A PWA model identification method based on optimal operating region partition with the output-error minimization for nonlinear systems

When piecewise affine (PWA) model-based control methods are applied to nonlinear systems, the first question is how to get sub-models and corresponding operating regions. Motivated by the fact that the operating region of each sub-model is an important component of a PWA model and the parameters of a sub-model are strongly coupled with the operating region, a new PWA model identification method based on optimal operating region partition with the output-error minimization for nonlinear systems is initiated. Firstly, construct local data sets from input-output data and get local models by using the least square (LS) method. Secondly, cluster local models according to the feature vectors and identify the parameter vectors of sub-models by weighted least squares (WLS) method. Thirdly, get the initial operating region partition by using a normalized exponential function, which is to partition the operating space completely. Finally, simultaneously determine the optimal parameter vectors of sub-models and the optimal operating region partition underlying the output-error minimization, which is executed by particle swarm optimization (PSO) algorithm. Simulation results demonstrate that the proposed method can improve model accuracy compared with two existing methods.     

Winkler地基梁动力学系统的无量纲化与参数识别

为简化Winkler地基梁动力学系统的双参数识别计算,提出一种新无量纲方法,通过对系统时间、空间坐标进行线性变换,实现动力学方程系数的彻底归一化,得到与系统参数解耦的广义频率方程,发现频率、频率比仅由无量纲梁长决定的本质.提出基于频率比互等关系的双参数识别算法,该算法通过对广义频率方程进行一次求解即可在相应边界条件下得到频率、频率比关于无量纲梁长的预解集,在得到该系统任意两阶实测频率后,即可依托于时间、空间还原系数所建立的线性转换关系实现对双系统参数的定解.较之于传统双参数识别算法,该算法具有两个特点：(1)识别计算仅涉及单变量超越方程的求解与线性转换,避免了双参数超越方程组的非线性迭代问题,可使识别计算得到有效简化.(2)任意系统参数值的变化仅影响时空、空间还原系数的大小,预解集具有适用于系统参数值任意变化的一般性,可有效避免因系统参数值改变而导致重复迭代的情况,实现了解的一般化.     

Automatic modeling algorithm of stochastic error for inertial sensors

This paper proposes an automatic algorithm to determine the properties of stochastic processes and their parameters for inertial error. The proposed approach is based on a recently developed method called the generalized method of wavelet moments (GMWM), whose estimator was proven to be consistent and asymptotically normally distributed. This algorithm is suitable mainly (but not only) for the combination of several stochastic processes, where the model identification and parameter estimation are quite difficult for the traditional methods, such as the Allan variance and the power spectral density analysis. This algorithm further explores the complete stochastic error models and the candidate model ranking criterion to realize automatic model identification and determination. The best model is selected by making the trade-off between the model accuracy and the model complexity. The validation of this approach is verified by practical examples of model selection for MEMS-IMUs (micro-electro-mechanical system inertial measurement units) in varying dynamic conditions.     

基于残差方差的系统阶次和参数辨识算法

系统辨识的研究一般是将系统的阶次辨识和参数估计分开的,但实际应用过程中这两个问题又是紧密相关的。有的模型阶次辨识过程是伴随着模型的参数估计,因此可以对这类阶次辨识方法同参数估计的方法进行融合和扩展。针对输出误差系统,借助辅助模型推导出基于残差方差递推算法,利用该算法辨识出了模型的阶次和参数,减少了传统系统辨识过程的计算量和辨识时间。     

Identification of piecewise affine systems based on statistical clustering technique

This paper is concerned with the identification of a class of piecewise affine systems called a piecewise affine autoregressive exogenous (PWARX) model. The PWARX model is composed of ARX sub-models each of which corresponds to a polyhedral region of the regression space. Under the temporary assumption that the number of sub-models is known a priori, the input-output data are collected into several clusters by using a statistical clustering algorithm. We utilize support vector classifiers to estimate the boundary hyperplane between two adjacent regions in the regression space. In each cluster, the parameter vector of the sub-model is obtained by the least squares method. It turns out that the present statistical clustering approach enables us to estimate the number of sub-models based on the information criteria such as CAIC and MDL. The estimate of the number of sub-models is performed by applying the identification procedure several times to the same data set, after having fixed the number of sub-models to different values. Finally, we verify the applicability of the present identification method through a numerical example of a Hammerstein model.     

Fault detection and identification relying on set-membership identifiability

Identifiability is the property that a mathematical model must satisfy to guarantee an unambiguous mapping between its parameters and the output trajectories. It is of prime importance when parameters must be estimated from experimental data representing input–output behavior and clearly when parameter estimation is used for fault detection and identification. Definitions of identifiability and methods for checking this property for linear and nonlinear systems are now well established and, interestingly, some scarce works (Braems et al., 2001, Jauberthie et al., 2011) have provided identifiability definitions and numerical tests in a bounded-error context. This paper resumes and better formalizes the two complementary definitions of set-membership identifiability and μ-set-membership identifiability of Jauberthie et al. (2011) and presents a method applicable to nonlinear systems for checking them. This method is based on differential algebra and makes use of relations linking the observations, the inputs and the unknown parameters of the system. Using these results, a method for fault detection and identification is proposed. The relations mentioned above are used to estimate the uncertain parameters of the model. By building the parameter estimation scheme on the analysis of identifiability, the solution set is guaranteed to reduce to one connected set, avoiding this way the pessimism of classical set-membership estimation methods. Fault detection and identification are performed at once by checking the estimated values against the parameter nominal ranges. The method is illustrated with an example describing the capacity of a macrophage mannose receptor to endocytose a specific soluble macromolecule.     

Parameter identification of linear structural dynamic systems

The parameter estimations of linear multi-degree-of-freedom structural dynamic systems are carried out in time domain. Methods for estimating the system parameters and the modal parameters are presented. The equation of motion is transformed into the state space equation of the observable canonical form, and then into the auto-regressive and moving average model with auxiliary stochastic input (ARMAX) model to process the measurement data contaminated by the system noise as well as the output noise. The parameters of the ARMAX model are estimated by using the sequential prediction error method. Then, the parameters of equation of motion are recovered thereafter. In order to verify the accuracy of the estimation method, analytical simulation studies are performed for a model with two degrees of freedom on the basis of simulated data under various noise conditions. It is shown that the presented methods yield good estimates even under large noise conditions. The method is also applied to the identification of the modal parameters of a building model based on the experimental data.     

具有多层感知器力矩补偿的机器人自抗扰控制

本文针对机器人系统的控制特性, 提出了一种基于自抗扰控制(ADRC)的关节控制算法, 该算法可以克服 传统控制算法中存在的如系统抗干扰能力弱, 控制性能受限于建模精度, 动态性能与稳态性能难以兼顾, 控制律设 计较为复杂等问题. 针对受控系统特性给出了一套实际控制器的完整设计方法与参数整定方法, 并根据控制性能指 标设计优化函数完成了最优控制参数的优化, 在系统参数辨识的基础上利用多层感知器(MLP)设计了对建模不确 定性的补偿网络. 数值仿真和实验结果均表明该算法能够实现机器人快速稳定的轨迹跟踪, 具有良好的控制精度 与很强的抗干扰能力, 此外该算法不依赖于精确的系统模型, 降低了实际设计和应用的难度, 具有很好的工程应用 价值.     

一种带有色量测噪声的非线性系统辨识方法

利用最大似然判据, 本文提出了一种带有色量测噪声的非线性系统辨识方法. 首先, 利用量测差分方法将有色量测噪声白色化, 获得新的量测方程, 从而将带有色量测噪声的非线性系统辨识问题转化成带白色量测噪声和一步延迟状态的非线性系统辨识问题. 其次, 利用期望最大化(Expectation maximization, EM)算法提出了一种新的基于最大似然估计的非线性系统辨识方法, 该算法由期望步骤(Expectation step, E-step)和最大化步骤(Maximization step, M-step)两部分组成. 在期望步骤中, 基于当前估计的参数并利用带有色量测噪声的高斯近似滤波器和平滑器, 近似计算完整的对数似然函数的期望. 在最大化步骤中, 近似计算的似然函数期望值被最大化, 并且通过解析更新获得噪声参数估计, 通过Newton更新方法获得模型参数的估计. 最后, 数值仿真验证了本文提出算法的有效性.     

Maximum likelihood least squares‐based iterative methods for output‐error bilinear‐parameter models with colored noises

This article is concerned with the parameter identification of output‐error bilinear‐parameter models with colored noises from measurement data. An auxiliary model least squares‐based iterative method is developed through the overparameterization model. It examines the difficulty of estimating the overparameterized vector, which usually presents a heavy computational burden in the identification process. To overcome this drawback, a parameter separation technique is introduced and the nonlinear model is reformulated as a refined identification model through eliminating the crossmultiplying terms. In this regard, a parameter separation least squares‐based iterative (PS‐LSI) algorithm is derived by avoiding estimating the redundant parameters. On the basis of the PS‐LSI algorithm, we derive a maximum likelihood least squares‐based iterative method to further improve the numerical accuracy. The identification is dependent on the formulation of a pseudolinear regression relationship, which contains two linear prefilters constructed from the system and noise models. The performance of this proposed method is confirmed by the numerical simulations as well as direct comparisons with other existing algorithms.     

Time-varying parametric system multiresolution identification by wavelets

In this paper, the problem of time-varying parametric system identification by wavelets is discussed. Employing wavelet operator matrix representation, we propose a new multiresolution least squares (MLS) algorithm for time-varying AR (ARX) system identification and a multiresolution least mean squares (MLMS) algorithm for the refinement of parameter estimation. These techniques can achieve the optimal tradeoff between the over-fitted solution and the poorly represented identification. The main features of time-varying model parameters are extracted in a multiresolution way, which can be used to represent the smooth trends as well as track the rapidly changing components of time-varying parameters simultaneously and adaptively. Further, a noisy time-varying AR (ARX) model can also be identified by combining the total least squares algorithm with the MLS algorithm. Based on the proposed AR (ARX) model parameter estimation algorithm, a novel identification scheme for time-varying ARMA (ARMAX) system is presented. A higher-order time-varying AR (ARX) model is used to approximate the time-varying ARMA (ARMAX) system and thus obtain an initial parameter estimation. Then an iterative algorithm is applied to obtain the consistent and efficient estimates of the ARMA (ARMAX) system parameters. This ARMA (ARMAX) identification algorithm requires linear operations only and thus greatly saves the computational load. In order to determine the time-varying model order, some modified AIC and MDL criterions are developed based on the proposed wavelet identification schemes. Simulation results verify that our methods can track the rapidly changing of time-varying system parameters and attain the best balance between parsimonious modelling and accurate identification.     

Identification Scheme for Fractional Hammerstein Models With the Delayed Haar Wavelet

The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix(HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.     

A hybrid clustering and gradient descent approach for fuzzymodeling

In this paper, a hybrid clustering and gradient descent approach is proposed for automatically constructing a multi-input fuzzy model where only the input-output data of the identified system are available. The proposed approach is composed of two steps: structure identification and parameter identification. In the process of structure identification, a clustering method is proposed to provide a systematic procedure to determine the number of fuzzy rules and construct an initial fuzzy model from the given input-output data. In the process of parameter identification, the gradient descent method is used to tune the parameters of the constructed fuzzy model to obtain a more precise fuzzy model from the given input-output data. Finally, two examples of nonlinear system are given to illustrate the effectiveness of the proposed approach.     

EFFECTIVE DECENTRALIZED TITO PROCESS IDENTIFICATION FROM CLOSED‐LOOP STEP RESPONSES

In this paper, a new identification method performed in the time domain based on the decentralized step‐test is proposed for two inputs and two outputs (TITO) processes with significant interactions. In terms of parameter identification, the coupled closed‐loop TITO system is decoupled to obtain four individual single open‐loop systems with the same input signal. As in the SISO case, new linear regression equations are derived, from which the parameters of a first‐ or second‐order plus dead‐time model can be obtained directly. The proposed method outperforms the existing estimation methods for multivariable control systems that use step‐test responses. Furthermore, the method is robust in the presence of high levels of measurement noise. Simulation examples are given to show both effectiveness and practicality of the identification method for a wide range of multivariable processes. The usefulness of the identified method in multivariable process modeling and controller design is demonstrated.     

基于改进粒子群算法的Hammerstein模型辨识

提出辨识非线性Hammerstein模型的新方法。将非线性系统的辨识问题转化为参数空间上的函数优化问题,采用粒子群算法获得该优化问题的解。为了进一步增强粒子群优化算法的辨识性能,提出采用速度变异粒子群对整个参数空间进行搜索得到系统参数的最优估计。仿真结果验证了该方法的有效性。     

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.     

具有惯量特性的并网逆变器黑箱模型辨识

针对具有惯量特性的并网逆变器,提出了一种统一虚拟同步发电机(VSG)模型和基于智能算法的惯量阻尼参数辨识方法,实现了对未知模型的商业化并网逆变器装置的数学建模和惯量评估.基于将具有惯量特性的并网逆变器装置等值为一台VSG的思想,总结了现有各种VSG的实现方法,归纳出一种包含锁相环和动稳态阻尼特性的统一VSG模型;利用遗传算法实现了统一VSG模型惯量和阻尼参数的准确辨识,但锁相环的控制参数却无法准确辨识,为此,从系统闭环极点的角度详细分析了锁相环参数辨识的准确性与其带宽之间的关系,并提出了选取高带宽锁相环的统一 VSG模型进行并网逆变器等值惯量和阻尼辨识的解决方案.最后,通过MATLAB/simulink仿真验证了所提模型辨识方法在多种不同VSG控制策略下的适用性和有效性.     

铅锌烧结过程烧穿点的集成预测模型

针对影响铅锌烧结过程烧穿点的因素具有不确定性的特点, 提出一种基于信息熵技术的烧穿点集成预测模型. 首先利用软测量技术获得烧穿点. 然后建立基于满意聚类的T-S预测模型以降低不确性因素所带来的影响,并将共轭梯度法和粒子群优化算法有机结合起来进行T-S模型中各个子模型的参数辨识, 以提高辨识精度. 接着建立基于工艺参数的神经网络预测模型. 最后考虑到信息熵技术具有信息融合和降低不确定性的能力, 利用其将以上预测模型进行集成. 实验结果表明所提出的集成预测模型具有较高的预测精度和较强的适应性.     

Parameter independent model order reduction

Several recently developed model order reduction methods for fast simulation of large-scale dynamical systems with two or more parameters are reviewed. Besides, an alternative approach for linear parameter system model reduction as well as a more efficient method for nonlinear parameter system model reduction are proposed in this paper. Comparison between different methods from theoretical elegancy to complexity of implementation are given. By these methods, a large dimensional system with parameters can be reduced to a smaller dimensional parameter system that can approximate the original large sized system to a certain degree for all the parameters.