by applying a polynomial embedding to the input/output data. We show that the dynamics of this lifted model do not depend on the value of the discrete state or the switching mechanism, and are linear on the so-called hybrid model parameters. Therefore, one can identify the parameters of the lifted model using a standard recursive identifier applied to the embedded input/output data. The estimated hybrid model parameters are then used to build a polynomial whose derivatives at a regressor give an estimate of the parameters of the ARX model generating that regressor. The estimated ARX model parameters are shown to converge exponentially to their true values under a suitable persistence of excitation condition on a projection of the embedded input/output data. Such a condition is a natural generalization of the well known result for ARX models. Although our algorithm is designed for perfect input/output data, our experiments also evaluate its performance as a function of the level of noise for different choices of the number of models and model orders. We also present an application to temporal video segmentation.     

Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models

A maximum likelihood parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) models based on the maximum likelihood principle. In this derivation, we use an estimated noise transfer function to filter the input–output data. The simulation results show that the proposed estimation algorithm can effectively estimate the parameters of such class of CARAR systems and give more accurate parameter estimates than the recursive generalized least-squares algorithm.