The Numerical Solution Of Nonlinear Dynamic System And Image Segmentation Based On Neural Network

In the past two decades,the research on nonlinear science has developed rapidly.The nonlinear dynamical system has diversity,and it is more complicated to rely on the previous state,so it is difficult to obtain the analytic solution in general.Therefore,it is very necessary to solve the numerical solution of nonlinear dynamical system by using the numerical method with high accuracy and simplicity.Rock Painting in Helan Mountain has the characteristics of long time span,ancient and outdoors,which widely exists the problems of information missing and fuzzy uncertainty because of the influence of nature and human factors.The traditional methods will result in complex structure,slow training process,and low precision.This paper focuses on the theory of rough set,fuzzy set and wavelet neural network.On the basis of traditional fuzzy C means,the rough set wavelet neural network based on fuzzy set is proposed to segment the rock image.The research worked in this paper is organized as follows:1.The numerical solution of the nonlinear dynamic system is studied based on the cubic spline function.Compared with the existing methods,the results show that the proposed method not only has high approximation precision,but also avoids the Runge phenomenon.The numerical examples show the error analysis of several methods,so the proposed method is more effective in engineering practice.2.Because the rough set only can deal with attribute of discrete type,the traditional fuzzy C means combined with space constraints is introduced,such that each successive attribute in the initial decision table is represented by a fuzzy variable.This part utilizes the fuzzy membership function to partion the universe,and then applied to segment the rock images and noise images.Finally the clustering validity indicators are used to evaluate the segmentation effect.3.After obtaining the optimal partition of the universe,the model of rough wavelet neural network is constructed,and experiment is designed.The experiment results are compared with wavelet neural network and traditional rough wavelet neural network.Meanwhile the four indicators of UM,GC,UMA and running time are used to analyze the segmentation effect.The results show that the proposed.method has advantages of high segmentation accuracy,low running time,and stronger generalization.It is a feasible method for image segmentation.Finally,the main contents and achievements of the paper 'are summarized,and some expectations are bring forward.