Alternatively to empirical prediction methods, methods based on influential functions and on mechanical model, artificial neural networks (ANNs) can be used for the surface subsidence prediction. In our case, the mult...
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Alternatively to empirical prediction methods, methods based on influential functions and on mechanical model, artificial neural networks (ANNs) can be used for the surface subsidence prediction. In our case, the multi-layer feed-forward neural network was used. The training and testing of neural network is based on the available data. Input variables represent extraction parameters and coordinates of the points of interest, while the output variable represents surface subsidence data. After the neural network has been successfully trained, its performance is tested on a separate testing set. Finally, the surface subsidence trough above the projected excavation is predicted by the trained neural network. The applicability of ANN for the prediction of surface subsidence was verified in different subsidence models and proved on actual excavated levels and in levelled data on surface profile points in the Velenje Coal Mine. (C) 2003 Elsevier Science Ltd. All rights reserved.
Linguistic Fuzzy Logic Controller (LFLC) 2000 is a complex tool for the design of linguistic descriptions and fuzzy control based on these descriptions. Unique methodology and theoretical results upon which is LFLC 20...
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Linguistic Fuzzy Logic Controller (LFLC) 2000 is a complex tool for the design of linguistic descriptions and fuzzy control based on these descriptions. Unique methodology and theoretical results upon which is LFLC 2000 based are presented. Then, main purposes of it are sketched and some implementation aspects are discussed. Presentation of existing and perspective applications concludes the paper. (C) 2003 Elsevier B.V. All rights reserved.
We derive several sufficient conditions for the uniform approximability of fulictions by polynomial solutions of homogeneous elliptic equations of second order with constant coefficients on Caratheodory compact sets i...
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We derive several sufficient conditions for the uniform approximability of fulictions by polynomial solutions of homogeneous elliptic equations of second order with constant coefficients on Caratheodory compact sets in R-2.
The investigation of a q-analogue of the convolution on the line, started in conjunction with Koornwinder, is continued, with special attention to the approximation of functions by means of the convolution. A new spac...
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The investigation of a q-analogue of the convolution on the line, started in conjunction with Koornwinder, is continued, with special attention to the approximation of functions by means of the convolution. A new space of functions that forms an increasing chain of algebras (with respect to the q-convolution), depending on a parameter s > 0, is constructed. For a special value of the parameter the corresponding algebra is commutative and unital, and is shown to be the quotient of an algebra studied in a previous paper modulo the kernel of a q-analogue of the Fourier transform. This result has an analytic interpretation in terms of analytic functions, whose q-moments have a (fast) decreasing behavior and allows the extension of Koornwinder's inversion formula for the q-Fourier transform. A few results on the invertibility of functions with respect to the q-convolution are also obtained and they are applied to the solution of certain simple linear q-difference equations with polynomial coefficients.
The paper deals with approximations of functions with bounded mixed difference by Haar polynomials. approximations of the following two different types are studied: the classical best approximation by Haar polynomials...
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The paper deals with approximations of functions with bounded mixed difference by Haar polynomials. approximations of the following two different types are studied: the classical best approximation by Haar polynomials with indices lying in hyperbolic crosses and the best m-term approximation by Haar polynomials.
We examine the effect of constraining the number of hidden units. For one-hidden-layer networks with a fairly general type of units (including perceptrons with any bounded activation function and radial-basis-function...
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We examine the effect of constraining the number of hidden units. For one-hidden-layer networks with a fairly general type of units (including perceptrons with any bounded activation function and radial-basis-function units), we show that when also the size of parameters is bounded, the best approximation property is satisfied, which means that there always exists a parametrization achieving the global minimum of any error function generated by a supremum or L(p)-norm. We also show that the only functions that can be approximated with arbitrary accuracy by increasing parameters in networks with a fixed number of Heaviside perceptrons are functions equal almost everywhere to functions that can be exactly computed by such networks. We give a necessary condition on values that such piecewise constant functions must achieve.
We estimate variation with respect to half-spaces in terms of ''flows through hyperplanes''. Our estimate is derived from an integral representation for smooth compactly supported multivariable functio...
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We estimate variation with respect to half-spaces in terms of ''flows through hyperplanes''. Our estimate is derived from an integral representation for smooth compactly supported multivariable functions proved using properties of the Heaviside and delta distributions. Consequently we obtain conditions which guarantee approximation error rate of order O(1/root n) by one-hidden-layer networks with n sigmoidal perceptrons. (C) 1997 Elsevier Science Ltd.
Lanczos and Ortiz placed the canonical polynomials (c.p.'s) in a central position in the Tau Method. In addition, Ortiz devised a recursive process for determining c.p.'s consisting of a generating formula and...
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Lanczos and Ortiz placed the canonical polynomials (c.p.'s) in a central position in the Tau Method. In addition, Ortiz devised a recursive process for determining c.p.'s consisting of a generating formula and a complementary algorithm coupled to the formula. In this paper a) We extend the theory so as to include in the formalism also the ordinary linear differential operators with polynomial coefficients D with negative height [GRAPHICS] where m(n) denotes the degree of Dx(n). b) We establish a basic classification of the c.p.'s Q(m)(x) and their orders m is an element of M, as primary or derived, depending, respectively, on whether There Exists n is an element of N: m(n) = m or such n does not exist;and we state a classification of the indices n is an element of N, as generic (m(n) = n+h), singular (m(n) < n+h), and indefinite (Dx(n) = 0). Then a formula which gives the set of primary orders is proved. c) In the rather frequent case in which all c.p.'s are primary, we establish, for differential operators D with any height h, a recurrency. formula which generates bases of the polynomial space and their multiple c.p.'s arising from distinct x(n), n is an element of N, so that no complementary algorithmic construction is needed;the (primary) c.p.'s so produced are classified as generic or singular, depending on the index n. d) We establish the general properties of the multiplicity relations of the primary c.p.'s and of their associated indices. It becomes clear that Ortiz's formula generates, for h greater than or equal to 0, the generic c.p.'s in terms of the singular and derived c.p.'s, while singular and derived c.p.'s and the multiples of distinct indices are constructed by the algorithm.
A large class of functions (in one or more variables) can be approximated by a, generally, multilayer feed-forward network, in which only the weights of the last layer need to be trained. All others can be selected ap...
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ISBN:
(纸本)0780333675
A large class of functions (in one or more variables) can be approximated by a, generally, multilayer feed-forward network, in which only the weights of the last layer need to be trained. All others can be selected appropriately dependent upon the desired accuracy with which the training examples are to be approximated, but independently of the examples. Thus only a perceptron remains to be trained.
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