Identification of multiple-input single-output Hammerstein models using Bezier curves and Bernstein polynomials

This paper considers the implementation of Bezier–Bernstein polynomials and the Levenberg–Marquart algorithm for identifying multiple-input single-output (MISO) Hammerstein models consisting of nonlinear static functions followed by a linear dynamical subsystem. The nonlinear static functions are approximated by the means of Bezier curves and Bernstein basis functions. The identification method is based on a hybrid scheme including the inverse de Casteljau algorithm, the least squares method, and the Levenberg–Marquart (LM) algorithm. Furthermore, results based on the proposed scheme are given which demonstrate substantial identification performance.     

Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling

This paper decomposes a Hammerstein nonlinear system into two subsystems, one containing the parameters of the linear dynamical block and the other containing the parameters of the nonlinear static block, and presents a hierarchical multi-innovation stochastic gradient identification algorithm for Hammerstein systems based on the hierarchical identification principle. The proposed algorithm is simple in principle and easy to implement on-line. A simulation example is provided to test the effectiveness of the proposed algorithm.     

Volterra-type models for nonlinear systems identification

In this work, multi-input multi-output (MIMO) nonlinear process identification is dealt with. In particular, two Volterra-type models are discussed in the context of system identification. These models are: Memory Polynomial (MP) and Modified Generalized Memory Polynomial (MGMP), which can be considered as a generalization of Hammerstein and Wiener models, respectively. Both of them are appealing representations as they allow to describe larger model sets with less parametric complexity. Simulation example is given to illustrate the quality of the obtained models.     

Gradient based estimation algorithm for Hammerstein systems with saturation and dead-zone nonlinearities

This paper focuses on identification problems for Hammerstein systems with saturation and dead-zone nonlinearities. An appropriate switching function is introduced to derive an identification model with fewer parameters and all the unknown parameters can be estimated by using an iterative method. A numerical simulation is carried out to show the effectiveness of the proposed method.     

Severity modeling of extreme insurance claims for tariffication

Generalized linear models are common instruments for the pricing of non-life insurance contracts. They are used to estimate the expected frequency and severity of insurance claims. However, these models do not work adequately for extreme claim sizes. To accommodate for these extreme claim sizes, we develop the threshold severity model, that splits the claim size distribution in areas below and above a given threshold. More specifically, the extreme insurance claims above the threshold are modeled in the sense of the peaks-over-threshold methodology from extreme value theory using the generalized Pareto distribution for the excess distribution, and the claims below the threshold are captured by a generalized linear model based on the truncated gamma distribution. Subsequently, we develop the corresponding concrete log-likelihood functions above and below the threshold. Moreover, in the presence of simulated extreme claim sizes following a log-normal as well as Burr Type XII distribution, we demonstrate the superiority of the threshold severity model compared to the commonly used generalized linear model based on the gamma distribution.     

Identification of MIMO systems using radial basis function networks with hybrid learning algorithm

When a radial basis function network (RBFN) is used for identification of a nonlinear multi-input multi-output (MIMO) system, the number of hidden layer nodes, the initial parameters of the kernel, and the initial weights of the network must be determined first. For this purpose, a systematic way that integrates the support vector regression (SVR) and the least squares regression (LSR) is proposed to construct the initial structure of the RBFN. The first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the SVR method. Then the weights of the RBFN are determined by solving a simple minimization problem based on the concept of LSR. After initialization, an annealing robust learning algorithm (ARLA) is then applied to train the RBFN. With the proposed initialization approach, one can find that the designed RBFN has few hidden layer nodes while maintaining good performance. To show the feasibility and superiority of the annealing robust radial basis function networks (ARRBFNs) for identification of MIMO systems, several illustrative examples are included.     

Schedule-an expert-like system for machine scheduling

The construction of an expert-like system for machine scheduling called SCHEDULE is presented. Essential parts of SCHEDULE were developed by students in a laboratory course Operations Research on Microcomputers at the University of Karlsruhe, Germany. SCHEDULE consists of the components data base, knowledge base, inference engine, explanation facility, dialog component, and knowledge acquisition component. The knowledge base contains an algorithm base for solving different types of scheduling problems. To establish the rules of the knowledge base the well-known three-field classification of deterministic machine scheduling problems and the concept of the reduction digraph are exploited. Experiences gained during building and demonstrating SCHEDULE are reported.     

Solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via rationalized Haar functions

Rationalized Haar functions are developed to approximate of the nonlinear Volterra–Fredholm–Hammerstein integral equations. The properties of rationalized Haar functions are first presented, and the operational matrix of integration together with the product operational matrix are utilized to reduce the computation of integral equations into some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.     

Estimation of nonlinear systems without a priori structural information and its application in Hammerstein model identification with dynamic nonlinearities

Email: er-wei-bai{at}uiowa.edu Received on July 30, 2005; Accepted on July 23, 2006 In the paper, we discuss identification of a nonlinear systemwithout structural information and propose two methods, thekernel method and the orthonormal basis method. The convergenceresults are established for both methods without a priori structuralinformation. We then apply the results to identification ofHammerstein models with an unknown dynamic nonlinearity. Itis also shown that identification of the linear part in Hammersteinmodels is possible with no knowledge of the dynamic nonlinearity.     

Sensitivity analysis and parameter identification for a nonlinear time-delay system in microbial fed-batch process

Developing suitable dynamic models of bioprocess is a difficult issue in bioscience. In this paper, considering the microbial metabolism mechanism, i.e., the production of new biomass is delayed by the amount of time it takes to metabolize the nutrients, in glycerol bioconversion to 1,3-propanediol, we propose a nonlinear time-delay system to formulate the fed-batch fermentation process. Some important properties are also discussed. Then, in view of the effect of time-delay and the high number of kinetic parameters in the system, the parametric sensitivity analysis is used to determine the key parameters. Finally, a parameter identification model is presented and a global optimization method is developed to seek the optimal key parameters. Numerical results show that the nonlinear time-delay system can describe the fed-batch fermentation process reasonably.     

Nonlinear system identification and control using a real-coded genetic algorithm

A real-coded genetic algorithm (GA) applied to the system identification and control for a class of nonlinear systems is proposed in this paper. It is well known that GA is a globally optimal method motivated from natural evolutionary concepts. For solving a given optimization problem, there are two different kinds of GA operations: binary coding and real coding. In general, a real-coded GA is more suitable and convenient to deal with most practical engineering applications. In this paper, in the beginning we attempt to utilize a real-coded GA to identify the unknown system which its structure is assumed to be known previously. Next, according to the estimated system model an optimal off-line PID controller is optimally solved by also using the real-coded GA. Two simulated examples are finally given to demonstrate the effectiveness of the proposed method.     

A class of nonlinear iterated function system attractors

In this article the theory of NIFS (nonlinear iterated function system) and the random iteration algorithm are expounded. By theoretical analysis, the definition domain of a class of complex polynomial hyperbolic NIFS in the complex c$c$-plane is given out and a series of the NIFS attractors are simulated. In the article, the changing regularity of the NIFS attractors are discussed when the control parameters are changed and the relationship between the totally disconnected NIFS attractor and its address set is discussed. Results show that: (1) the multiplicity of the NIFS inverse function leads to multiple addresses of the same region for NIFS attractors, and (2) the NIFS attractors have chaotic dynamic characteristics, and the evolution of the NIFS attractors depend on the choice of the range of the principal argument _θz${\theta }_z$.     

Feature selection algorithm in classification learning using support vector machines

An algorithm for selecting features in the classification learning problem is considered. The algorithm is based on a modification of the standard criterion used in the support vector machine method. The new criterion adds to the standard criterion a penalty function that depends on the selected features. The solution of the problem is reduced to finding the minimax of a convex-concave function. As a result, the initial set of features is decomposed into three classes—unconditionally selected, weighted selected, and eliminated features. Original Russian Text Yu.V. Goncharov, I.B. Muchnik, L.V. Shvartser @, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 7, pp. 1318–1336.     

基于小波包分解的非线性时变系统辩识

在实际应用中,经常会碰到非线性时变系统,它们的辨识和建模比较困难．本文采用时变Hammerstein模型描述时变非线性系统．该模型可以以较简单的方式刻划系统的时变特性和非线性特性．然后用小波包对时变系数进行展开,把时变系统的辨识转化为对时不变系数的辨识．     

Identification of LPV system using locally weighted technique

The problem of linear parameter varying （LPV） system identification is considered based on the locally weighted technique which provides estimation of the LPV model parameters at each distinct data time point by giving large weights to measurements that are ＂close＂ to the current time point and small weights to measurements ＂far＂ from the current time point. Issues such as choice of distance function, weighting function and bandwidth selection are discussed. The developed method is easy to implement and simulation results illustrate its efficiency.     

Online affine model identification of nonlinear processes using a new adaptive neuro-fuzzy approach

This paper presents a new online identification algorithm to drive an adaptive affine dynamic model for nonlinear and time-varying processes. The new algorithm is devised on the basis of an adaptive neuro-fuzzy modeling approach. Two adaptive neuro-fuzzy models are sequentially identified on the basis of the most recent input-output process data to realize an online affine-type model. A series of simulation test studies has been conducted to demonstrate the efficient capabilities of the proposed algorithm to automatically identify an online affine-type model for two highly nonlinear and time-varying continuous stirred tank reactor (CSTR) benchmark problems having inherent non-affine dynamic model representations. Adequacy assessments of the identified models have been explored using different evaluation measures, including comparison with an adaptive neuro-fuzzy inference system (ANFIS) as the pioneering and the most popular adaptive neuro-fuzzy system with powerful modeling features.     

Noisy image segmentation based on nonlinear diffusion equation model

This paper addresses the segmentation problem in noisy image based on nonlinear diffusion equation model and proposes a new adaptive segmentation model based on gray-level image segmentation model. This model also can be extended to the vector value image segmentation. By virtue of the prior information of regions and boundary of image, a framework is established to construct different segmentation models using different probability density functions. A segmentation model exploiting Gauss probability density function is given in this paper. An efficient and unconditional stable algorithm based on locally one-dimensional (LOD) scheme is developed and it is used to segment the gray image and the vector values image. Comparing with existing classical models, the proposed approach gives the best performance.     

Finite difference approximation of a nonlinear integro-differential system

Finite difference approximation of the nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is studied. The convergence of the finite difference scheme is proved. The rate of convergence of the discrete scheme is given. The decay of the numerical solution is compared with the analytical results proven earlier.