Identification of smooth nonlinear dynamical systems with non-smooth steady-state features

This work discusses the identification of single-block smooth nonlinear discrete-time polynomial models with non-smooth steady-state features. Based on bifurcation theory, conditions are developed and used to determine some general aspects of the model structure and also to determine some constraints on the parameters required to guarantee the aforementioned features. The procedure uses only smooth functions of the regressors, a single possibly smooth input and some prior knowledge about the steady-state behavior. The non-smooth static function is here obtained by interchanging the stability of two sets of equilibria at the break-point, which corresponds to guaranteeing a transcritical bifurcation. This work discusses how to determine the domain over which the results are valid. The procedure is illustrated with simulated and experimental data.     

System identification by operatorial cancellation of nonlinear terms and application to a class of Volterra models

In this paper, a method is proposed for the identification of some SISO nonlinear models with two ill‐known components of different nature: a linear (possibly dynamic) part and a static nonlinear one. This method is well adapted when no a priori information is available about the nonlinear component to be identified. It is based on a difference operator, which enables to cancel the nonlinear term when applied to the model. Only the ill‐known linear part remains in the transformed model; it can therefore be identified independently of the nonlinear term. Based on the identified linear component, we have access to a pseudograph of the nonlinear term, whose shape can give precious information for the parameterization of the unknown nonlinear part and its identification. The identification model under consideration is defined in an abstract framework, with very weak hypotheses, so that the proposed approach has a large scope. To highlight the method, a class of dynamic Volterra models including some hybrid models such as dynamic inclusions is considered for application. Copyright © 2016 John Wiley & Sons, Ltd.     

Regressor selection with the analysis of variance method

Identification of non-linear dynamical models of a black box nature involves both structure decisions, i.e., which regressors to use, the selection of a regressor function, and the estimation of the parameters involved. The typical approach in system identification seems to be to mix all these steps, which for example means that the selection of regressors is based on the fits that is achieved for different choices. Alternatively one could then interpret the regressor selection as based on hypothesis tests (F-tests) at a certain confidence level that depends on the data. It would in many cases be desirable to decide which regressors to use independently of the other steps.In this paper we investigate what the well-known method of analysis of variance (ANOVA) can offer for this problem. System identification applications violate many of the ideal conditions for which ANOVA was designed and we study how the method performs under such non-ideal conditions.ANOVA is much faster than a typical parametric estimation method, using e.g. neural networks. It is actually also more reliable, in our tests, in picking the correct structure even under non-ideal conditions. One reason for this may be that ANOVA requires the data set to be balanced, that is, all parts of the regressor space are weighted equally. Just applying tests of fit for the recorded data may give, for structure identification, improper weight to areas with many, or few, samples.     

A multi-variate Hammerstein model for processes with input directionality

A new formulation of a block-structured model based on the Hammerstein operator is presented for the identification of multi-variate systems with input directionality. In contrast to the existing formulations for multi-variate Hammerstein models, the proposed structure offers the possibility to independently model the dynamic and nonlinear characteristics of the system and at the same time preserves the possibility to use the new efficient algorithms developed for the identification of single input Hammerstein models. Further, the formulation allows for a representation of arbitrary static nonlinear coupling of input variables with a considerably lower amount of parameters compared to existing formulations. The new model structure is applied to the identification of a fluid catalytic cracking (FCC) unit and significantly outperforms all previous multi-variate Hammerstein model structures by reducing the prediction error by over 50%.     

An iterative algorithm for simulation error based identification of polynomial input–output models using multi-step prediction

Effective identification of polynomial input–output models for applications requiring long-range prediction or simulation performance relies on both careful model selection and accurate parameter estimation. The simulation error minimisation (SEM) approach has been shown to provide significant advantages in the model selection phase by ruling out candidate models with good short-term prediction capabilities but unsuitable long-term dynamics. However, SEM-based parameter estimation has been generally avoided due to excessive computational effort. This article extends to the nonlinear case a computationally efficient approach for this task, that was previously developed for linear models, based on the iterative estimation of predictors with increasing prediction horizon. Conditions for the applicability of the approach to various model classes are also discussed. Finally, some examples are provided to show the effectiveness and computational convenience of the proposed algorithm for polynomial input–output identification, as well as the improvements achievable by enforcing SEM parameter estimation. A benchmark for nonlinear identification is also analysed, with encouraging results.     

A revised Durbin-Wu-Hausman test for industrial robot identification

This paper addresses the topic of robot identification. The usual identification method makes use of the inverse dynamic model (IDM) and the least squares (LS) technique while robot is tracking exciting trajectories. Assuming an appropriate bandpass filtering, good results can be obtained. However, the users are in doubt whether the columns of the observation matrix (the regressors) are uncorrelated (exogenous) or correlated (endogenous) with the error terms. The exogeneity condition is rarely verified in a formal way whereas it is a fundamental condition to obtain unbiased LS estimates. In Econometrics, the Durbin-Wu-Hausman test (DWH-test) is a formal statistic for investigating whether the regressors are exogenous or endogenous. However, the DWH-test cannot be straightforwardly used for robot identification because it is assumed that the set of instruments is valid. In this paper, a Revised DWH-test suitable for robot identification is proposed. The revised DWH-test validates/invalidates the instruments chosen by the user and validates the exogeneity assumption through the calculation of the QR factorization of the augmented observation matrix combined with a F-test if required. The experimental results obtained with a 6 degrees-of-freedom (DOF) industrial robot validate the proposed statistic.     

Subspace identification by data orthogonalization and model decoupling

It has been observed that identification of state-space models with inputs may lead to unreliable results in certain experimental conditions even when the input signal excites well within the bandwidth of the system. This may be due to ill-conditioning of the identification problem, which occurs when the state space and the future input space are nearly parallel.We have in particular shown in the companion papers (Automatica 40(4) (2004) 575; Automatica 40(4) (2004) 677) that, under these circumstances, subspace methods operating on input-output data may be ill-conditioned, quite independently of the particular algorithm which is used. In this paper, we indicate that the cause of ill-conditioning can sometimes be cured by using orthogonalized data and by recasting the model into a certain natural block-decoupled form consisting of a “deterministic” and a “stochastic” subsystem. The natural subspace algorithm for the identification of the deterministic subsystem is then a weighted version of the PI-MOESP method of Verhaegen and Dewilde (Int. J. Control 56 (1993) 1187-1211). The analysis shows that, under certain conditions, methods based on the block-decoupled parametrization and orthogonal decomposition of the input-output data, perform better than traditional joint-model-based methods in the circumstance of nearly parallel regressors.     

Hammerstein-Wiener system estimator initialization

In nonlinear system identification, the system is often represented as a series of blocks linked together. Such block-oriented models are built with static nonlinear subsystems and linear dynamic systems. This paper deals with the identification of the Hammerstein-Wiener model, which is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output. The proposed identification scheme is iterative and will be demonstrated on measurements. It will be proven that on noiseless data and in absence of modeling errors, the optimization procedure converges to the true system locally.     

Takagi-Sugeno fuzzy modeling incorporating input variables selection

Fuzzy models, especially Takagi-Sugeno (T-S) fuzzy models, have received particular attention in the area of nonlinear modeling due to their capability to approximate any nonlinear behavior. Based only on measured data without any prior knowledge, there is no systematic way to obtain a T-S fuzzy model with a simple structure and sufficient accuracy. The main idea discussed in this paper is to reduce the complexity of T-S fuzzy models by estimating an optimal number of fuzzy rules and selecting relevant inputs as antecedent variables independently of the selection of consequent regressors. A systematic procedure is proposed here and illustrated on static and dynamical nonlinear systems.     

An Iterative Learning Approach to Identify Fractional Order KiBaM Model

This paper discusses the parameter and differentiation order identification of continuous fractional order KiBaM models in ARX (autoregressive model with exogenous inputs) and OE (output error model) forms. The least squares method is applied to the identification of nonlinear and linear parameters, in which the Grünwald-Letnikov definition and short memory principle are applied to compute the fractional order derivatives. An adaptive P-type order learning law is proposed to estimate the differentiation order iteratively and accurately. Particularly, a unique estimation result and a fast convergence speed can be arrived by using the small gain strategy, which is unidirectional and has certain advantages than some state-of-art methods. The proposed strategy can be successfully applied to the nonlinear systems with quasi-linear characteristics. The numerical simulations are shown to validate the concepts.      

A methodology for control-relevant nonlinear system identification using restricted complexity models

A broadly-applicable, control-relevant system identification methodology for nonlinear restricted complexity models (RCMs) is presented. Control design based on RCMs often leads to controllers which are easy to interpret and implement in real-time. A control-relevant identification method is developed to minimize the degradation in closed-loop performance as a result of RCM approximation error. A two-stage identification procedure is presented. First, a nonlinear ARX model is estimated from plant data using an orthogonal least squares algorithm; a Volterra series model is then generated from the nonlinear ARX model. In the second stage, a RCM with the desired structure is estimated from the Volterra series model through a model reduction algorithm that takes into account closed-loop performance requirements. The effectiveness of the proposed method is illustrated using two chemical reactor examples.     

Multiple model approach to nonlinear system identification with an uncertain scheduling variable using EM algorithm

This paper deals with system identification of general nonlinear dynamical systems with an uncertain scheduling variable. A multi model approach is developed; wherein, a set of local auto regressive exogenous (ARX) models are first identified at different process operating points, and are then combined to describe the complete dynamics of a nonlinear system. An expectation-maximization (EM) algorithm is used for simultaneous identification of local ARX models, and for computing the probability associated with each of the local ARX models taking effect. A smoothing algorithm is used to estimate the distribution of the hidden scheduling variables in the EM algorithm. If the dynamics of the scheduling variables are linear, Kalman smoother is used; whereas, if the dynamics are nonlinear, sequential Monte-Carlo (SMC) method is used. Several simulation examples, including a continuous stirred tank reactor (CSTR) and a distillation column, are considered to illustrate the efficacy of the proposed method. Furthermore, to highlight the practical utility of the developed identification method, an experimental study on a pilot-scale hybrid tank system is also provided.     

基于遗传算法和非线性规划求解信息交互的光伏阵列模型鲁棒参数辨识方法

对光伏阵列进行建模不仅可以研究温度、光照等因素对V-I特性曲线的影响,还可以用模型代替实际光伏阵列进行各种光伏实验,降低实验成本,节省实验时间;参数辨识可以使光伏阵列模型的参数值设置更精确,使其与实际值相一致;针对基于非线性规划的光伏阵列模型鲁棒参数辨识方法容易陷入局部搜索的问题,提出了遗传算法与非线性规划求解信息交互的鲁棒参数辨识方法;将遗传算法与非线性规划求解信息交互,既可以进行全局搜索,又可以进行局部搜索,以得到问题的全局最优解;通过仿真测试,使用该方法得到的结果均方误差降低了8倍,均方误差量级达到了1.0E-3,表明了该方法在光伏阵列模型参数辨识方面具有较高的精确度。     

Recursive identification for dynamic systems with backlash

A recursive algorithm for identification of nonlinear dynamic systems with backlash is proposed in this paper. In this method, the backlash, which is a non‐smooth function, is decomposed into a combination of a group of piecewise linearized models so that all the parameters of the backlash can be estimated separately. Moreover, the model of the backlash is embedded into a Hammerstein‐type model. Thus, a pseudo‐Hammerstein model with backlash is constructed. The estimation of the parameters for such a non‐smooth nonlinear system can be implemented through a so‐called recursive general identification algorithm (RGIA). Then, the corresponding convergence analysis of the RGIA for the model with backlash is also investigated. After that, two examples are presented to show the performance of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于模糊神经网络的非线性系统模型的辨识

该文提出一种非线性系统的模型辨识方法．利用关系聚类法来进行结构辨识，从而自动获得模糊规则库，并可以得到模糊系统的初始参数，在聚类的基础上，构造一个与之相匹配的模糊神经网络，用它的学习算法来训练网络，得到一个精确的模糊模型，从而实现参数辨识，通过对两个非线性系统辨识的仿真结果验证了该方法的有效性。     

Nonlinear identification and control of a high-purity distillation column: a case study

Identification and control of ill-conditioned, interactive and highly nonlinear processes pose a challenging problem to the process industry. In the absence of a reasonably accurate model, these processes are fairly difficult to control. Using a high-purity distillation column as an example, model identification and control issues are addressed in this paper. The structure of the identified models is that of the polynomial type nonlinear autoregressive models with exogenous inputs (NARX). While most of the work in this area has concentrated on linear models (one-time scale and two-time scale models), this work is aimed at identifying the inherent nonlinearities. Comparisons are drawn between the identified models based on statistical criteria (AIC etc.) and other validation tests. Simulation results are provided to demonstrate the closed-loop performance of the nonlinear ARX models in the control of the distillation column. The controller employed is based on a nonlinear model predictive scheme with state and parameter estimation.     

Particle swarm approaches using Lozi map chaotic sequences to fuzzy modelling of an experimental thermal-vacuum system

Particle Swarm Optimization (PSO) approach intertwined with Lozi map chaotic sequences to obtain Takagi–Sugeno (TS) fuzzy model for representing dynamical behaviours are proposed in this paper. The proposed method is an alternative for nonlinear identification approaches especially when dealing with complex systems that cannot always be modelled using first principles to determine their dynamical behaviour. Since modelling nonlinear systems is normally a difficult task, fuzzy models have been employed in many identification problems due its inherent nonlinear characteristics and simple structure, as well. This proposed chaotic PSO (CPSO) approach is employed here for optimizing the premise part of the IF–THEN rules of TS fuzzy model; for the consequent part, least mean squares technique is used. The proposed method is utilized in an experimental application; a thermal-vacuum system which is employed for space environmental emulation and satellite qualification. Results obtained with a variety of CPSO's are compared with traditional PSO approach. Numerical results indicate that the chaotic PSO approach succeeded in eliciting a TS fuzzy model for this nonlinear and time-delay application.     

一种非线性模型的在线辨识方法

提出一种用于非线性模型在线辨识的模糊算法。该算法将非线性输入输出系统用时变线性系统模型来拟和。并把此非线性系统模型表示成模糊模型的形式,用在线调节模糊模型的方法来辨识时变线性模型的相关参数。在以往的模糊辨识方法中,均未给出在线调整非线性系统的模糊辨识算法。将递推模糊聚类方法与卡尔曼滤波法用于在线调整模糊模型参数,仿真算例表明了此算法的有效性与良好的实用价值。     

基于SOKID的无人动力伞模型辨识

对具有独特飞行特性的无人动力伞(Unmanned Powered Parafoil,UPP)进行了研究,建立了无人动力伞九自由度非线性动力学方程,研究了观测器/卡尔曼滤波辨识算法和改进的子空间观测器/卡尔曼滤波辨识算法.根据系统的飞行数据,辨识得到系统的纵向状态空间模型,分析了两种辨识模型的俯仰角响应特性和辨识精度.仿...