更有效的非线性系统辨识新方法

介绍了一种基于量子粒子群算法构造径向基函数神经网络进行非线性系统辨识的新方法.在确定径向基函数网络的 隐层结点数后,将相应网络的参数,包括隐层基函数中心、扩展常数以及输出权值和偏移编码成学>-j算法中的粒子个体,在全 局空间中搜索具有最优适应值的参数向量.实例仿真通过和标准粒子群算法进行比较,表明了该方法的有效性和优越性.     

A survey of nonlinear prefiltering methods for efficient and accurate surface shading

Rendering a complex surface accurately and without aliasing requires the evaluation of an integral for each pixel, namely, a weighted average of the outgoing radiance over the pixel footprint on the surface. The outgoing radiance is itself given by a local illumination equation as a function of the incident radiance and of the surface properties. Computing all this numerically during rendering can be extremely costly. For efficiency, especially for real-time rendering, it is necessary to use precomputations. When the fine scale surface geometry, reflectance, and illumination properties are specified with maps on a coarse mesh (such as color maps, normal maps, horizon maps, or shadow maps), a frequently used simple idea is to prefilter each map linearly and separately. The averaged outgoing radiance, i.e., the average of the values given by the local illumination equation is then estimated by applying this equation to the averaged surface parameters. But this is really not accurate because this equation is nonlinear, due to self-occlusions, self-shadowing, nonlinear reflectance functions, etc. Some methods use more complex prefiltering algorithms to cope with these nonlinear effects. This paper is a survey of these methods. We start with a general presentation of the problem of prefiltering complex surfaces. We then present and classify the existing methods according to the approximations they make to tackle this difficult problem. Finally, an analysis of these methods allows us to highlight some generic tools to prefilter maps used in nonlinear functions, and to identify open issues to address the general problem.     

On identification of parallel block-cascade nonlinear models

The class of nonlinear systems studied in this paper is assumed to be modelled by parallel block-cascades. Such models are composed of parallel branches where each branch has a linear block in cascade with a zero-memory nonlinear block followed by another linear block. These types of models are extensively used to represent nonlinear dynamic systems and are known in the literature as Wiener-Hammerstein models. Using a zero-mean stationary white gaussian sequence as an input to such models, a structure identification criterion is developed, utilizing the bispectrum estimate of the output sequence only. The application of this criterion is shown by several simulation examples. Also, impulse response estimation of an example of such a model is considered to show the effectiveness of the proposed identification technique.     

Input design for structured nonlinear system identification

This paper is concerned with the input design problem for a class of structured nonlinear models. This class contains models described by an interconnection of known linear dynamic systems and unknown static nonlinearities. Many widely used model structures are included in this class. The model class considered naturally accommodates a priori knowledge in terms of signal interconnections. Under certain structural conditions, the identification problem for this model class reduces to standard least squares. We treat the input design problem in this situation.An expression for the expected estimate variance is derived. A method for synthesizing an informative input sequence that minimizes an upper bound on this variance is developed. This reduces to a convex optimization problem. Features of the solution include parameterization of the expected estimate variance by the input distribution, and a graph-based method for input generation.     

An algorithm for nonlinear system parameter identification

An algorithm for system parameter identification will be presented in this paper. The method is applicable to linear and nonlinear systems with known structures. It is applied in this paper to systems in which both system and measurement noises can be neglected. The algorithm requires less time per iteration and less computer storage than the quasilinearization method. A shaft position control system with multiple nonlinearities will be used to illustrate the method.     

Robust nonlinear system identification using neural-network models.

We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. Our objective is to resolve the difficulty associated with the persistency of excitation condition inherent to the standard schemes in the neural identification literature. This difficulty is circumvented here by a novel formulation and by using a new class of identification algorithms recently obtained by Didinsky et al. (1995). We present a class of identifiers which secure a good approximant for the system nonlinearity provided that some global optimization technique is used. Subsequently, we address the same problem under a third, worst case L(infinity) criterion for an RBF modeling. We present a neural-network version of an H(infinity)-based identification algorithm from Didinsky et al., and show how it leads to satisfaction of a relevant persistency of excitation condition, and thereby to robust identification of the nonlinearity.     

On the choice of norms in system identification

In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all l_p-norms, p⩽2<∞ for F(C)     

Optimal levels of perturbation signals for nonlinear system identification

A method is developed for determining the optimal levels of multilevel perturbation signals for nonlinear system identification, using condition numbers of submatrices of the Vandermonde matrix of the input levels vector. It is applicable when the perturbation signal is applied directly to a static nonlinearity. Optimal levels can be obtained for every order of nonlinearity less than the number of levels, and in most cases the optimal levels are not all distinct. The results show that there is no advantage in using signals with more than the minimum necessary number of distinct levels, although it may be advantageous if some of the distinct levels appear more than once in the input levels vector. The optimal levels are unchanged by multiple occurrences of every level of the input levels vector during a measurement period, and they are shown to be the global optima for pseudorandom perturbation signals derived from maximum-length sequences, in which the occurrence of the zero level is one less than the occurrences of the other levels during a period.     

On the observability codistributions of a nonlinear system

The purpose of this is to introduce the notion of observability codistribution for a nonlinear system, which extends the (dual of the) notion of “unobservability subspace”. Then, we study its properties, which bear important similarities with a number of properties which render the notion of unobservability subspace powerful in the solution of certain design problems.     

On the controllability of a nonlinear control system

This paper considers the problem of controllability of a class of nonlinear systems. Sufficient conditions are given for a nonlinear system to be locally controllable and globally completely controllable. In the case of a linear time-invariant system, these conditions are also necessary. Furthermore, our result reveals that, for a nonlinear control system, there is a relationship among controllability, stability and optimality.     

An adaptive robust M-estimator for nonparametric nonlinear system identification

An adaptive robust M-estimator for nonparametric nonlinear system identification is proposed. This M-estimator is optimal over a broad class of distributions in the sense of maximum likelihood estimation. The error distributions are described by the generalized exponential distribution family. It combines non-parametric regression techniques to form a powerful procedure for nonlinear system identification. The adaptive procedure's excellent performance characteristics are illustrated in a Monte Carlo study by comparing the results with previous methods.     

A constructive approach for nonlinear system identification usingmultilayer perceptrons

This paper combines a conventional method of multivariable system identification with a dynamic multi-layer perceptron (MLP) to achieve a constructive method of nonlinear system identification. The class of nonlinear systems is assumed to operate nominally around an equilibrium point in the neighborhood of which a linearized model exists to represent the system, although normal operation is not limited to the linear region. The result is an accurate discrete-time nonlinear model, extended from a MIMO linear model, which captures the nonlinear behavior of the system.     

一种新型的非线性系统模型参数辨识方法

针对传统模型参数辨识方法和遗传算法用于模型参数辨识时的缺点,提出了一种基于微粒群优化(PSO)算法的模型参数辨识方法,利用PSO算法强大的优化能力,通过对算法的改进,将过程模型的每个参数作为微粒群体中的一个微粒,利用微粒群体在参数空间进行高效并行的搜索来获得过程模型的最佳参数值,可有效提高参数辨识的精度和效率.     

A new class of wavelet networks for nonlinear system identification

A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions.     

On the boundedness properties of a perturbed nonlinear system

It is shown that certain asymptotic equivalence hypotheses on the equationsu(t) = F(t, u(t))+G(t, u(t)) andv(t) = F(t, v(t)) imply that uniform boundedness in the second equation induces eventual uniform boundedness in the first. Also, under these hypotheses, a characterization is given of the unbounded solutions of the first equation.     

On the stability of a second-order time-varying nonlinear system

This correspondence presents some results pertaining to the stability of a second-order time-varying nonlinear differential equation. The system considered is a motor control system with a time-varying load and Coulomb friction. A comparison is made between several methods for investigating the stability of such a system.     

On the time complexity of worst-case system identification

In this paper we treat a general worst-case system identification problem. This problem is worst-case with respect to both noise and system modeling uncertainty. We consider this problem under various a priori information structures. We determine bounds on the minimum duration identification experiment that must be run to identify the plant to within a specified guaranteed worst-case error bound. Our results are algorithm independent. We show that this minimum duration is prohibitively long. Based on our results, we suggest that worst-case (with respect to noise) system identification requires unrealistic amounts of experimental data     

On the identification of parameters for a nonlinear integrodifferential population balance equation

In this article, we consider the problem of parameter estimation for an integrodifferential population balance equation model which describes the crystal size distribution for a continuous crystallizer at steady state with random growth dispersion and particle agglomeration. In order to obtain a physically meaningful positive solution to the problem, we formulate the model as a boundary value problem (BVP) on [0, L], and apply a modified shooting method to obtain its solution. We then couple the shooting method with an optimization scheme in order to estimate the constant parameters. To test this optimization scheme, we generate a synthetic data set from the physically meaningful part of an analytical solution and then show that it is possible to recapture the values of the parameters used to generate the data by solving the inverse BVP.     

Stationary linear and nonlinear system identification and predictor set completeness

A general consistency theorem for stationary nonlinear prediction error estimators is presented. Since this theorem does not require the existence of a parameterized system generating the observations, it applies to the practical problem of modeling complex systems with simple parameterized models. In order to measure the quality of fit between a set of observed processes and a given candidate set of predictors, the notion of predictor set completeness is introduced. Several examples are given to illustrate this idea; in particular, a negative result concerning the completehess of certain sets of linear predictors is presented. The relationship of Ljung's definitions of identifiability to various notions of predictor set completeness is examined, and the strong consistency of maximum likelihood estimators for Gaussian autoregressive moving average systems is obtained via an application of our techniques. Finally, problems for future research are described.     

Practical nonlinear system identification using a modified volterra series approach

A functional approach has been developed to represent continuous separable, nonlinear systems of a general type based on a modified Volterra series. The importance of this is that the effects of bias or mean signal level within the nonlinear system can be separated from dynamic effects. This has particular significance in the development of identification procedures based on cross-correlation functions, as these functions can now be estimated practically without any influence from the bias level. Practical identification of the gain characteristics for an electrohydraulic servo is described using three-level pseudorandom input signals which are cross-correlated with the sampled system response in a minicomputer to provide an automated procedure. Good accuracy is achieved even in the presence of severe noise.