基于自适应密度估计的系统参数辨识

针对噪声分布未知的ARMAX系统,提出了一种自适应非参数噪声密度估计方法,由估计误差动态调整高斯核函数的全局带宽和局部带宽,实现了未知噪声分布密度的自适应估计;通过极小化似然函数,给出了基于噪声密度估计的参数辨识迭代算法,分析了算法的收敛性并给出了算法收敛的充分条件.仿真结果表明本文提出的算法在系统噪声未知时具有较强的抗噪能力和良好的收敛性.     

基于去噪优化的动力系统关键参数辨识算法

由于传统方法没有对模型噪声实现有效处理,导致辨识精度与辨识速度较低,为此提出基于调制函数法的动力学系统参数辨识算法.对模型噪声进行表示与替换,通过调制函数法构造辨识模型,通过递推算法对辨识模型进行处理以实现噪声的处理.为构造出与动力学系统模型相一致的参数辨识模型,以动力学系统模型为基础对参数辨识模型的神经网络拓扑结构进...     

Wiener系统的变聚点样条逼近递推贝叶斯算法

为了辨识过程噪声干扰的Wiener非线性系统,提出了一种基于三样条函数逼近的递推贝叶斯算法.众所周知,传统的多项式逼近具有不能外推、高阶易震荡等缺点.为了克服这些缺点,首先利用三样条函数对Wiener系统的非线性反函数进行逼近,在此基础上将待辨识系统参数化为伪线性回归系统.然后把估计到的噪声方差融入算法,接着使用递推贝叶斯算法对参数进行了估计.为了提高三样条函数对非线性反函数的逼近能力,一种基于均值的变聚点选择方法被应用于算法.文中还对算法的收敛性进行了分析,并用数值仿真和案例建模验证了算法的有效性.     

一种新的时变大纯滞后对象在线辨识方法

对具有时变特性的大纯滞后对象进行参数估计是系统辨识的一项重要课题,该文结合递归遗忘最小二乘法和互相关函数,提出了一种联合辨识算法,该方法扩展了递归遗忘最小二乘算法的应用范围。其中,递归遗忘最小二乘法用于快速地辨识对象的动态参数,而对输入输出信号进行滤波后,对象的滞后时间参数的辨识由互相关函数实现。仿真结果表明,此种方法对于时变大纯滞后对象的在线辨识是有效的,并且优于间接估计法;该文的方法具有算法简便,实用性强的特点。     

模型参考自适应IIR递归滤波器辨识新算法

针对自适应IIR滤波器算法容易陷入局部极小点的缺陷,提出了一种新的自适应递归滤波辨识算法.该算法采用模型参考自适应系统设计了辨识参数自适应律,基于Lyapunov理论保证了自适应递归算法的稳定性,而且辨识参数收敛.仿真结果表明了该算法的可行性和滤波器结构的正确性.     

基于混沌策略状态转移算法的混沌系统参数辨识*

针对混沌系统的参数辨识是一个多维参数的优化问题,提出了基于混沌策略状态转移算法的混沌系统参数辨识方法。该方法是在初始化时以混沌序列初始化种群,在搜索过程中引入混沌变异机制,利用遍历性对状态进行变异操作,避免了过早收敛,提高了全局搜索能力。利用该算法辨识Lorenz混沌系统参数,并与基本状态转移算法和粒子群算法进行比较。仿真结果表明,在有无噪声干扰的情况下,该算法比粒子群算法和基本状态转移算法具有更好的辨识精度且比粒子群算法具有更好的收敛速度,证明了该算法的有效性和抗干扰性,对混沌理论的发展有重要的意义。     

航空发动机MIMO系统的闭环辨识与故障诊断算法

针对航空发动机结构复杂、易发生故障的特点以及机理分析建模方法存在过程繁琐、运算效率低下等问题,提出了一种基于数据的航空发动机燃油机构MIMO(multiple-input multiple-output)闭环系统的参数辨识和故障诊断算法.算法先通过估计辅助模型系统的阶次间接求得时延参数,再通过多阶段最小二乘算法辨识得到前向通道和反馈通道的参数.以某型双轴涡扇航空发动机为例进行验证.结果表明,在应用中辨识结果与系统真值基本吻合,当遗忘因子取值随辨识结果的收敛程度变化时,算法可以有效地应用于气路故障的诊断当中,及时辨识出故障参数值.最后,对算法的两方面特点进行了说明:一是遗忘因子选取的重要性及选取的原则,二是算法可以有效排除噪声对辨识结果带来的干扰.     

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.     

结构未知系统降维辨识方法-----变量消去算法

针对结构未知的系统提出一种新的降维辨识方法.借助核函数方法,利用一个高维Volterra模型逼近未知系统.由于Volterra模型未知参数维数较高,为避免高阶矩阵求逆和求特征值,提出变量消去算法,将高维系统的辨识问题转化为两个低维系统辨识问题.通过理论证明采用降维算法后降维系统信息矩阵条件数变小,参数收敛速度得到提高.进一步引入Aitken加速方法提高算法收敛速度,增强算法对步长的鲁棒特性.最后通过仿真例子验证所提出方法的有效性.     

基函数可递归的泛函神经元网络学习算法

将泛函神经元结构做了一个变形,给出了一种基函数可递归的泛函神经元网络学习算法,该算法借助于矩阵伪逆递归求解方法,完成对泛函神经元网络基函数的自适应调整,最终实现泛函网络结构和参数共同的最优求解。数值仿真实验结果表明,该算法具有自适应性、鲁棒性和较高的收敛精度,将在实时在线辨识中有着广泛的应用。     

Recursive identification of Hammerstein systems with dead-zone nonlinearity in the presence of bounded noise

The existing identification algorithms for Hammerstein systems with dead-zone nonlinearity are restricted by the noise-free condition or the stochastic noise assumption. Inspired by the practical bounded noise assumption, an improved recursive identification algorithm for Hammerstein systems with dead-zone nonlinearity is proposed. Based on the system parametric model, the algorithm is derived by minimising the feasible parameter membership set. The convergence conditions are analysed, and the adaptive weighting factor and the adaptive covariance matrix are introduced to improve the convergence. The validity of this algorithm is demonstrated by two numerical examples, including a practical DC motor case.     

Self-tuning control based on generalized minimum variance criterion for auto-regressive models

Theoretical problems on self-tuning control include stability, performance and convergence of the recursive algorithm involved. In this paper, the problem of controlling minimum or non-minimum phase auto-regressive models with constant but unknown parameters is considered. The stability of an algorithm obtained by combining a recursive estimator for the controller parameters and a generalized minimum variance criterion is proved. The main result is the theorem which assures the overall stability for the closed-loop system in presence of white noise in the input-output relation, where the estimated parameters do not necessarily converge to the true values. The algorithm is proved by the Lyapunov theory.     

Adaptive recursive algorithm with logarithmic transformation for nonlinear system identification in α-stable noise

Although the least mean pth power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filters outperform the conventional least mean square (LMS) algorithm in the presence of α-stable noise, they still exhibit slow convergence and high steady-state kernel error in nonlinear system identification. To overcome these limitations, an enhanced recursive least mean pth power algorithm with logarithmic transformation (RLogLMP) is proposed in this paper. The proposed algorithm is adjusted to minimize the new cost function with the p-norm logarithmic transformation of the error signal. The logarithmic transformation, which can diminish the significance of outliers under α-stable noise environment, increases the robustness of the proposed algorithm and reduces the steady-state kernel error. Moreover, the proposed method improves the convergence rate by the enhanced recursive scheme. Finally, simulation results demonstrate that the proposed algorithm is superior to the LMP, NLMP, normalized least mean absolute deviation (NLMAD), recursive least squares (RLS) and nonlinear iteratively reweighted least squares (NIRLS) algorithms in terms of convergence rate and steady-state kernel error.     

非均匀采样多率ARMAX系统RELS算法性能分析

针对一类有色噪声干扰的非均匀采样多率ARMAX系统的辩识问题,基于增广参数维数理论,将系统模型参数化,将信息向量中含有的不可测噪声项用其估计残差代替,推导了非均匀采样ARMAX系统的递推增广最小二乘(RELS)算法;利用鞅收敛定理对该算法的收敛性进行了理论分析,结果表明该算法在噪声方差有界和广义持续激励的条件下能够收敛到真参数.仿真例子验证了该算法具有良好的收敛速度与估计精度.     

An optimal stochastic multivariable PID controller: a direct output tracking approach

This paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise. We consider multi-input multi-output linear time-invariant systems and a proportional-integral-derivative (PID) controller. The system under consideration needs not be stable. A recursive algorithm providing optimal time-varying PID gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs. The development of the proposed algorithm aims for per-time-sample minimisation of the mean-square output error in the presence of erroneous initial conditions, measurement noise, and process noise. Necessary and sufficient conditions are provided for the convergence of the output error covariance. In addition, convergence results are presented for discretised continuous-time plants. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. Performance comparison with an optimal stochastic iterative learning control scheme, an optimal PID controller, an adaptive PID controller, and a recent optimal stochastic PID controller are also included.     

Robust recursive identification of multidimensional linear regression models

Stochastic adaptive estimation and control algorithms involving recursive prediction estimates have guaranteed convergence rates when the noise is not ‘too’ coloured, as when a positive-real condition on the noise mode is satisfied. Moreover, the whiter the noise environment the more robust are the algorithms. This paper shows that for linear regression signal models, the suitable introduction of while noise into the estimation algorithm can make it more robust without compromising on convergence rates. Indeed, there are guaranteed attractive convergence rates independent of the process noise colour. No positive-real condition is imposed on the noise model.     

Recursive projection algorithm on FIR system identification with binary-valued observations

This paper studies the identification of finite impulse response (FIR) systems with binary-valued observations. Combining with the stochastic gradient algorithm and statistical property of the system noise, a recursive projection algorithm is proposed to estimate the unknown system parameters. Under some mild conditions on the a priori knowledge of the unknown parameters and inputs, the algorithm is proved to be convergent in the almost sure and mean square sense. Furthermore, the almost sure and mean square convergence rates of estimation errors are also obtained. A numerical example is given to demonstrate the effectiveness of the algorithm and the main results obtained.     

Development of multivariable PID controller gains in presence of measurement noise

This paper examines the ability of a multivariable PID controller rejecting measurement noise without the use of any external filter. The work first provides a framework for the design of the PID gains comprising of necessary and sufficient conditions for boundedness of trajectories and zero-error convergence in presence of measurement noise. It turns out that such convergence requires time-varying gains. Subsequently, novel recursive algorithms providing optimal and sub-optimal time-varying PID gains are proposed for discrete-time varying linear multiple-input multiple-output (MIMO) systems. The development of the proposed optimal algorithm is based on minimising a stochastic performance index in presence of erroneous initial conditions, white measurement noise, and white process noise. The proposed algorithms are shown to reject measurement noise provided that the system is asymptotically stable and the product of the input–output coupling matrices is full-column rank. In addition, convergence results are presented for discretised continuous-time plants. Simulation results are included to illustrate the performance capabilities of the proposed algorithms.     

An ordinary differential equation technique for continuous-timeparameter estimation

An ordinary differential equation technique is developed via averaging theory and weak convergence theory to analyze the asymptotic behavior of continuous-time recursive stochastic parameter estimators. This technique is an extension of L. Ljung's (1977) work in discrete time. Using this technique, the following results are obtained for various continuous-time parameter estimators. The recursive prediction error method, with probability one, converges to a minimum of the likelihood function. The same is true of the gradient method. The extended Kalman filter fails, with probability one, to converge to the true values of the parameters in a system whose state noise covariance is unknown. An example of the extended least squares algorithm is analyzed in detail. Analytic bounds are obtained for the asymptotic rate of convergence of all three estimators applied to this example     

多层前馈网络的一种快速算法

多层前馈网络是目前研究得最多和应用最广泛的神经网络之一，其基本算法为误差反向传播（ＥＢＰ）算法，但存在收敛速度慢和局部极小的问题。本文利用递归最小二乘算法来训练多层前馈网络，ＲＬＳ算法具有收敛速度快，抗噪声能力强等优点，还克服了常规ＢＰ算法中学习率选取困难的缺点。仿真结果说明了本文方法的有效性。