新型模糊混沌神经网络模型及特性研究
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摘要
近年来,人们对人脑局部功能的认识有所提高,但是对人脑完整工作过程仍缺乏认识。模糊逻辑和混沌动力学都是人脑所具有的特征,将现有的人工神经网络、模糊逻辑和混沌动力学相融合构成模糊混沌神经网络是一个新的方法和思路,对于模拟人脑整体功能,处理非线性系统建模和联想记忆等问题具有理论和现实的意义。目前模糊混沌神经网络技术的研究尚处于一个初步探索阶段。本文基于几种模糊神经网络模型和混沌神经网络模型,对模糊混沌神经网络新模型的构成方法和实际应用进行研究。
首先,针对模糊径向基函数神经网络,提出了一种新型的混合混沌BP算法。针对几种典型的混沌映射函数进行混沌特性和概率密度分析,为构造混沌BP算法时混沌映射函数的选取提供了依据。给出了模糊径向基函数神经网络两阶段学习方法的步骤,提出一种能够根据可调参数的值进行自动调节,并由退火系数控制算法收敛性的混沌BP算法。用所提出的算法对混沌时间序列建模,验证了算法的有效性。
其次,基于现有的递归模糊神经网络模型,构造了一种混沌递归模糊神经网络模型。推导了网络的数学模型和基于动态BP算法的权值训练公式。在此基础上,对学习算法的收敛性进行分析,推导出学习速率调整的范围。分别用自适应模糊推理系统、递归模糊神经网络、混沌递归模糊神经网络和变学习速率的混沌递归模糊神经网络对两个典型的非线性混沌系统建模,仿真结果验证了所提模型和算法的有效性。
再次,分析了一种带有微分环节的动态模糊神经元和动态模糊神经网络的混沌特性。通过对耗散性和Lyapunov特征指数的分析,推导出了单个动态模糊神经元具有耗散性的必要条件、Lvapunov特征指数大于0的必要条件;以及动态模糊神经网络具有耗散性的充分条件、Lyapunov特征指数大于0的必要条件。
最后,根据模糊Hopfield神经网络模型的构成方法和自发展混沌神经网络的工作原理,构造了一个自发展模糊混沌神经网络模型。首先分析了自发展混沌神经网络的周期特性和混沌特性。然后将自发展混沌神经网络模型进行模糊化处理,构成了自发展模糊混沌神经网络模型。证明了该模型在模糊聚类时的收敛性和稳定性,分析了其联想记忆特性。仿真实验结果表明,自发展模糊混沌神经网络不但能够完成模糊聚类功能,还能对聚类结果进行联想记忆。
The recognition for human brain's local function has improved in the recent years. But the cognition of human brain's working process as a whole is still obscure. Both of fuzzy logic and chaos dynamic are internal features of human brain. Therefore, to fuse artificial neural networks, fuzzy logic and chaotic dynamic together to constitute fuzzy chaotic neural networks is a novelty method. It is helpful to simulate the whole function of human brain, and very meaningful in disposing nonlinear and associate memory problems from the view of both theory and reality. Study on fuzzy chaotic neural networks technology is still being a preliminary exploration phase. This dissertation is focus on the new ways of fuzzy neural networks construction and its application based on the existing achievement of this field.
Firstly, a new chaotic Back-Propagation hybrid learning algorithm is proposed to training fuzzy radial basis function neural network. The analysis of chaotic characters and probability density is processed aiming at a few of typical chaotic mapping functions, which offers theoretical foundation for the choosing of chaotic mapping function in the construction process of chaotic Back-Propagation algorithm. A two stage learning method of fuzzy radial basis function neural network is given subsequently. The proposed chaotic Back-Propagation hybrid learning algorithm could be adaptively adjusted according to the parameters, and the convergence is guaranteed by annealing coefficient. The effectiveness of algorithm is validated throughout approximate chaos time series.
Then, a chaotic recurrent fuzzy neural networks model is developed based on existing recurrent fuzzy neural networks. The mathematical model of neural networks and weight learning formulas based on dynamic Back-Propagation algorithm are deduced. After that, the convergence of learning algorithm is analyzed. A theorem is deduced to verify the range of adaptive learning rate. Using adaptive networks based fuzzy inference systems, recurrent fuzzy neural networks, chaotic recurrent fuzzy neural networks and chaotic recurrent fuzzy neural networks with adaptive adjustment learning rate to construct and simulate two typical nonlinear chaotic systems respectively. The validity of the proposed model and algorithm is testified at last.
Next, the chaotic feature of dynamic fuzzy neuron with differential links is studied. The dynamic fuzzy neural networks are analyzed in the same way subsequently. Throughout the analysis, the necessary condition for single dynamic fuzzy neuron to have a dissipation and the necessary condition for its Lyapunov exponents to be more than zero are deduced. The sufficient condition of dynamic fuzzy neural networks to be a dissipation system and the necessary condition for its Lyapunov exponents to be more than zero are also list.
At last, according to the composition principle of fuzzy Hopfield neural network and the trait of self-evolution neural network, a self-evolution fuzzy chaotic neural network is proposed. The chaotic character and period character of self-evolution neural networks are analyzed at first. And then the model is going through a fuzzification process to constitute a self-evolution fuzzy chaotic neural network. The convergence and stability of the model during the process of fuzzy clustering are proved, and the associate memory ability is analyzed. As shown by the result of the simulation test, the self-evolution fuzzy chaotic neural networks could not only accomplish the fuzzy cluster function, but also realized chaotic associate memory.
首先,针对模糊径向基函数神经网络,提出了一种新型的混合混沌BP算法。针对几种典型的混沌映射函数进行混沌特性和概率密度分析,为构造混沌BP算法时混沌映射函数的选取提供了依据。给出了模糊径向基函数神经网络两阶段学习方法的步骤,提出一种能够根据可调参数的值进行自动调节,并由退火系数控制算法收敛性的混沌BP算法。用所提出的算法对混沌时间序列建模,验证了算法的有效性。
其次,基于现有的递归模糊神经网络模型,构造了一种混沌递归模糊神经网络模型。推导了网络的数学模型和基于动态BP算法的权值训练公式。在此基础上,对学习算法的收敛性进行分析,推导出学习速率调整的范围。分别用自适应模糊推理系统、递归模糊神经网络、混沌递归模糊神经网络和变学习速率的混沌递归模糊神经网络对两个典型的非线性混沌系统建模,仿真结果验证了所提模型和算法的有效性。
再次,分析了一种带有微分环节的动态模糊神经元和动态模糊神经网络的混沌特性。通过对耗散性和Lyapunov特征指数的分析,推导出了单个动态模糊神经元具有耗散性的必要条件、Lvapunov特征指数大于0的必要条件;以及动态模糊神经网络具有耗散性的充分条件、Lyapunov特征指数大于0的必要条件。
最后,根据模糊Hopfield神经网络模型的构成方法和自发展混沌神经网络的工作原理,构造了一个自发展模糊混沌神经网络模型。首先分析了自发展混沌神经网络的周期特性和混沌特性。然后将自发展混沌神经网络模型进行模糊化处理,构成了自发展模糊混沌神经网络模型。证明了该模型在模糊聚类时的收敛性和稳定性,分析了其联想记忆特性。仿真实验结果表明,自发展模糊混沌神经网络不但能够完成模糊聚类功能,还能对聚类结果进行联想记忆。
The recognition for human brain's local function has improved in the recent years. But the cognition of human brain's working process as a whole is still obscure. Both of fuzzy logic and chaos dynamic are internal features of human brain. Therefore, to fuse artificial neural networks, fuzzy logic and chaotic dynamic together to constitute fuzzy chaotic neural networks is a novelty method. It is helpful to simulate the whole function of human brain, and very meaningful in disposing nonlinear and associate memory problems from the view of both theory and reality. Study on fuzzy chaotic neural networks technology is still being a preliminary exploration phase. This dissertation is focus on the new ways of fuzzy neural networks construction and its application based on the existing achievement of this field.
Firstly, a new chaotic Back-Propagation hybrid learning algorithm is proposed to training fuzzy radial basis function neural network. The analysis of chaotic characters and probability density is processed aiming at a few of typical chaotic mapping functions, which offers theoretical foundation for the choosing of chaotic mapping function in the construction process of chaotic Back-Propagation algorithm. A two stage learning method of fuzzy radial basis function neural network is given subsequently. The proposed chaotic Back-Propagation hybrid learning algorithm could be adaptively adjusted according to the parameters, and the convergence is guaranteed by annealing coefficient. The effectiveness of algorithm is validated throughout approximate chaos time series.
Then, a chaotic recurrent fuzzy neural networks model is developed based on existing recurrent fuzzy neural networks. The mathematical model of neural networks and weight learning formulas based on dynamic Back-Propagation algorithm are deduced. After that, the convergence of learning algorithm is analyzed. A theorem is deduced to verify the range of adaptive learning rate. Using adaptive networks based fuzzy inference systems, recurrent fuzzy neural networks, chaotic recurrent fuzzy neural networks and chaotic recurrent fuzzy neural networks with adaptive adjustment learning rate to construct and simulate two typical nonlinear chaotic systems respectively. The validity of the proposed model and algorithm is testified at last.
Next, the chaotic feature of dynamic fuzzy neuron with differential links is studied. The dynamic fuzzy neural networks are analyzed in the same way subsequently. Throughout the analysis, the necessary condition for single dynamic fuzzy neuron to have a dissipation and the necessary condition for its Lyapunov exponents to be more than zero are deduced. The sufficient condition of dynamic fuzzy neural networks to be a dissipation system and the necessary condition for its Lyapunov exponents to be more than zero are also list.
At last, according to the composition principle of fuzzy Hopfield neural network and the trait of self-evolution neural network, a self-evolution fuzzy chaotic neural network is proposed. The chaotic character and period character of self-evolution neural networks are analyzed at first. And then the model is going through a fuzzification process to constitute a self-evolution fuzzy chaotic neural network. The convergence and stability of the model during the process of fuzzy clustering are proved, and the associate memory ability is analyzed. As shown by the result of the simulation test, the self-evolution fuzzy chaotic neural networks could not only accomplish the fuzzy cluster function, but also realized chaotic associate memory.
引文
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