Parameter estimation for coupled multivariable error models

An adaptive algorithm is developed for estimating the parameters of a linear multivariable error model with coupled dynamics, using estimation errors for coupling inputs. Coupled dynamics in an error equation lead to a new type of error models which have different regressors but the same parameter error. A total cost function is used to derive a desired adaptive law for updating the parameter estimates. As an application, this algorithm is employed for control and identification of multivariable systems with actuator uncertainties. Copyright © 1999 John Wiley & Sons, Ltd.     

Combined estimation of the parameters and states for a multivariable state-space system in presence of colored noise

This article addresses the combined estimation issues of parameters and states for multivariable systems in the state-space form disturbed by colored noises. By utilizing the Kalman filtering principle and the coupling identification concept, we derive a Kalman filtering based partially coupled recursive generalized extended least squares (KF-PC-RGELS) algorithm to jointly estimate the parameters and the states. Using the past and the current data in parameter estimation, we propose a Kalman filtering based multi-innovation partially coupled recursive generalized extended least-squares algorithm to enhance the parameter estimation accuracy of the KF-PC-RGELS algorithm. Finally, a simulation example is provided to test and compare the performance of the proposed algorithms.     

基于改进微分进化算法的负荷模型参数辨识

为了提高电力系统中负荷模型的精确度,提出了一种改进的微分进化算法(IDE)以辨识负荷模型参数。采用不依赖于优化问题的控制参数自适应调整机制,同时考虑搜索速度和搜索精度,使算法摆脱后期易于陷入局部极值点的束缚,克服了微分进化算法参数调整困难的不足,提高了算法的寻优能力。将改进算法应用于静态负荷模型参数辨识的工程实例并与其他算法对比的结果表明,改进DE算法的全局搜索能力强,搜索精度高。     

Three-stage least squares-based iterative estimation algorithms for bilinear state-space systems based on the bilinear state estimator

Because of the product item of the control input and the state vector, the identification of bilinear systems is difficult. This paper considers the combined parameter and state estimation problems of bilinear state-space systems. On the basis of the observability canonical form and the model transformation, an identification model with a linear combination of the system parameters is obtained. Using the hierarchical principle, the identification model is decomposed into three submodels with fewer variables, and a three-stage least squares-based iterative (3S-LSI) algorithm is presented to estimate the system parameters. Furthermore, we derive a state estimator (SE) for estimating the unknown states, and present an SE-3S-LSI algorithm for estimating the unknown parameters and states simultaneously. After that, the least squares-based iterative algorithm is presented as a comparison. By analyzing the estimation results and the calculation amount, these two algorithms can identify the bilinear system effectively but the 3S-LSI algorithm can improve the computational efficiency. The simulation results indicate the effectiveness of the proposed algorithms.     

Separable multi-innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems

This article is concerned with the parameter identification problem of nonlinear dynamic responses for the linear time-invariant system by means of an impulse excitation signal and discrete observation data. Using the impulse signal as the input, the impulse response experiment is carried out and the dynamical moving sampling is designed to generate the measured data for deriving new identification algorithms. By applying the moving window data that contain the dynamical information of the system to be identified, an objective function with respect to the parameters of the systems is constructed according to the impulse response. In accordance with different functional relations between the system parameters and the system output response, the unknown parameter vector of the system is separated into a linear parameter vector and a nonlinear parameter vector. Based on the separated parameter vectors, two subidentification models are constructed and a separable identification algorithm is presented through the gradient search to improve the accuracy. Moreover, for the purpose of enhancing the estimation accuracy and capturing the dynamical feature of the systems, the moving window data are employed to develop the separable identification algorithm. The performance of the proposed separable identification method is illustrated via a numerical example.     

The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

For a special class of nonlinear systems (ie, bilinear systems) with autoregressive moving average noise, this paper gives the input‐output representation of the bilinear systems through eliminating the state variables in the model. Based on the obtained model and the maximum likelihood principle, a filtering‐based maximum likelihood hierarchical gradient iterative algorithm and a filtering‐based maximum likelihood hierarchical least squares iterative algorithm are developed for identifying the parameters of bilinear systems with colored noises. The original bilinear systems are divided into three subsystems by using the data filtering technique and the hierarchical identification principle, and they are identified respectively. Compared with the gradient‐based iterative algorithm and the multi‐innovation stochastic gradient algorithm, the proposed algorithms have higher computational efficiency and parameter estimation accuracy. The simulation results indicate that the proposed algorithms are effective for identifying bilinear systems.     

The innovation algorithms for multivariable state‐space models

This paper derives the input‐output representation of the dynamical system described by a linear multivariable state‐space model and the corresponding multivariate linear regressive model (ie, multivariate equation‐error model). A projection identification algorithm, a multivariate stochastic gradient identification algorithm, and a multi‐innovation stochastic gradient (MISG) identification algorithm are proposed for multivariate equation‐error systems by using the negative gradient search and the multi‐innovation identification theory. The convergence analysis of the MISG algorithm indicates that the parameter estimation errors converge to zero under the persistent excitation condition. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.     

一种求解电力经济负荷分配问题的改进微分进化算法

针对电力系统经济负荷分配(economic dispatch,ED)这一典型的非凸、非线性、组合优化问题,提出一种改进的微分进化(improved differential evolution,IDE)算法。微分进化(differential evolution,DE)算法虽有简单、搜索效率高的优点,但是仍然有局部最优的问题。该文在对DE算法搜索机理进行分析的基础上,针对DE算法参数难于动态调整的问题,提出不依赖于优化问题的控制参数自适应调整机制,并根据动态监视群体适应度方差的变化,增加个体迁移策略,进一步提高DE算法的全局寻优能力和鲁棒性。运用该算法对IEEE3机、40机及69机300节点标准测试用例进行计算,并考虑机组的爬坡约束、出力限制区约束、非光滑费用函数曲线等非线性特性,将其计算结果与遗传算法(genetic algorithm,GA)及粒子群算法(particle swarm optimization,PSO)进行比较,分析表明该方法是可行的、有效的。     

Iterative identification methods for a class of bilinear systems by using the particle filtering technique

This article mainly studies the iterative parameter estimation problems of a class of nonlinear systems. Based on the auxiliary model identification idea, this article utilizes the estimated parameters to construct an auxiliary model, and uses its outputs to replace the unknown noise-free process outputs, and develops an auxiliary model least squares-based iterative (AM-LSI) identification algorithm. For further improving the parameter estimation accuracy, we use a particle filter to estimate the unknown noise-free process outputs, and derive a particle filtering least squares-based iterative (PF-LSI) identification algorithm. During each iteration, the AM-LSI and PF-LSI algorithms can make full use of the measured input–output data. The simulation results indicate that the proposed algorithms are effective for identifying the nonlinear systems, and can generate more accurate parameter estimates than the auxiliary model-based recursive least squares algorithm.     

Estimation of induction motor parameters using shuffled frog-leaping algorithm

This paper introduces a shuffled frog-leaping algorithm based method to approximate the equivalent circuit parameters of induction machines from the manufacturer data, such as nameplate data and motor performance characteristics. The steady-state equivalent circuit is applied for the simulations. The circuit parameters are found as the result for the error minimization function between the estimated and maker data. The suggested algorithm solves the parameter estimation problem and surpasses the solutions reached by differential evolution, particle swarm optimization and genetic algorithms. Therefore, this algorithm can be employed in motor energy management system for bettering the overall energy savings in industry.     

基于TVFFRLS-ACKF的锂离子电池SOC估算

实现电池荷电状态(SOC)的估算预测是电池管理系统(BMS)的重要任务之一。电池模型参数的辨识是实现锂离子电池SOC估算的前提,也是决定其估算精度的关键因素。本文以18650型锂离子单体电池为研究对象,采用带时变遗忘因子的递推最小二乘法(TVFFRLS)对电池参数进行在线辨识,实现遗忘因子自适应的自动寻优,提高参数在线辨识的稳定性。在此基础上,采用自适应容积卡尔曼滤波(ACKF)对锂离子电池SOC进行估算,对过程噪声、量测噪声的协方差实时更新,并在不同工况下进行算法验证。结果表明,该算法噪声抑制性能良好,可以提高SOC的估算精度,最大估算误差不超过1.5%,且ACKF算法具有较强的鲁棒性。     

MULTIVARIABLE CONSTRAINED ADAPTIVE GPC: THEORY AND EXPERIMENTAL EVALUATION

This paper deals with on-line identification and constrained long-range predictive control of multivariable systems. It extends a recently proposed augmented upper diagonal factorization identification (AUDI) algorithm to identify input–output models of multivariable systems with distinct time delays. The multi-input, multi-output (MIMO AUDI) algorithm can simultaneously identify the process model order and process parameters. The MIMO AUDI algorithm is implemented by decomposing a MIMO system into as many multi-input, single-output (MISO) subsystems as the number of outputs and then identifying each MISO subsystem separately. The performance of the new MIMO AUDI algorithm is demonstrated by application to input–output data from a real process. The extension of this algorithm by incorporating a variable forgetting factor with a lower bound in its value is implemented on real plant data to demonstrate ‘alertness’ of the estimator. This paper evaluates the performance of the MIMO adaptive generalized predictive control algorithm with and without constraints by experimental application on a computer-interfaced, pilot-scale process. The MIMO adaptive GPC is shown to have good regulatory plus servo-tracking properties. © 1997 John Wiley & Sons, Ltd.     

基于ACDE-SVM的引水隧洞施工仿真参数动态更新

施工仿真参数的更新对于施工仿真结果的准确性具有重要影响。然而目前的引水隧洞施工进度仿真参数更新多采用贝叶斯更新方法,存在需要假定参数分布形式,且无法得到预测参数的序列来描述参数动态变化过程的不足。针对上述问题,文章提出了基于自适应混沌差分进化支持向量机（adaptive chaos differential evolution- support vector machine,ACDE-SVM）的引水隧洞施工仿真参数动态更新方法。首先,采用自适应缩放因子和混沌理论对差分进化算法进行改进,提出自适应混沌差分进化算法（ACDE）,ACDE算法既使搜索时间大大缩减,又弥补了差分进化算法后期局部搜索弱而使群体陷入早熟的缺陷;其次,基于现场施工参数时间序列,采用ACDE算法对支持向量机（SVM）进行参数寻优,进而构建基于ACDE-SVM的施工仿真参数预测模型,克服了传统SVM参数选择效率低、泛化能力弱的不足;最后,采用误差指标对模型性能进行评价,并与常规仿真方法及贝叶斯更新方法的仿真结果进行对比,验证基于ACDE-SVM的仿真参数动态更新方法的一致性和优越性。工程实例表明,该方法能够较好地拟合仿真参数随时间变化趋势,并能够提高引水隧洞钻爆法施工进度动态仿真的准确性。     

Consistent parameter estimation for deterministic mimo systems with overparametrized models

In this paper the parameter estimation problem for deterministic MIMO systems with overparametrized models will be addressed. In SISO systems overparametrized signal models might arise if the order of the plant model is set too high. For MIMO systems this problem will arise whenever its observability indices are different or, as in SISO systems, the order of the system is set too high. With a proper definition of persistent excitation it is shown that the estimated parameters will converge to a set of parameters. Each point of this set will result in the same transfer function as that of the system under consideration. A very efficient correction algorithm will be used to remove the greatest left common divisor of the estimated system parameters. Hence adaptive control algorithms, which may not be suitable if the estimated system parameters are not left coprime, can then be implemented.     

静态无功补偿器鲁棒控制的一种新自适应逆推方法

针对一般的参数反馈型非线性系统提出了一种扩展自适应逆推方法。该方法不仅保留系统的非线性特性和对未知参数的实时在线估计,而且突破了经典的确定性等价性原理。将该方法应用到含有未知参数带有静态无功补偿器 (SVC)的单机无穷大系统。将这种新自适应机制引入电力系统,得到了带有SVC单机无穷大系统的自适应控制律。仿真结果表明,该方法在提高系统稳定性和参数估计方面优于传统的逆推方法,为工程应用提供了一种有效的选择。另外, 该文中的算法可以应用到其他控制系统。     

重载机车粘着性能参数的极大似然辨识方法

针对重载机车运行中机车的粘着利用率低、易空转、易打滑的问题,提出一种对轨面粘着性能参数的实时在线估计算法。首先从分析机车粘着行为出发,选用Kiencke的粘着-蠕滑模型作为辨识模型,然后算法利用极大似然意义下的模型参数辨识框架,将参数估计转化为二次规划问题求解,进而构造出辨识的迭代算法。同时考虑到轮轨环境突变的不可测,辨识算法引入时变遗忘因子来适应轨面环境的切换。仿真结果表明,该算法能及时跟踪上轮轨环境的变化,有效辨识出粘着性能参数。     

Persistent tracking and identification of regime‐switching systems with structural uncertainties: unmodeled dynamics,observation bias,and nonlinear model mismatch

This work focuses on tracking and system identification of systems with regime‐switching parameters, which are modeled by a Markov process. It introduces a framework for persistent identification problems that encompass many typical system uncertainties, including parameter switching, stochastic observation disturbances, deterministic unmodeled dynamics, sensor observation bias, and nonlinear model mismatch. In accordance with the ‘frequency’ of the parameter switching process, we divide the problems into two classes. For fast‐switching systems, the switching parameters are stochastic processes modeled by irreducible and aperiodic Markov chains. Because accurately tracking real‐time parameters in such systems is not possible because of the uncertainty principles, the effect of parameter switching is evaluated on their average by the stationary distribution of the Markovian chain and estimated by the least squares algorithms. We derive upper and lower bounds on identification errors, which characterize how identification accuracy depends on the earlier uncertainty terms. When the system parameters switch their values infrequently in a probabilistic sense, their values can be tracked based on input/output observations. Stochastic approximation algorithms with adaptive step sizes are used for such systems. Simulation studies are carried out to demonstrate that slowly varying parameters could be tracked with reasonable accuracy.Copyright © 2012 John Wiley & Sons, Ltd.     

基于自适应容积卡尔曼滤波算法的电力系统动态谐波状态估计

由于传统的谐波状态估计的参数辨识算法要求噪声的协方差矩阵固定不变,而实际工程中噪声的协方差矩阵是随时间变化的,工程中存在错误的量测数据,导致传统参数辨识算法估计的谐波电流参数的准确度较低。因此,提出自适应容积卡尔曼滤波算法来提高辨识谐波电流参数的准确度。首先,针对时变噪声干扰,采用基于渐消记忆指数加权法的噪声估值器算法生成时变噪声的协方差矩阵;其次,针对错误的量测数据,采用开窗估计算法修正错误的量测数据;然后,将修正的噪声协方差矩阵和量测数据代入容积卡尔曼滤波算法中,对谐波电流参数进行估计;最后,搭建IEEE 13节点系统仿真模型,验证了自适应容积卡尔曼滤波算法在时变噪声干扰及量测数据错误情况下仍可准确地估计谐波电流参数,确保了动态谐波状态估计的准确性。     

Filtering-based recursive least squares estimation approaches for multivariate equation-error systems by using the multiinnovation theory

This article researches the filtering-based parameter estimation issues for a class of multivariate control systems with colored noise. A filtering-based recursive generalized extended least squares algorithm is derived, in which the data filtering technique is used for transforming the original system into two subidentification systems and the least squares principle is used for estimating parameters of these two subsystems. Furthermore, in order to improve the parameter estimation accuracy, the multiinnovation theory is added for deducing a filtering-based multiinnovation recursive generalized extended least squares algorithm. The numerical example confirms that these two proposed algorithms are effective.     

基于抗差最小均方估计的输电线路参数辨识

输电线路数学模型广泛运用于电力系统分析计算中,其参数的准确性与电网的安全稳定运行密切相关,广域测量系统的发展为获取输电线路参数提供了新的手段。针对目前参数辨识算法缺乏测量误差对辨识结果影响的研究,提出基于抗差最小均方估计（robust least mean squares,RLMS）的输电线路参数辨识算法,该算法以抗差函数代替传统最小均方估计算法中的均方误差,并通过自适应阈值法调节阈值,进而使得辨识算法在抗噪声方面具有较强的适应能力;对不同时刻的计算结果,提出了基于核密度估计和点估计法提取结果的统计特征,最后通过仿真分析与实测数据对比验证了所述算法的有效性。