Multiple model reduction approach using gap metric and stability margin for control nonlinear systems

This paper deals with the control of nonlinear systems using multimodel approach. The main idea of this work consists on the association of the gap metric and the stability margin tools to reduce the number of models constituting the multimodel bank. In fact, the self-organisation map (SOM) algorithm is used, firstly, to develop a preliminary multimodel bank. Then, the gap metric and the stability margin are computed to determine the redundancy of the initial multimodel bank. So, the multimodel controller is elaborated based on the reduced model bank. Simulations confirm the method for selecting the appropriate number of local models which should be used in the controller design.

     

Multilinear model decomposition of MIMO nonlinear systems and its implication for multilinear model-based control

In order to accomplish the multilinear model decomposition of MIMO nonlinear processes with multiple scheduling variables, a systematic division algorithm based on gap metric together with a supporting dichotomy gridding algorithm is proposed by using the gap metric as a measuring tool. For a prescribed distance level, this gap metric based division algorithm effectively decomposes a MIMO nonlinear system into a set of linear subsystems which provide enough model information for multilinear model-based controller design without linear model redundancy. Based on the linear models, a set of linear MPC controllers are designed and combined into a global controller for setpoint tracking control. Two benchmark nonlinear processes are studied to demonstrate the effectiveness of the proposed method.     

A gap metric based multiple model approach for nonlinear switched systems

Many applications in chemical engineering often exhibit a switching character due to the presence of discrete modes in the course of their operation. First principles models of such systems constructed using process simulators are far too complex for use in online applications, especially in model-based control. For such systems, numerous control-relevant modeling approaches have been reported in the literature such as mixed logic dynamical (MLD) models [1] and piece wise affine (PWA) [2] models among others. These models describe the evolution of states in each discrete mode using linear equations. Fewer control-relevant models have been reported that address the nonlinear behavior of switched systems. To model nonlinear hybrid systems, Nandola and Bhartiya [3] proposed a multiple linear model approach wherein multiple linear models are used to describe the dynamic behavior in each mode of the hybrid system. However, no guidelines were provided to select the number of models necessary in each mode and their region of validity. In this work, we address these lacunae by presenting a systematic multiple model approach to describe nonlinear switched systems. The method involves a trajectory based linearization and employs a model bank with a set of local linear models for each discrete operational mode. The model bank is generated by linearizing the first principles model across a carefully designed trajectory based on accuracy of multi-step ahead predictions. The numerous models thus obtained are clustered using the gap metric as the distance measure and representative models are selected. The selected linear models are aggregated using Bayesian or Fuzzy approaches to obtain the global model for the nonlinear switched system. A simulation case study of spherical two-tank system and an experimental case study of a benchmark problem consisting of three tanks are used to validate the proposed modeling strategy.     

Control-relevant nonlinearity measure and integrated multi-model control

A control-relevant nonlinearity measure (CRNM) method is proposed based on the gap metric and the gap metric stability margin to measure the nonlinear degree of a system once a linear control strategy is selected. Supported by the CRNM method, an integrated multi-model control framework is developed, in which the multi-model decomposition and local controller design are closely integrated, model redundancy is avoided, computational load is reduced, and dependency on a prior knowledge is reduced. Besides, a 1/δ gap-based weighting method is put forward to combine the local controllers. On one hand, the 1/δ gap-based weighting method has merely one tuning parameter and can be computed off-line; on the other hand, it is sensitive to the tuning parameter, flexible and easy to tune. Two continuous stirred tank reactor (CSTR) systems are investigated. Closed-loop simulations validate the effectiveness and benefits of the proposed integrated multi-model control approach based on CRNM.     

Application of gap metric to model bank determination in multilinear model approach

This paper presents a gap metric based method which aims to perform the operating range decomposition and the minimum linear model bank determination of a nonlinear system when multilinear model approach is employed to design a controller for this nonlinear system. For a prescribed distance level, the minimum linear model bank determined by the proposed method can provide sufficient information for multilinear model controller design of the nonlinear system. To illustrate the usefulness of the proposed method, two examples of nonlinear systems are presented. Moreover, a mixed logical dynamical model-based MPC (MLD–MPC) controller is designed based on the minimum model bank. Simulations confirm the method for selecting linear model bank in multilinear model approach.     

Initializing Wiener–Hammerstein models based on partitioning of the best linear approximation

This paper describes a new algorithm for initializing and estimating Wiener–Hammerstein models which consist of two linear parts with a static nonlinearity in between. The algorithm makes use of the best linear model of the system, which is a consistent estimate of the systems dynamics for Gaussian excitations. The linear model is split in all possible ways into two sub-models. For all possible splits, a Wiener–Hammerstein model is initialized which means that a nonlinearity is introduced in between the two sub-models. The linear parameters of this nonlinearity can be estimated using least-squares. All initialized models can then be ranked depending on the fit. Typically, one is only interested in the best one, for which all parameters are fitted using prediction error minimization.The paper explains the algorithm in detail and consistency of the initialization is proven. Computational aspects are investigated, showing that in most realistic cases, the number of splits of the initial linear model remains low enough to make the algorithm useful. The algorithm is illustrated on an example where it is shown that the initialization is a tool to avoid many local minima.     

Analysis and control of a nonlinear boiler-turbine unit

A distance measure is proposed via the gap metric in this paper, and the concept is applied to a boiler-turbine unit to analyze its dynamics. It is shown that the unit shows severe nonlinearity, but the nonlinearity can be avoided by careful choice of the operating range. A single linear controller can be designed to work in such an operating range. It is also shown that the controller constraint is another source of the nonlinearity, which can be compensated using anti-windup techniques. Simulation results are given to verify the conclusions.     

迟滞非线性系统的建模与控制

介绍了对不平滑、多映射迟滞非线性系统的研究成果,重点阐述了迟滞建模与控制器设计的研究现状.详细地分析比较了Preisach模型和线性迟滞模型优缺点.在控制器设计方法方面,比较了常用的两类基于逆模型补偿方案的特点、差别和适应范围,并扼要论述了其他控制方案.最后,对迟滞研究中仍需解决的问题和未来发展方向进行了探讨.     

Performance evaluation of nonlinear weighted T-system

This article deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGMs). These graphs are an extension of weighted T-systems studied in the Petri net literature. These models do not admit a linear representation in (min,?+) algebra. This nonlinearity is due to the presence of weights on arcs. To mitigate this problem of nonlinearity and to apply some basic results used to analyse the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min,?+) linear model.     

Identification of IIR Wiener systems with spline nonlinearities that have variable knots

An algorithm is developed for the identification of Wiener systems, linear dynamic elements followed by static nonlinearities. In this case, the linear element is modeled using a recursive digital filter, while the static nonlinearity is represented by a spline of arbitrary but fixed degree. The primary contribution in this note is the use of variable knot splines, which allow for the use of splines with relatively few knot points, in the context of Wiener system identification. The model output is shown to be nonlinear in the filter parameters and in the knot points, but linear in the remaining spline parameters. Thus, a separable least squares algorithm is used to estimate the model parameters. Monte-Carlo simulations are used to compare the performance of the algorithm identifying models with linear and cubic spline nonlinearities, with a similar technique using polynomial nonlinearities.     

A comparison of error metrics and constraints for multiple endmember spectral mixture analysis and spectral angle mapper

Spectral matching algorithms can be used for the identification of unknown spectra based on a measure of similarity with one or more known spectra. Two popular spectral matching algorithms use different error metrics and constraints to determine the existence of a spectral match. Multiple endmember spectral mixture analysis (MESMA) is a linear mixing model that uses a root mean square error (RMSE) error metric. Spectral angle mapper (SAM) compares two spectra using a spectral angle error metric. This paper compares two endmember MESMA and SAM using a spectral library containing six land cover classes. RMSE and spectral angle for models within each land cover class were directly compared. The dependence of RMSE on the albedo of the modeled spectrum was also explored. RMSE and spectral angle were found to be closely related, although not equivalent, due to variations in the albedo of the modeled spectra. Error constraints applied to both models resulted in large differences in the number of spectral matches. Using MESMA, the number of spectra modeled within the error constraint increased as the albedo of the modeled spectra decreased. The value of the error constraint used was shown to make a much larger difference in the number of spectra modeled than the choice of spectral matching algorithm.     

保持视觉外观特征的网格简化

针对附有纹理属性的网格模型,提出并实现了一种保持模型基本外观和形状特征的多分辨率网格简化算法.采用半边折叠操作,综合考虑了网格模型半边的几何重要性和纹理属性重要性,将其作为各半边的折叠代价来确定模型中所有边的折叠顺序.预先对网格模型中的边界边和纹理边进行标记,并在简化过程中进行加权处理.实验结果表明,即使在急剧的模型简化后,该方法仍能很好地保持原有模型的视觉外观和形状特征.     

基于马氏距离度量的局部线性嵌入算法

局部线性嵌入算法(LLE)中常用欧氏距离度量样本间相似度。而对于图像等高维数据,欧氏距离不能准确体现样本间的相似程度。文中提出基于马氏距离度量的局部线性嵌入算法(MLLE)。算法首先从现有样本中学习到一个马氏度量,然后在LLE算法的近邻选择、现有样本及新样本降维过程中用马氏度量作为相似性度量。将MLLE算法及其它典型的流形学习算法在ORL和USPS数据库上进行对比实验,结果表明MLLE算法具有良好的识别性能。     

Identification of Friction and Rigid-Body Dynamics of Parallel Kinematic Structures for Model-Based Control

Until now, the experimental identification of the dynamics of parallelrobots is restricted to simple models in combination with adaptivecontrol algorithms. This gap is closed by a new approach presented inthis paper, which is suited for even complex parallel kinematicstructures. The approach consists of two steps and utilizes simplepoint-to-point (PTP) motions that lead to a separation of friction andrigid-body dynamics. In the first step, local models are determined fora lot of different configurations, i.e. end-effector positions. In thesecond step, the overall friction model and the overall rigid-bodymodel are calculated from the local models by linear Least-Squaresestimators. The use of linear estimators is based on a formulation ofthe dynamic equations, which is linear with respect to a dynamicparameter vector of minimal dimension. This formulation is automaticallyobtained by an algorithm, which utilizes Jourdain's principle of virtualpower. The experimental application of the identified model tomodel-based feedforward control of the innovative hexapod PaLiDA, whichhas been developed by the Institute of Production Engineering andMachine Tools of the University of Hannover, proves the capability andefficiency of the presented algorithms.     

基于混合互信息的医学图像配准

通常的互信息测度是基于Shannon熵的,对Renyi熵进行分析,根据某些参数下的Renyi熵可以消除局部极值、而Shannon熵对于局部极值具有很强吸引域的特点,提出一种使用Renyi熵和Shannon熵的混合互信息测度,将两种测度分别用于不同的搜索阶段,首先使用全局搜索算法寻找基于Renyi熵的归一化互信息测度的局部极值,再通过局部优化方法对当前的局部最优解进行局部寻优以找到全局最优解,在局部优化阶段使用基于Shannon熵的归一化互信息测度作为目标函数。实验表明,这种配准算法比单纯使用Shannon熵能够取得更准确的配准结果,而且求解速度得到提高。     

信息量加权的梯度显著度图像质量评价

目的：针对信息量加权结构化图像质量评价算法(Information Content Weighted SSIM, IW-SSIM)对图像局部失真度量能力的不足,提出了一种被称为信息量加权的梯度显著度图像质量评价改进算法(Information Content Weighted Gradient Salience SSIM, IW-GS-SSIM)。方法：该算法首先根据人眼视觉系统响应亮度刺激的韦伯定律,仅在空域内利用一次滤波快速计算出当前像素点与背景之间的对比度并将其非线性映射为该像素点的视觉显著度。然后,将视觉显著度与梯度特征结合后获得了一种新的被称为梯度显著度局部失真度量(GS-SSIM)并将其替换IW-SSIM算法中的SSIM局部结构化度量。结果：在六大公开基准数据库上完成的大量对比实验表明：对于图像的各种噪声和模糊等类型失真,GS-SSIM较SSIM局部失真度量具有更高的评价准确率。与IW-SSIM算法和其它被广泛引用的图像质量评价算法相比,改进算法评价结果总体上与主观评价结果具有更高的一致性。结论：视觉显著度与梯度特征相结合后所构成的结构化度量能够有效提高经典SSIM结构化度量对图像局部失真度量的准确性,未来可以考虑将人类视觉系统(HVS)的其它特性融入到图像质量评价算法中,以进一步提高算法的准确性。     

Wiener-Hammerstein modeling of nonlinear effects in bilinear systems

The modeling of nonlinear effects in bilinear systems using Wiener-Hammerstein models is considered. Such models are chosen based on the block-oriented structure of bilinear systems and the shapes of their Volterra kernels. Theoretical analysis is given for first-order bilinear systems, and simulation results are presented for first- and second-order systems. While the nonlinearity is only approximately Wiener-Hammerstein, the models are able to capture a significant part of the nonlinear dynamics. In order to reduce the complexity of optimizing the model parameters, the linear subsystems are estimated using the technique of linear interpolation in the frequency domain.