Research On Wavelet Process Neural Network Correlative Theory And Its Application

Wavelet process neural network model which combines the virtue of wavelet analysis and process neural network model is proposed in this dissertation under the support of the National Natural Science Foundation of China. Wavelet process neural network employs wavelet analysis theory as its scientific guides, incorporates the capacity of time-frequency local property of wavelet analysis and the capacity of process neural network to deal with continuous input signals. Wavelet analysis theory assists the network to define topology structure and network parameters. It provides theoretic guarantee for the network structure design and predigests the network training. Time-frequency localization property of wavelet facilitates in dealing with fluctuant input signals. Comparing with traditional neural network, process neural network can avoid maladjustment in tackle with nonlinear time-varying system signals. Wavelet process neural network model and correlative theoretic are in-depth researched in this dissertation. On this condition, wavelet process neural network model is used to solve the problem of aeroengine deterioration forecasting. This provides an effective way for the problem of aeroengine performance deterioration forecasting.Continuous wavelet process neuron and discrete wavelet process neuron are proposed in this dissertation. Common activation functions of wavelet process neuron are given to compare with activation functions of feedforward process neuron. Multiform wavelet process neural network models are given in succession.Three forms of wavelet neural network models are proposed such as continuous wavelet process neural network, multiresolution wavelet process neural network and frame wavelet process neural network based on continuous wavelet transform, wavelet multiresolution analysis and wavelet frame respectively in this dissertation. Firstly, based on continuous wavelet transform theory, the dissertation presents continuous wavelet process neural network whose activation function is continuous wavelet function. The corresponding learning algorithm based on the Expansion of the Orthogonal Basis Functions and Gradient Descent is given. Three difficult problems such as how to select wavelet functions, how to decide the number of hidden units and how to initialize weights of these units are researched. According to the different adjustable hidden layer basis function parameters of continuous wavelet process neural network, wavelet basis function process neural network model and its learning algorithm are presented. Secondly, based on wavelet multiresolution analysis and orthogonal wavelet decompose, multiresolution wavelet process neural network is proposed. The network employs the orthogonal wavelet function and orthogonal scaling function as the activation functions. Utilizing the characteristics of hierarchical, multiresolution and local learning capability, a multiresolution wavelet process neural network learning algorithm is given. Multiresolution scaling wavelet process neural network is proposed as the simple form of multiresolution wavelet process neural network model. The network makes use of scaling wavelet functions as its activation functions and the corresponding learning algorithm is given subsequently. Finally, frame wavelet process neural network model and its learning algorithm are presented. Various forms of wavelet process neural network models and their learning algorithm are proved by simulation tests. According to the different learning capacity for different signals, the applicable scope of three forms of wavelet process neural network is given, which provides the guidance for wavelet process neural network to solve practical applications. These three forms of wavelet process neural network mentioned above make up of the whole structure of wavelet process neural network.Using the integral characteristics and compact support of wavelet function, the continuity of the operator theory and the topology structure of the relatively compact set in the function space are applied to research problem of wavelet process neural network performance analysis. Proof the existence of wavelet process neural network solution theorem, proof the wavelet process neural network continuity theorem, proof the wavelet process neural network approximation theorem and proof the wavelet process neural network calculation capacity theorem. Analyze the learning algorithm of Wavelet Process Neural Network. Compare the characteristic of wavelet process neural network and feedforward process neural network. The characters that wavelet process neural network owns are the theoretic guarantee for validity of practical problem.Aim to meet the needs in the field of the aeronautics condition forecasting, three forms of wavelet process neural network proposed in this dissertation are adopted to solve practical problems such as deterioration trend forecasting of the iron concentration in the aeroengine lubricating oil, the aeroengine rotor vibrational signals and the aeroengine exhaust gas temperature. Which make it possible to forecast signals with different characteristics. Wavelet process neural network exhibits good convergence and generalization for different signals. The application test results also indicate that in comparison with other neural networks, wavelet process neural network proposed in this dissertation seems to perform well in the theoretic aspect and appears more suitable for solving problems related to time-varying processes and broad prospect for grasping and reappearing break signals character.