Research On Key Technologies Of Wavelet Neural Network

The theoretic analysis and study of wavelet neural networks are main contents of this thesis. Wavelet neural network is the key object in this article, a novel weighted wavelet base is presented, and its favorablecharacters are analyzed and proved. The uniform approximation of normal wavelet neural network and the robust analysis of wavelet neural networks of the combination of Sigmoid function are detailedly introduction; Multiple model failure detection based on wavelet neural network is demonstrated detailedly; At last, the failure diagnosis results of aerocraft is present seperately by employing wavelet neural network and BP neural network, and the fault diagnosis of areocraft system by wavelet neural network is achieved.At first, a new weighted wavelet is constructed by utilizing the subsection scheme and recursive average interpolated technique, without employing familiar Fourier transform. The weighted wavelet are proved to have such normal characteristics: compactly supported, smooth, vanishing moment, and orthogonal. Though the decay of weighted wavelet coefficient is the same as the common wavelet, the computable complication is observably reduced. The given simulation illustrates that the weighted wavelet and scaling functions are sufficiently smooth even though the weighted function has a large jump, and the approximate convergent rate of weighted wavelet base is faster than that of common wavelet. Compared with approximation rate, the weighted wavelet has faster convergent and more exact approximation.Next, using the integral characteristics and compact support of wavelet function, the traits of Lebesgue partition, the continuity of the operator theory and the topology structure of the relatively compact set in the Hilbert space are applied to the proof of the approximation of the wavelet neural networks. The wavelet neural networks universally approximating the nonlinear function in compact set with arbitrary precision has been proved in the abstractin theory. It extends the application of wavelet network, and supplies sufficient guidance.The simulation shows that the wavelet neural network can uniformly approximate the nonlinear function. In the following chapter, the disturbing sensitivity and robust of combination of sigmoid function wavelet neural network is discussed by making use of probability statistics and symbolic logic. If the faint perturbation appears, the robust invariability condition of wavelet neural network is obtained, and if the sensitive disturbation appreas, the sensitivity formula and robust formula are given. It proved theoretically that to a certain extent, the more hidden wavelet nerve cells, the less robust of wavelet neural network. Consequently, it validates analytically the intuitionistic hypothesis of the relationship between hidden layer wavelet nerve cells numbers and the robust of wavelet neural network.Then, the characteristic of wavelet neural network in system identification is introduced.Tthe state estimation error is proved to converge to zero asymptotically with the basic conception of stability analysis, in the mean time, parameters of the identifier can converge to the ideal identifier values. The multiple model failure detection using wavelet neural networks identifiers is also analyzed.The simulation result shows this detection method is effective and feasible.Finally, the familiar failure of areocraft is detected seperately by normal wavelet neural network and BP neural network. The simulation result shows this fault diagnosis method of wavelet neural network is effective and feasible.