Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies.     

Recursive generalized extended least squares and RML algorithms for identification of bilinear systems with ARMA noise

Bilinear systems are considered as a particular class of nonlinear systems including the state variables which are typically used for online identification. By using a recursive identification method and the maximum likelihood principle, this paper presents two recursive-based algorithms to identify the parameters of bilinear in parameter systems with ARMA noise. In this regard, recursive generalized extended least squares (RGELS) and recursive Maximum Likelihood (RML) algorithms have been proposed for identification of bilinear systems. These algorithms can be used as an alternative choice in system identification with acceptable performance. The proposed algorithms estimate the correlated noise parameters with high accuracy by making full use of the measurement data. Simulation results indicate that the proposed algorithms are effective for online identification of bilinear in parameter systems with high convergence speed.     

A least squares support vector regression coupled linear reconstruction algorithm for ECT

Linearization error of the simplified linear electrical capacitance tomography (ECT) model is one of the leading causes of ECT reconstruction errors. In this paper, the least squares support vector regression (LSSVR) is used to fit the correlation between the capacitance vector and the linearization error. And it is trained by the training samples of typical phase distributions. When removing the linearization error from equations derived by the linear model, the reconstruction problem becomes an exact linear inverse problem because the nonlinearity of ECT is completely included in the linearization error. Then a reconstruction algorithm combining the LSSVR and the Landweber iteration is proposed. Numerical results show that the proposed algorithm achieves significantly better reconstruction accuracies than the linear back projection and the Landweber algorithm for both the noise-free and noisy cases. Compared with the Landweber algorithm, The image errors of the reconstructions are reduced by about 23%–68%, and the correlation coefficient increased by about 0.04–0.14. And the calculation time of the proposed algorithm for all the tested cases is about 0.4–0.6s, which makes it have the potential for real-time imaging. Static experimental results show that the reconstructions of the proposed algorithm have more accurate phase boundary shapes and fewer artifacts.     

基于非线性GA算法的MFF透射模型的参数辨识与优化

基于磁性流体(MF)磁链理论,建立了磁流体薄膜(MFF)传感模型,并通过Monte Carlo法分析了MF透射特性,建立了MFF透射模型。采用非线性遗传算法(GA)对MFF透射模型进行了参数辨识,分析了种群规模、进化代数、交叉率、变异率等参数选值对算法运行结果的影响,并选取了最佳参数组合,搭建了MFF电流传感器实验平台,分析了MFF厚度和粒子浓度对MFF透射性的影响,运用MFF透射模型对MFF电流传感器进行了仿真预测。实验及仿真结果表明该模型具有较好的预测性,预测误差在2.29%以内,所设计的MFF电流传感器的测量灵敏度达到11μW/A。     

基于最小二乘支持向量机的传感器非线性动态补偿

提出了一种基于最小二乘支持向量机的非线性传感器动态测量误差的校正方法，使得通过该方法补偿的传感器具有理想的输入输出特性。先将传感器的非线性动态系统分解成线性动态子环节和非线性静态子环节串联；与之对应，非线性动态补偿过程也包含2个阶段：线性动态补偿和非线性静态校正。然后，通过函数展开将补偿器的非线性传递函数转换为等价的类线性形式一中间模型；再通过LS-SVM回归算法求取中间模型参数；最后，推导出中间模型参数与补偿器2个子模型参数之间的关系，并通过该关系实现非线性静态校正和线性动态补偿环节的同时辨识。与常规非线性动态补偿方法比较，该方法优点是明显的：（1）只需进行一次动态标定实验；（2）能给出非线性动态补偿器的数学解析表达式；（3）充分利用LS—SVM的优点，使辨识的补偿器具有更好的抗干扰能力。仿真与实际实验结果均表明该传感器非线性动态补偿方法有效。     

A least squares support vector machine model for prediction of the next day solar insolation for effective use of PV systems

Accurate prediction of daily solar insolation has been one of the most important issues of solar engineering. The amount of solar insolation on a given location is a vital data for photovoltaic plants. Systems efficiency is easily affected by the changes in solar radiation so, this study is aimed to develop a Least Squares Support Vector Machine (LS-SVM) based intelligent model to predict the next day’s solar insolation for taking measures. Daily temperature and insolation data measured by Turkish State Meteorological Service for three years (2000–2002) were used as training data and the values of 2003 used as testing data. Numbers of the days from 1st January, daily mean temperature, daily maximum temperature, sunshine duration and the solar insolation of the day before parameters have been used as inputs to predict the daily solar insolation. The simulations were carried out with SVM Toolbox of MATLAB software. As a conclusion the results show that LS-SVM is a good method in estimating the amount of solar insolation of a given location with 99.294% accuracy.     

基于非线性GA算法的动态P模型的参数辨识与验证

针对现有的GMM-FBG电流传感器的磁滞非线性问题,提出了一种改进的动态Preisach磁滞模型。采用非线性遗传算法对改进动态Preisach磁滞数学模型进行参数辨识,提高了动态磁滞曲线的预测精度。运用改进动态Preisach模型对GMMFBG电流传感器进行建模及实验验证,实验及仿真结果表明该模型具有较好的预测性,预测误差在3.0%以内。经过磁滞补偿使得传感系统电流的测量灵敏度达到0.050 nm/A。     

Tracking control of nonlinear lumped mechanical continuous-time systems: A model-based iterative learning approach

This paper presents a nonlinear model-based iterative learning control procedure to achieve accurate tracking control for nonlinear lumped mechanical continuous-time systems. The model structure used in this iterative learning control procedure is new and combines a linear state space model and a nonlinear feature space transformation. An intuitive two-step iterative algorithm to identify the model parameters is presented. It alternates between the estimation of the linear and the nonlinear model part. It is assumed that besides the input and output signals also the full state vector of the system is available for identification. A measurement and signal processing procedure to estimate these signals for lumped mechanical systems is presented. The iterative learning control procedure relies on the calculation of the input that generates a given model output, so-called offline model inversion. A new offline nonlinear model inversion method for continuous-time, nonlinear time-invariant, state space models based on Newton's method is presented and applied to the new model structure. This model inversion method is not restricted to minimum phase models. It requires only calculation of the first order derivatives of the state space model and is applicable to multivariable models. For periodic reference signals the method yields a compact implementation in the frequency domain. Moreover it is shown that a bandwidth can be specified up to which learning is allowed when using this inversion method in the iterative learning control procedure. Experimental results for a nonlinear single-input-single-output system corresponding to a quarter car on a hydraulic test rig are presented. It is shown that the new nonlinear approach outperforms the linear iterative learning control approach which is currently used in the automotive industry on durability test rigs.     

Nonlinear modeling and identification of the electro-hydraulic control system of an excavator arm using BONL model

Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear（BONL） models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener（H-W） model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener（P-H-W） model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters struc~tres. Then, a modified recursive least square algorithm（MRLSA） with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive （ARX） model, respectively. This research is helpful in controller design, system monitoring and diagnosis.     

Estimation of region of attraction for polynomial nonlinear systems: A numerical method

This paper introduces a numerical method to estimate the region of attraction for polynomial nonlinear systems using sum of squares programming. This method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. The invariant set is an estimation of the region of attraction for the equilibrium point. In order to enlarge the estimation, a subset of the invariant set defined by a shape factor is enlarged by solving a sum of squares optimization problem. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. The efficiency of the proposed method is shown by a few numerical examples.     

The study of hybrid model identification,computation analysis and fault location for nonlinear dynamic circuits and systems

This paper presents the hybrid model identification for a class of nonlinear circuits and systems via a combination of the block-pulse function transform with the Volterra series. After discussing the method to establish the hybrid model and introducing the hybrid model identification, a set of relative formulas are derived for calculating the hybrid model and computing the Volterra series solution of nonlinear dynamic circuits and systems. In order to significantly reduce the computation cost for fault location, the paper presents a new fault diagnosis method based on multiple preset models that can be realized online. An example of identification simulation and fault diagnosis are given. Results show that the method has high accuracy and efficiency for fault location of nonlinear dynamic circuits and systems. __________ Translated from Chinese Journal Of Scientific Instrument, 2005, 26(8) (in Chinese)     

A new discrete-time robust adaptive time-delay control for a class of uncertain nonlinear strict-feedback systems using sliding mode

This paper presents a new discrete-time adaptive second-order sliding mode control with time delay estimation (TDE) for a class of uncertain nonlinear time-varying strict-feedback systems. The existing researches on time delay control (TDC) are conventionally established based on a stability criterion that is subject to the infinitesimal time delay assumption. Recently, this criterion was rejected and a new criterion was proposed for the development of a controller for systems with fully known dynamics. In this study, this approach is extended to uncertain systems. Specifically, a new criterion is developed for the stability of the TDE-error within an adaptive robust controller design without the infinitesimal time delay assumption. With the proposed adaptive robust control, there is no need for determination of uncertainties upper-bounds. Simulation results illustrate the efficacy of the proposed controller.