小波过程神经网络相关理论及其应用研究
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摘要
本文在国家自然科学基金的资助下,将小波分析理论和过程神经网络模型相结合,提出小波过程神经网络的概念。小波过程神经网络以小波分析作为其理论基础,结合小波良好的局部化特性和过程神经网络能够处理时变信号的能力。小波分析理论在网络设计过程中帮助确定网络的拓扑结构和网络参数,为网络结构的确定提供理论依据,简化了网络的训练问题。小波的时—频局部化特性有利于处理非平稳的输入信号,而过程神经网络能够避免传统神经网络在大容量非线性时变系统的信号处理方面存在的不适应性。本文对小波过程神经网络模型及其相关理论进行深入分析和研究。在此基础上,将小波过程神经网络模型应用于航空发动机性能衰退预测中,为航空发动机性能衰退预测提供一种有效的方法。
论文提出连续小波过程神经元和离散小波过程神经元模型,给出常用的小波过程神经元的激励函数并与前馈过程神经网络的激励函数进行对比分析,给出小波过程神经网络模型的分类方式。
以小波分析理论中的连续小波变换、小波多分辨分析和小波框架为理论依据,提出三类小波过程神经网络模型——连续小波过程神经网络、多分辨小波过程神经网络和框架小波过程神经网络。首先,以连续小波变换为理论依据,采用连续小波函数作为过程神经网络的激励函数构建连续小波过程神经网络,给出基于正交基展开的学习算法和梯度下降的学习算法,对网络的隐层激励函数的选择、隐层节点的确定以及网络参数初始化三个难点问题作了深入的研究。根据连续小波过程神经网络中隐层基函数调节参数的不同,又提出一种小波基函数过程神经网络模型并给出学习算法。其次,以多分辨分析和正交小波分解为理论依据,采用正交小波和正交尺度函数共同作为过程神经网络隐含层激励函数,构建多分辨小波过程神经网络。利用多分辨分析逐层逼近的性质,给出多分辨小波过程神经网络的学习算法。作为多分辨小波过程神经网络的一种简化形式,采用正交尺度函数作为过程神经网络的激励函数构建多分辨尺度小波过程神经网络并给出学习算法。最后,以离散小波变换和小波框架为理论依据,提出框架小波过程神经网络模型并给出学习算法。本文还对上述网络模型及其学习算法的相关性能进行分析和仿真试验,针对小波过程神经网络模型对于不同类型信号的处理能力,给出三类小波过程神经网络模型的信号处理范围,为小波过程神经网络的实际应用提供指导。以上三类小波过程神经网络构成了小波过程神经网络完整的结构体系。
利用小波函数的可积性和紧支撑的性质,利用实变函数和泛函分析中函数空间和算子理论等性质特点,开展小波过程神经网络的性能分析研究。从理论上证明了小波过程神经网络解的存在性、小波过程神经网络的连续性、小波过程神经网络的逼近能力以及小波过程神经网络计算能力等定理。对学习算法的性能进行了分析,并对小波过程神经网络和前馈过程神经网络进行比较。小波过程神经网络所具有的性质是保证其对实际问题应用有效性的理论基础。
针对航空发动机状态监控问题的实际需求,本文将三类小波过程神经网络模型分别应用于航空发动机滑油金属含量、转子振动信号和排气温度裕度的趋势预测问题,实现了对特征不同的信号选取不同的网络模型进行预测。对于不同类型的预测信号,小波过程神经网络模型表现出良好的收敛性能和泛化能力。实际应用结果表明:相对于其它的神经网络,小波过程神经网络在处理时变问题以及对突变信号的捕捉及复现等方面具有独特的功能和广阔的应用前景。
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.
论文提出连续小波过程神经元和离散小波过程神经元模型,给出常用的小波过程神经元的激励函数并与前馈过程神经网络的激励函数进行对比分析,给出小波过程神经网络模型的分类方式。
以小波分析理论中的连续小波变换、小波多分辨分析和小波框架为理论依据,提出三类小波过程神经网络模型——连续小波过程神经网络、多分辨小波过程神经网络和框架小波过程神经网络。首先,以连续小波变换为理论依据,采用连续小波函数作为过程神经网络的激励函数构建连续小波过程神经网络,给出基于正交基展开的学习算法和梯度下降的学习算法,对网络的隐层激励函数的选择、隐层节点的确定以及网络参数初始化三个难点问题作了深入的研究。根据连续小波过程神经网络中隐层基函数调节参数的不同,又提出一种小波基函数过程神经网络模型并给出学习算法。其次,以多分辨分析和正交小波分解为理论依据,采用正交小波和正交尺度函数共同作为过程神经网络隐含层激励函数,构建多分辨小波过程神经网络。利用多分辨分析逐层逼近的性质,给出多分辨小波过程神经网络的学习算法。作为多分辨小波过程神经网络的一种简化形式,采用正交尺度函数作为过程神经网络的激励函数构建多分辨尺度小波过程神经网络并给出学习算法。最后,以离散小波变换和小波框架为理论依据,提出框架小波过程神经网络模型并给出学习算法。本文还对上述网络模型及其学习算法的相关性能进行分析和仿真试验,针对小波过程神经网络模型对于不同类型信号的处理能力,给出三类小波过程神经网络模型的信号处理范围,为小波过程神经网络的实际应用提供指导。以上三类小波过程神经网络构成了小波过程神经网络完整的结构体系。
利用小波函数的可积性和紧支撑的性质,利用实变函数和泛函分析中函数空间和算子理论等性质特点,开展小波过程神经网络的性能分析研究。从理论上证明了小波过程神经网络解的存在性、小波过程神经网络的连续性、小波过程神经网络的逼近能力以及小波过程神经网络计算能力等定理。对学习算法的性能进行了分析,并对小波过程神经网络和前馈过程神经网络进行比较。小波过程神经网络所具有的性质是保证其对实际问题应用有效性的理论基础。
针对航空发动机状态监控问题的实际需求,本文将三类小波过程神经网络模型分别应用于航空发动机滑油金属含量、转子振动信号和排气温度裕度的趋势预测问题,实现了对特征不同的信号选取不同的网络模型进行预测。对于不同类型的预测信号,小波过程神经网络模型表现出良好的收敛性能和泛化能力。实际应用结果表明:相对于其它的神经网络,小波过程神经网络在处理时变问题以及对突变信号的捕捉及复现等方面具有独特的功能和广阔的应用前景。
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.
引文
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