多自由度非线性系统动态参数化模型建模方法研究

针对多自由度非线性系统的动态模型辨识问题,基于NARX(Non-linear Autoregressive with Exogenous inputs)模型的建模方法,考虑系统的物理设计参数,建立非线性系统动态参数化模型.首先,根据系统输入、输出数据建立系统不同参数下的NARX模型,并通过EFOR(Extended Forward Orthogonal Regression)算法对不同参数下NARX模型进行修正,以统一辨识得到的系统模型结构.随后,建立NARX模型系数与物理设计参数间的函数关系,得到多自由度非线性系统的动态参数化模型.以单输入、单输出两自由度非线性系统为例,根据数值仿真结果,对系统的动态参数化模型建模过程进行说明.最后,以带非线性涂层阻尼的悬臂梁作为试验对象,建立其动态参数化模型以反映其动力学特性.试验结果表明,非线性系统动态参数化模型能准确预测多自由度非线性系统的输出响应,为非线性系统的分析与优化设计提供了理论基础.     

Model validation for structural dynamic analysis: An approach to the Sandia Structural Dynamics Challenge

The validation of mathematical models constructed for the dynamic analysis of critical structures is a very important, but complex, process. The essential requirement is to provide confirmation, using independent and more reliable data than that presented by the model in question, that the subject model is capable of describing the essential physics of the structure’s behaviour within the required accuracy. In this paper, the procedures of model validation using experimental data on a structure are summarised and applied to a structural dynamics validation problem developed by Sandia National Laboratories. One of the essential issues is to separate out any non-linear features of the system and to construct an appropriate linear model that is as accurate as possible to cope with variability of the subsystem structures. The linear model, which is constructed using simulated test data from an assembly of sample subsystems, is expressed as a mean model with a standard deviation. It is further used in the system response prediction for system accreditation and target application under specified excitation loads. The influence of the weak non-linearity features are neglected in the system response prediction because the experimental method used to derive the test data obscured the non-linear effects and precluded their identification. Further consideration of identification and modelling of the non-linear element for the Sandia 3DOF calibration system is discussed to evaluate its influence on the accuracy of the spatial model.     

Variable selection algorithm for the construction of MIMO operatingpoint dependent neurofuzzy networks

An input variable selection procedure is introduced for the identification and construction of multi-input multi-output (MIMO) neurofuzzy operating point dependent models. The algorithm is an extension of a forward modified Gram-Schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting. The proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice-based modeling algorithms such as radial basis function neurofuzzy networks, enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation. Some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm     

Dynamic modeling of SOFC based on a T–S fuzzy model

The operating temperature and voltage are the key parameters affecting the performance of Solid Oxide Fuel Cell (SOFC). In this article a Takagi–Sugeno (T–S) fuzzy model is proposed to describe the nonlinear temperature and voltage dynamic properties of the SOFC system. During the process of modeling, a Fuzzy Clustering Means (FCM) method is used to determine the nonlinear antecedent parameters, and the linear consequent parameters are identified by a recursive least squares algorithm. The validity and accuracy of modeling are tested by simulations. The simulation results show that it is feasible to establish the dynamic model of SOFC by using the T–S fuzzy identification method.     

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.     

Analysis of an electrohydraulic servo system subject to Stribeck-type friction

The main objective of this paper is to study the phenomena of the electrohydraulic servo system under the influence of the Stribeck-type friction. Owing to the nonlinear nature of this friction, a sustained oscillation, or limit cycle, might appear in the system behaviour. The system is first divided into two parts, the linear and the nonlinear. For the nonlinear Stribeck-type friction, a flexible model is proposed to represent the whole friction family, and the describing function of this nonlinear friction is generated. The system characteristic equation is established by correlating the frequency response of the linear part and the describing function of the nonlinear part. The existence and stability of the limit cycle are predicted based on the characteristic equation. Finally, by using the sinusoidal, step and ramp input, respectively, the numerical simulation is adopted to observe the system response. All predicted limit cycles can be verified by the simulation results, and the effects of stable and unstable limit cycles are clarified. The dynamic characteristics obtained in this study help to bring insight into this important engineering configuration and throw some light on the possibilities for improvement.     

Optimal experiment design based on local model networks and multilayer perceptron networks

This paper addresses the topic of model based design of experiments for the identification of nonlinear dynamic systems. Data driven modeling decisively depends on informative input and output data obtained from experiments. Design of experiments is targeted to generate informative data and to reduce the experimentation effort as much as possible. Furthermore, design of experiments has to comply with constraints on the system inputs and the system output, in order to prevent damage to the real system and to provide stable operational conditions during the experiment. For that purpose a model based approach is chosen for the optimization of excitation signals in this paper. Two different modeling architectures, namely multilayer perceptron networks and local model networks are chosen and the experiment design is based on the optimization of the Fisher information matrix of the associated model architecture. The paper presents and discusses feasible problem formulations and solution approaches for the constrained dynamic design of experiments. In this context the effects of the Fisher information matrix in the static and the dynamic configurations are discussed. The effectiveness of the proposed method is demonstrated on a complex nonlinear dynamic engine simulation model and an analysis as well as a comparison of the presented model architectures for model based experiment design is given.     

Modeling of a dynamic dual-input dual-output fast steeringmirror system

A modeling method is proposed for a dynamic fast steering mirror (FSM) system with dual inputs and dual outputs. A physical model of the FSM system is derived based on first principles, describing the dynamics and coupling between the inputs and outputs of the FSM system. The physical model is then represented in a state-space form. Unknown parameters in the state-space model are identified by the subspace identification algorithm, based on the measured input-output data of the FSM system. The accuracy of the state-space model is evaluated by comparing the model estimates with measurements. The variance-accounted-for value of the state-space model is better than 97%, not only for the modeling data but also for the validation data set, indicating high accuracy of the model. Comparison is also made between the proposed dynamic model and the conventional static model, where improvement in model accuracy is clearly observed. The model identified by the proposed method can be used for optimal controller design for closed-loop FSM systems. The modeling method is also applicable to FSM systems with similar structures.     

线性参数变化系统建模与控制研究进展

在描述实际系统的非线性和时变特性方面,线性参数变化(Linear parameter varying,LPV)模型有着巨大的优越性,对于使用一些成熟的线性系统控制理论来解决非线性系统的控制问题,提供了良好的手段.文章对LPV系统的模型结构和建模方法,模型参数辨识方法,控制方法以及应用领域等方面的近几年的研究成果,做了比...     

Non-linear system identification using closed-loop data with no external excitation: The case of a lean combustion chamber

This paper deals with the analysis of a set of measurements collected on a lean premixed combustion process operating in a limit cycle. Due to the fact that the data are collected in closed-loop and the system has no external excitation, the identification task is particularly challenging. This work mainly focuses on the issue of the feasibility of the identification task. It will be shown that, despite the paucity of information available, a grey-box non-linear model can be estimated. The model provides an explanation both of the limit-cycle fundamental oscillation and of a non-harmonic high-frequency signal affecting the pressure of the combustion chamber.     

Set Membership identification of nonlinear systems

In the paper the problem of identifying nonlinear dynamic systems, described in nonlinear regression form, is considered, using finite and noise-corrupted measurements. Most methods in the literature are based on the estimation of a model within a finitely parametrized model class describing the functional form of involved nonlinearities. A key problem in these methods is the proper choice of the model class, typically realized by a search, from the simplest to more complex ones (linear, bilinear, polynomial, neural networks, etc.). In this paper an alternative approach, based on a Set Membership framework is presented, not requiring assumptions on the functional form of the regression function describing the relations between measured input and output, but assuming only some information on its regularity, given by bounds on its gradient. In this way, the problem of considering approximate functional forms is circumvented. Moreover, noise is assumed to be bounded, in contrast with statistical methods, which rely on assumptions such as stationarity, ergodicity, uncorrelation, type of distribution, etc., whose validity may be difficult to test reliably and is lost in presence of approximate modeling. In this paper, necessary and sufficient conditions are given for the validation of the considered assumptions. An optimal interval estimate of the regression function is obtained, providing its uncertainty range for any assigned regressor values. The set estimate allows to derive an optimal identification algorithm, giving estimates with minimal guaranteed L_p error on the assigned domain of the regressors. The properties of the optimal estimate are investigated and its worst-case L_p identification error is evaluated. The presented approach is tested and compared with other nonlinear methods on the identification of a water heater, a mechanical system with input saturation and a vehicle with controlled suspensions.     

Identification of Wiener–Hammerstein benchmark model via rank minimization

In this paper, a Wiener–Hammerstein system identification problem is formulated as a semidefinite programming (SDP) problem which provides a sub-optimal solution for a rank minimization problem. In the proposed identification method, the first linear dynamic system, the static nonlinear function, and the second linear dynamic system are parameterized as an FIR model, a polynomial function, and a rational transfer function respectively. Subsequently the optimization problem is formulated by using the over-parameterization technique and an iterative approach is proposed to update two unmeasurable intermediate signals. For the modeling of static nonlinearity, the monotonically non-deceasing condition was applied to limit the number of possible selections for intermediate signals. At each step of iteration, the over-parametrized parameters are estimated and then system parameters are separated by using a singular value decomposition (SVD). The proposed method is applied to the benchmark problem and the estimation result shows the effectiveness of the proposed algorithm.     

Describing function analysis of uncertain fuzzy vehicle control systems

In this paper, some useful frequency domain methods including describing function, parameter space, and Kharitonov approach are applied to analyze the stability of an uncertain fuzzy vehicle control system for limit cycle prediction. A systematic procedure is proposed to solve this problem. The fuzzy controller can be linearized by the use of classical describing function firstly. By doing so, it is feasible to treat the stability problem of a fuzzy control system as linear one. In order to consider the robustness of a fuzzy vehicle control system, parameter space method and Kharitonov approach are then employed for plotting the stability boundaries. Furthermore, the effect of transport delay is also addressed. More information of limit cycles can be obtained by this approach. This work shows that the limit cycles caused by a static fuzzy controller can be easily suppressed if the system parameters are chosen carefully.     

Prediction error methods for limit cycle data

Prediction error methods are considered for identification of the forward linear dynamics of nonlinear feedback closed-loop systems which operate in a perturbed stable limit cycle. A model of the signals measured in a neighborhood of the limit cycle is presented and shown to satisfy a quasistationarity property. Quasistationarity is then used to prove that prediction error methods are both convergent and consistent for our data model.     

神经网络在热电厂对象建模中的应用

针对一个375 MW热电厂的锅炉-汽轮机系统仿真模型,采用多层前向神经网络进行离线建模;讨论了网络结构设计、训练算法等神经网络建模问题;采用相同的固定负荷数据分别建立了线性ARX模型和局部神经网络模型并做多步预测比较;通过对基于一层隐层的全局神经网络模型的训练和仿真,结果证实了神经网络在非线性系统建模和辨识上的有效性.     

A quadratic empirical model formulation for dynamical systems using a genetic algorithm

A new procedure to formulate nonlinear empirical models of a dynamical system is presented. This nonlinear modeling technique generalizes the Markovian techniques used to build linear empirical models, but incorporates a quadratic nonlinearity. The model fit is accomplished using a genetic algorithm.The nonlinear empirical model is applied to two low order model test cases demonstrating different forms of nonlinearity. The two equation predator/prey model (Lotka-Volterra equations) is modeled in the regime of a stable limit cycle. The nonlinear empirical model is able to capture the general shape of the limit cycle, but does not display the long time stability. The second example is the three dimensional Lorenz system forced in the chaotic regime. The general shape and location in phase space of the chaotic attractor is reproduced by the nonlinear empirical model.The results presented here demonstrate that nonlinear empirical models may be able to reproduce some of the nonlinear behaviors of dynamical systems.     

Modeling of pH process using wavenet based Hammerstein model

This paper outlines an approach for developing a Hammerstein model for nonlinear dynamic systems. The nonlinearity is sought to be captured through functional approximation using wavelets cast in a wavenet structure. Nonlinear block of wavenet at input side is cascaded with a linear dynamic block described by a state space model. A sequential approach is used for development of static nonlinear and linear dynamic parts of the model. Configuration and parameters of the nonlinear wavenet structure are determined from near steady state data extracted from dynamic test data while the state space model parameters of the linear dynamic part are obtained using a subspace identification approach. This approach has been applied for modeling a strongly nonlinear pH process operated over a wide range of operating conditions.     

A nonlinear functional approach to LFT model validation

Model validation provides a useful means of assessing the ability of a model to account for a specific experimental observation, and has application to modeling, identification and fault detection. In this paper, we consider a new approach to the model validation problem by deploying quadratic functionals, and more generally nonlinear functionals, to specify noise and dynamical perturbation sets. Specifically, we consider a general linear fractional transformation framework for the model structure, and use constraints involving nonlinear functional inequalities to specify model non-linearities and unknown perturbations, and characteristics of noise and disturbance signals. Sufficient conditions for invalidation of such models are provided in terms of semidefinite programming problems.     

一种通用直升机飞行动力学建模软件

直升机因为特有的旋翼气动特性,使得其飞行建模较为复杂,而实时仿真系统的建立在飞机研制、性能验证及改型等各环节中都起到了一个重要的作用.文章介绍了一个单旋翼带尾桨直升机通用的建模工具,在此工具下,只需要输入直升机的构型参数以及相应的风洞气动数据,就可以建立起直升机的全量非线性动力学数学模型,并提供相应的配平程序以及动态响应计算程序.相比较于国外同类型的软件,文中提出的建模工具建立的模型可以运行在实时操作系统上.     

Constrained multisine input signals for plant-friendly identification of chemical process systems

This paper considers the use of constrained minimum crest factor multisine signals as inputs for plant-friendly identification testing of chemical process systems. The methodology presented here effectively integrates operating restrictions, information-theoretic requirements, and state-of-the-art optimization techniques to design minimum crest factor multisine signals meeting important user-specified time and frequency domain properties. A series of optimization problem formulations relevant to problems in linear, nonlinear, and multivariable system identification are presented; these culminate with their application to the modeling of the Weischedel–McAvoy high-purity distillation column problem, a demanding nonlinear and highly interactive system. The effectiveness of these signals for modeling for control purposes and the ability to incorporate a priori nonlinear models in the signal design procedure are demonstrated in this distillation system case study.