Research On Neural Network Implicit Method And Its Application In The Petrolic Data

This thesis studied the method of constructing implicit curves and surfaces based on multilayer feed-forward neural network, selection of constraint point based on dilation and erosion, and its application. The developments of research are above:1. Neural networks, combined with implicit polynomials, can be employed to represent 2D curves as well as 3D surfaces by the zero-set of a neural network. First, an explicit function is constructed based on the implicit function. Then the explicit function is approximated by a neural network. Finally, the zero-set of the neural network which is the implicit surface is extracted from the simulation surface. The neural network fitting algorithms developed aim to reduce the learning time of neural network by selecting the exterior and interior constraint points simultaneously and improve the fitting performance by using the linear transfer function at the output layers and sigmoid transfer function at the implicit layers.2. The control points can be selected based on the normal of curve. But it is only true for convex object, and always gets wrong exterior points and interior points. Based on binary mathematical morphological operator process, a new method of selecting constraint points was produced, which is not likely to be influenced by boundary topology. A adaptive method of selecting constraint points is also produced, which is helpful to describe the specific part.3. Neural network can only approximate and interpolate the explicit function, which limits its application scope. By combining the principle of implicit curves and surfaces with the neural networks, repairing the partial implicit data and mapping the vector data, a new data processing method is developed, which can process the data that can not be described by an explicit function, and the data that can be described by a certain kind of multivariate vector function. The method includes several steps: firstly, the data are repaired or mapped into a closed curve; secondly, choosing constraint data; thirdly, constructing a virtual explicit function based on the constraint points; fourthly, constructing the input and output vector, and training the neural network; fifthly, extracting the isoline from the simulation surface; lastly, postprocessing the isoline. An experiment is given to explore the characteristic of the method: combining the time factor and dimensional factor together.4. A method of processing time Vector-Valued series was produced based on approximation and function interpolation. Many data can be described as y = f(X,t) . where X is vector of two dimension or more high dimension. Let Y_t={(X_i,t,f(X_i,t))|i= 1, …,n} , where t is constant and Q = {Y_t|t= 1,…,m} In the hole, the data set of Q is got at the different time. For the single Y_t, the value changed along the X So, the ideal method to process data Q is to describe the change of time in the whole and to describe the change of X locally. Combined the principal of constructing implicit curves and surfaces with the mapping, the time Vector-Valued series can be seen as a kind of scattered data. Thus, the theory and methods of function approximation and the multivariate function interpolation can be used to process the data. The methods will widely used for prediction, reparation and scientific visualization.