Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited

Score Function Features for Discriminative Learning: Matrix and Tensor Framework

Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we consider a novel class of matrix and tensor-valued features, which can be pre-trained using unlabeled samples. We present efficient algorithms for extracting discriminative information, given these pre-trained features and labeled samples for any related task. Our class of features are based on higher-order score functions, which capture local variations in the probability density function of the input. We establish a theoretical framework to characterize the nature of discriminative information that can be extracted from score-function features, when used in conjunction with labeled samples. We employ efficient spectral decomposition algorithms (on matrices and tensors) for extracting discriminative components. The advantage of employing tensor-valued features is that we can extract richer discriminative information in the form of an overcomplete representations. Thus, we present a novel framework for employing generative models of the input for discriminative learning.Comment: 29 page

A Bayesian approach to robust identification: application to fault detection

In the Control Engineering field, the so-called Robust Identification techniques deal with the problem of obtaining not only a nominal model of the plant, but also an estimate of the uncertainty associated to the nominal model. Such model of uncertainty is typically characterized as a region in the parameter space or as an uncertainty band around the frequency response of the nominal model. Uncertainty models have been widely used in the design of robust controllers and, recently, their use in model-based fault detection procedures is increasing. In this later case, consistency between new measurements and the uncertainty region is checked. When an inconsistency is found, the existence of a fault is decided. There exist two main approaches to the modeling of model uncertainty: the deterministic/worst case methods and the stochastic/probabilistic methods. At present, there are a number of different methods, e.g., model error modeling, set-membership identification and non-stationary stochastic embedding. In this dissertation we summarize the main procedures and illustrate their results by means of several examples of the literature. As contribution we propose a Bayesian methodology to solve the robust identification problem. The approach is highly unifying since many robust identification techniques can be interpreted as particular cases of the Bayesian framework. Also, the methodology can deal with non-linear structures such as the ones derived from the use of observers. The obtained Bayesian uncertainty models are used to detect faults in a quadruple-tank process and in a three-bladed wind turbine

Physical parameters identification for a prototype of active magnetic bearing system

In this thesis the algorithms and strategies for active magnetic bearing should be analysed, implemented and simulated in Matlab as well as experimentally tested in the real-time computation system for a prototype of active magnetic bearing. Develop a general method and algorithm identi cation for active magnetic bearings prototype and get real system parameters that allow generate the equation of state of the system to control its further development. The specific objectives in this Thesis are: Develop a data acquisition system for the AMBs. Analyse the mathematical model of the system from the real system. Conduct experiments of a physical model for data collection. Develop an identification algorithm for the parameters of the real AMBs. Validate system developed by testing the prototype.Tesi

Analysis and control of power systems using orthogonal expansions

In recent years, considerable attention has been focused on the application of orthogonal expansions to system analysis, parameter identification, model reduction and control system design. However, little research has been done in applying their useful properties to Power System analysis and control. This research attempts to make some inroads in applying the so called " orthogonal expansion approach " to analysis and control of Power systems, especially the latter. A set of orthogonal functions commonly called Walsh functions in system science after it's discoverer J.L. Walsh [1923] have been successfully used for parameter identification in the presence of severe nonlinearities. The classical optimal control problem is applied to a synchronous machine infinite bus system via the orthogonal expansion approach and a convenient method outlined for designing PID controllers which can achieve prespecified closed loop response characteristics. The latter is then applied for designing a dynamic series capacitor controller for a single machine infinite bus system