Comparative analysis of Kolmogorov ANN and process characteristic input-output modes

In the past decades, representation models of dynamical processes have been developed via both traditional math-analytical and less traditional computational-intelligence approaches. This challenge to system sciences goes on because essentially involves the mathematical approximation theory. A comparison study based on cybernetic input-output view in the time domain on complex dynamical processes has been carried out. An analytical decomposition representation of complex multi-input-multi-output thermal processes is set relative to the neural-network approximation representations, and shown that theoretical background of both emanates from Kolmogorov's theorem. The findings provided a new insight as well as highlighted the efficiency and robustness of fairly simple industrial digital controls, designed and implemented in the past, inherited from input-output decomposition model approximation employed

Invariance transformations for processing NDE signals

The ultimate objective in nondestructive evaluation (NDE) is the characterization of materials, on the basis of information in the response from energy/material interactions. This is commonly referred to as the inverse problem. Inverse problems are in general ill-posed and full analytical solutions to these problems are seldom tractable. Pragmatic approaches for solving them employ a constrained search technique by limiting the space of all possible solutions. A more modest goal is therefore to use the received signal for characterizing defects in objects in terms of the location, size and shape. However, the NDE signal received by the sensors is influenced not only by the defect, but also by the operational parameters associated with the experiment. This dissertation deals with the subject of invariant pattern recognition techniques that render NDE signals insensitive to operational variables, while at the same time, preserve or enhance defect related information. Such techniques are comprised of invariance transformations that operate on the raw signals prior to interpretation using subsequent defect characterization schemes. Invariance transformations are studied in the context of the magnetostatic flux leakage (MFL) inspection technique, which is the method of choice for inspecting natural gas transmission pipelines buried underground;The magnetic flux leakage signal received by the scanning device is very sensitive to a number of operational parameters. Factors that have a major impact on the signal include those caused by variations in the permeability of the pipe-wall material and the velocity of the inspection tool. This study describes novel approaches to compensate for the effects of these variables;Two types of invariance schemes, feature selection and signal compensation, are studied. In the feature selection approach, the invariance transformation is recast as a problem in interpolation of scattered, multi-dimensional data. A variety of interpolation techniques are explored, the most powerful among them being feed-forward neural networks. The second parametric variation is compensated by using restoration filters. The filter kernels are derived using a constrained, stochastic least square optimization technique or by adaptive methods. Both linear and non-linear filters are studied as tools for signal compensation;Results showing the successful application of these invariance transformations to real and simulated MFL data are presented

Best Approximation Results for Fuzzy-Number-Valued Continuous Functions

In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then, we prove the existence of the best approximation of a fuzzy-number-valued continuous function to the space of real-valued continuous functions by using the well-known Michael selection theorem

Heterogeneous neural networks: theory and applications

Aquest treball presenta una classe de funcions que serveixen de models neuronals generalitzats per ser usats en xarxes neuronals artificials. Es defineixen com una mesura de similitud que actúa com una definició flexible de neurona vista com un reconeixedor de patrons. La similitud proporciona una marc conceptual i serveix de cobertura unificadora de molts models neuronals de la literatura i d'exploració de noves instàncies de models de neurona. La visió basada en similitud porta amb naturalitat a integrar informació heterogènia, com ara quantitats contínues i discretes (nominals i ordinals), i difuses ó imprecises. Els valors perduts es tracten de manera explícita. Una neurona d'aquesta classe s'anomena neurona heterogènia i qualsevol arquitectura neuronal que en faci ús serà una Xarxa Neuronal Heterogènia.En aquest treball ens concentrem en xarxes neuronals endavant, com focus inicial d'estudi. Els algorismes d'aprenentatge són basats en algorisms evolutius, especialment extesos per treballar amb informació heterogènia. En aquesta tesi es descriu com una certa classe de neurones heterogènies porten a xarxes neuronals que mostren un rendiment molt satisfactori, comparable o superior al de xarxes neuronals tradicionals (com el perceptró multicapa ó la xarxa de base radial), molt especialment en presència d'informació heterogènia, usual en les bases de dades actuals.This work presents a class of functions serving as generalized neuron models to be used in artificial neural networks. They are cast into the common framework of computing a similarity function, a flexible definition of a neuron as a pattern recognizer. The similarity endows the model with a clear conceptual view and serves as a unification cover for many of the existing neural models, including those classically used for the MultiLayer Perceptron (MLP) and most of those used in Radial Basis Function Networks (RBF). These families of models are conceptually unified and their relation is clarified. The possibilities of deriving new instances are explored and several neuron models --representative of their families-- are proposed. The similarity view naturally leads to further extensions of the models to handle heterogeneous information, that is to say, information coming from sources radically different in character, including continuous and discrete (ordinal) numerical quantities, nominal (categorical) quantities, and fuzzy quantities. Missing data are also explicitly considered. A neuron of this class is called an heterogeneous neuron and any neural structure making use of them is an Heterogeneous Neural Network (HNN), regardless of the specific architecture or learning algorithm. Among them, in this work we concentrate on feed-forward networks, as the initial focus of study. The learning procedures may include a great variety of techniques, basically divided in derivative-based methods (such as the conjugate gradient)and evolutionary ones (such as variants of genetic algorithms).In this Thesis we also explore a number of directions towards the construction of better neuron models --within an integrant envelope-- more adapted to the problems they are meant to solve.It is described how a certain generic class of heterogeneous models leads to a satisfactory performance, comparable, and often better, to that of classical neural models, especially in the presence of heterogeneous information, imprecise or incomplete data, in a wide range of domains, most of them corresponding to real-world problems.Postprint (published version

Applications of fuzzy counterpropagation neural networks to non-linear function approximation and background noise elimination

An adaptive filter which can operate in an unknown environment by performing a learning mechanism that is suitable for the speech enhancement process. This research develops a novel ANN model which incorporates the fuzzy set approach and which can perform a non-linear function approximation. The model is used as the basic structure of an adaptive filter. The learning capability of ANN is expected to be able to reduce the development time and cost of the designing adaptive filters based on fuzzy set approach. A combination of both techniques may result in a learnable system that can tackle the vagueness problem of a changing environment where the adaptive filter operates. This proposed model is called Fuzzy Counterpropagation Network (Fuzzy CPN). It has fast learning capability and self-growing structure. This model is applied to non-linear function approximation, chaotic time series prediction and background noise elimination

New Optimal Approach for the Identification of Takagi-Sugeno Fuzzy Model

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model

An Optimal T-S Model for the Estimation and Identification of Nonlinear Functions

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model

Web Shopping Expert Systems Using New Interval Type-2 Fuzzy Reasoning

Finding a product with high quality and reasonable price online is a difficult task due to the fuzzy nature of data and queries. In order to handle the fuzzy problem, a new type-2 fuzzy reasoning based decision support system, the Web Shopping Expert for online users is proposed. In the Web Shopping Expert, an interval type-2 fuzzy logic system is used and a fuzzy output can be obtained using the up-low limit technique, which offers an opportunity to directly employ all the rules and methods of the type-1 fuzzy sets onto the type-2 fuzzy sets. To achieve the best performance the fuzzy inference system is optimized by the least square and numerical method. The key advantages of the least square method are the efficient use of samples and the simplicity of the implementation. The Web Shopping Expert based on the interval type-2 fuzzy inference system provides more reasonable conclusions for online users