多变量系统状态空间模型的递阶辨识

研究多变量系统状态空间模型的递阶辨识问题,推广了作者提出的标量系统状态和参数联合辨识算法.当状态可量测时,利用最小二乘原理直接辨识状态空间模型的参数矩阵;当状态不可测时,利用递阶辨识原理提出了状态空间模型递阶辨识方法,使用系统输入输出数据来估计系统的未知状态和参数.状态空间模型递阶辨识方法分为两步:首先假设系统状态是已知的(即参数估计算法中的未知系统状态用其估计代替),基于状态估计和系统输入输出数据递归计算系统参数估计;然后基于系统输入输出数据和获得的参数估计,递归计算系统的状态估计.     

等效建模与SR-UKF算法的SOC估算研究

荷电状态(SOC)用于表征动力锂电池剩余电量。选用Thevenin等效模型作为模拟电池工作状态的等效电路模型,结合试验测量相关参数,运用电路以及多种数理知识,对构建的锂电池等效电路模型进行参数辨识,并通过曲线拟合等方法对辨识结果进行优化处理。在脉冲特性能力测试(HPPC)中对模型精度进行验证,模型表征误差稳定在1.1%以内。采用平方根无迹卡尔曼算法用状态变量的误差协方差的平方根代替状态变量的误差协方差,直接将协方差的平方根值进行传递。利用平方根无迹卡尔曼算法对荷电状态进行估计,对比无迹卡尔曼算法与平方根无迹卡尔曼算法的SOC估计效果。在25℃的条件下对三元锂电池进行动态应力测试工况(DST)试验,平方根无迹卡尔曼算法和无迹卡尔曼算法锂电池SOC估计的最大误差分别为0.55%与1.5%。试验结果表明,平方根无迹卡尔曼算法的跟踪效果较优,具有更高的SOC估计精度和稳定性。     

基于神经网络的一类生化反应器状态在线估计

提出一种随机非线性系统状态和参数同时估计的神经网络新方法，并证明了该方法的无偏性和是小方差性，将其用于乙醇间歇发酵器的状态和参数估计，结果表明估计值民实验值相吻合，此方法对噪声特片无特殊要求，对初始状态估值不敏感，对初始参数值具有一定的鲁棒性，可利用有限的状态量测信息在线估计不可测量的状态变量和物理参数。     

一类MIMO状态可测的非线性连续系统的激励辨识方法

研究一类 MIMO 状态可测的非线性连续系统的激励辨识问题. 输入激励信号采用高斯白噪声, 均匀采样获得输出状态数据. 根据 Girsanov 定理获得系统参数的渐近无偏估计. 数值仿真试验说明了该方法的有效性并发现耦合多变量系统辨识中的 NNR 现象. 最后给出该系统的分步激励辨识算法.     

船舶同步发电机参数蚁群算法辨识研究

以考虑饱和效应的船舶同步发电机五阶综合稳定计算模型为研究对象,建立了以电流为状态变量的五阶同步发电机的状态增量方程,由于d、q轴可以直接解耦,可以对d、q轴分开进行辨识;以现代系统辨识理论为基础,提出了一种基于蚁群算法的同步发电机参数辨识优化方法,设计了参数辨识算法的详细流程,推导了辨识过程,并证明了该方法的收敛性.利...     

基于系统辨识算法的风力机桨距系统故障诊断

针对风力机桨距系统故障,提出一种基于观测器的多新息随机梯度辨识算法的故障诊断方法．多新息随机梯度辨识算法通过扩展新息长度能够改进随机梯度辨识算法的估计精度,根据系统的规范状态空间模型,结合状态观测器可以实现系统状态和参数的交互估计．将桨距系统模型转换为可辨识的状态空间模型,依据桨距系统故障会引起系统参数变化的特点,采用所提出的算法对系统状态和参数进行估计,将桨距系统故障诊断问题转化为系统状态和参数估计问题．仿真结果表明,所提出的方法能够有效诊断桨距系统故障．     

状态空间双线性系统的极大似然辨识

提出了状态空间双线性系统的极大似然辨识方法。得到了以输入-输出序列为条件概率的似然函数解析表达式,推导了极大化似然函数的参数矩阵计算公式,给出适用于双线性系统状态估计的改进卡尔曼滤波方法,以及辨识系统参数的迭代估计算法。最后进行了数值仿真,结果说明了该方法的有效性。     

一般双率随机系统状态空间模型及其辨识

对于双率采样数据系统,本文使用提升技术,推导了双率系统的提升状态空间模型.对 于系统状态可测量的双率系统,利用最小二乘原理辨识提升系统模型的参数矩阵;对于状态不 可测的未知参数双率系统,利用递阶辨识原理,提出了双率系统递阶状态空间模型辨识方法,来 辨识系统的状态和参数.具体做法:基于获得的状态估计和提升系统的输入输出数据递归估计 系统参数,然后基于获得的参数估计,计算系统的状态.     

一类有输入噪声扰动的逆系统无偏参数辨识算法研究

对逆系统建模时,原系统的输出作为逆系统参数辨识时的输入.由于原系统输出存在测量噪声,且噪声方差未知,采用普通最小二乘法辨识,无法得到逆系统参数的一致无偏估计.为此,本文研究了一种有输入扰动的的逆系统无偏参数辨识算法,该算法先通过小波变换估计输入信号噪声的方差,再由估计得到的方差,通过偏差消除的递推最小_乘法,对逆系统的参数进行无偏辨识.该算法降低了对输入辨识信号为白噪声的要求,具有较强的实用性.由于采用递推运算,该算法也可以用于逆系统参数的在线辨识.最后,通过实验验证了该算法的有效性.     

大系统的递阶辨识

大系统的特点是维数高、待估计的参数数目多,使得辨识方法的计算量和存储量急 剧增加,以致常规辨识算法难以实现.为了减少大系统辨识的计算量,提出了计算量较小的递 阶辨识算法,并用鞅超收敛定理证明了它的收敛性.结果说明该算法可以给出大系统参数的 一致估计.     

Identification of Constant Parameters of Dynamic Systems by a Time-Frequency Method

A time-frequency method for identifying linear dynamic systems of a general form with constant parameters and delays in their observable variables is considered. The identification problem is found to be decomposable into the problem of estimating unknown parameters and the problem of estimating the initial conditions. Applying the time-frequency method to identify the differential equation of the Van der Pol oscillator, which is nonlinear by both its state and parameters, is considered. Examples are used to show that the time-frequency method solves the identification problem both for stable and unstable dynamic systems.     

Identification of nonlinear systems using Polynomial Nonlinear State Space models

In this paper, we propose a method to model nonlinear systems using polynomial nonlinear state space equations. Obtaining good initial estimates is a major problem in nonlinear modelling. It is solved here by identifying first the best linear approximation of the system under test. The proposed identification procedure is successfully applied to measurements of two physical systems.     

Parameter identifiability of nonlinear systems: the role of initial conditions

Identifiability is a fundamental prerequisite for model identification; it concerns uniqueness of the model parameters determined from the input-output data, under ideal conditions of noise-free observations and error-free model structure. In the late 1980s concepts of differential algebra have been introduced in control and system theory. Recently, differential algebra tools have been applied to study the identifiability of dynamic systems described by polynomial equations. These methods all exploit the characteristic set of the differential ideal generated by the polynomials defining the system. In this paper, it will be shown that the identifiability test procedures based on differential algebra may fail for systems which are started at specific initial conditions and that this problem is strictly related to the accessibility of the system from the given initial conditions. In particular, when the system is not accessible from the given initial conditions, the ideal I having as generators the polynomials defining the dynamic system may not correctly describe the manifold of the solution. In this case a new ideal that includes all differential polynomials vanishing at the solution of the dynamic system started from the initial conditions should be calculated. An identifiability test is proposed which works, under certain technical hypothesis, also for systems with specific initial conditions.     

Modeling of pH process using wavenet based Hammerstein model

This paper outlines an approach for developing a Hammerstein model for nonlinear dynamic systems. The nonlinearity is sought to be captured through functional approximation using wavelets cast in a wavenet structure. Nonlinear block of wavenet at input side is cascaded with a linear dynamic block described by a state space model. A sequential approach is used for development of static nonlinear and linear dynamic parts of the model. Configuration and parameters of the nonlinear wavenet structure are determined from near steady state data extracted from dynamic test data while the state space model parameters of the linear dynamic part are obtained using a subspace identification approach. This approach has been applied for modeling a strongly nonlinear pH process operated over a wide range of operating conditions.     

Maximum likelihood estimation of linear stochastic systems in the class of sequential square-root orthogonal filtering methods

Theoretical and applied aspects are considered for development of numerically stable adaptive methods of the parametric identification of linear discrete stochastic systems in the space of states. The unknown system parameters to be estimated can enter into any matrices specifying a system and into initial conditions. The class of gradient methods is first suggested, which is developed on the basis of orthogonal square-root implementations of the discrete Kalman filter with the use of the technology of sequential data processing. It is shown that the algorithms of the given type can be effectively used to solve ill-conditioned problems of parametric identification. A test example is drawn. The practical significance of the suggested class of methods is illustrated by an example of the solution for one of the financial mathematics problems — the identification of a multidimensional model of stochastic volatility.     

Identification of noncontrollable systems from impulse response measurements

We analyze the problem of modeling an observed impulse response by means of a finite-dimensional, linear, time-invariant system. Our approach differs from classical realization theory in the following respects. The modeling problem is split in two steps, namely, identification for determining a model for the observations, and realization for determining parameters which describe the model. Systems are considered as sets of time series, not as input-output maps. In particular, the partitioning of variables into inputs and outputs need not be known, and it is not required that there exist a causal relationship between inputs and outputs. Further, we make no assumptions concerning initial conditions, which in particular may be nonzero. Determination of initial conditions is part of the modeling problem. A final significant distinction from classical realization theory is that the systems need not be controllable.We characterize the class of systems which can be identified from impulse response measurements. Necessary and sufficient conditions are formulated in terms of state-space realizations. It turns out that noncontrollable systems are also identifiable. For causal systems, the condition is that the state transition matrix, restricted to the noncontrollable states, has sufficiently small cyclic index. For noncausal systems, the condition is expressed in terms of the rank of the (singular) state evolution equation.     

Linear system identification from nonstationary cross-sectional data

The identification of time-invariant linear stochastic systems from cross-sectional data on nonstationary system behavior is considered. A strong consistency and asymptotic normality result for maximum likelihood and prediction error estimates of the system parameters, system and measurement noise covariances, and the initial state covariance is proven. A new tdentifiability property for the system model is defined and appears in the set of conditions for this result. The nonstationary stochastic realization (i.e, covariance factorization) theorem in [1] provides sufficient conditions for the identifiability property to hold. An application illusrating the use of a computer program implementing the identification method is presented.     

非均匀采样系统的一种递推辨识方法

在非均匀采样系统辨识方法中, 通常利用重采样、数值积分等方法来处理非均匀采样数据, 所用模型多为连续有理分式传递函数, 在递推形式下非均匀采样对象又常局限于``数据缺失'的情况. 本文研究更为一般的异步非均匀采样的多变量系统, 采用连续时间状态空间模型描述, 推导了模型参数、参数梯度和系统状态之间的相互递推关系, 构成一种可变迭代间隔的递推辨识算法, 在每次输出采样点上仅更新模型中受当前采样数据影响的参数. 这种辨识方法可以适用于任意非均匀采样系统, 多采样率系统也可作为一种特例适用于本算法. 仿真结果表明, 所提的方法是可行有效的.     

基于Haar函数的分布参数系统辨识

借助于正交函数序列对分布参数系统进行辨识，是一种妊之有效的辨识方法。     

Identification from step responses with transient initial conditions

Over the last few years there have been some interesting developments in system identification from step and step-like responses. New methods have been proposed to simultaneously estimate model parameters and the delay from step responses that require the process to be at steady state when the step is applied. To deal with transient initial conditions, methods based on pulse responses and the so called piece-wise step tests and iterative algorithm based on a single step response have also been proposed. In this article we propose a new method to estimate model parameters and the delay from a single step response in the presence of transient initial conditions, which does not require iteration. The performance of the proposed procedure is demonstrated through simulations as well as applications on experimental data from a continuous heating tank process and a mixing process.