基于多分辨率B样条小波网络的船体曲面光顺和重建
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摘要
为用于船体型线设计中船体曲面重建和光顺,基于多分辨率小波网络原理,引入三次B样条函数作为小波基函数,三次B样条基函数作为尺度函数,利用小波网络的权值和激励函数的线性组合,构造了新的二维多分辨率B样条小波网络(multi-resolution B-splinewavelet net work,MRBWN).将曲面分解为相互正交的u、v方向函数,用该网络来拟合自由曲面;并利用梯度下降法对网络进行训练.最后对船体曲面进行了光顺,实例证明了该方法的有效性和正确性.
To reconstruct and smooth the ship surface in ship form design,based on the multi-resolution wavelet network (MRWN) principle,cubic B-spline function was introduced as the wavelet function and cubic B-spline basis function as the scale function and the linear combination of the weights and the activation function of wavelet network was used,a novel two-dimensional multi-resolution B-spline wavelet network (MRBWN) was constructed. The surface was decomposed into orthogonal u,v direction function,and new network was used to approximate it. The gradient algorithm was adopted to train the network. The smooth ship surface is obtained in the experiment of hull surface,which shows the feasibility and validity of the approach.
To reconstruct and smooth the ship surface in ship form design,based on the multi-resolution wavelet network (MRWN) principle,cubic B-spline function was introduced as the wavelet function and cubic B-spline basis function as the scale function and the linear combination of the weights and the activation function of wavelet network was used,a novel two-dimensional multi-resolution B-spline wavelet network (MRBWN) was constructed. The surface was decomposed into orthogonal u,v direction function,and new network was used to approximate it. The gradient algorithm was adopted to train the network. The smooth ship surface is obtained in the experiment of hull surface,which shows the feasibility and validity of the approach.
引文
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[2]朱学军,董洪智,王安麟,等.模糊罚函数遗传算法及其在曲线光顺中的应用[J].上海交通大学学报,2000,34(10):1424-1425
[3]GU P,YAN X.Neural network approach to the reconstruction of freeform surfaces for reverse engineering[J].Computer-Aided Design,1995,27(1):59-64
[4]PRAHAKAR S,HENDERSON M R.Automatic form-feature recognition using neural network-based techniques on boundary representation of solid models[J].Computer-Aided Design,1992,24(7):381-393
[5]BARHAK J,FISCHER A.Parameterization and reconstruction from3D scattered points based on neural network and PDE techniques[J].IEEE Transaction on Visualization and Computer Graphics,2001,7(1):1-16
[6]张伟,姜献峰,陈丽能,等.基于神经网络的三角形网格智能重建[J].工程图学学报,2004,25(1):71-75
[7]ZHANG Q,BENVENISTE A.Wavelet network[J].IEEE Transactions on Neural Networks,1992,3(6):889-898
[8]ZHANG Q H.Using wavelet network in nonparametric esti mation[J].IEEE Transactions on Neural Networks,1997,8(2):227-236
[9]张邦礼,李银国,曹长修.小波神经网络的构造及其算法的鲁棒性分析[J].重庆大学学报,1995,15(6):88-95
[10]宋维琪,赵万金,吴华,等.利用多分辨率小波网络进行地震资料反演[J].地震地质,2005,3(1):98-104
[11]赵其刚,李群湛,彭虎.小波神经网络在NGN流量预测中的应用[J].计算机工程,2006,16(8):20-22
[12]LI X L,GAO X P.Multi-wavelet neural work:Anovel model[C]//Proceedings of2003IEEE International Conference on Systems,Man and Cybernetics.Washington D C:IEEE,2003:2629-2632
[13]於东军,王士同.B样条神经网络的构造原理[J].计算机研究与发展,1999,36(5):534-540
[14]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京:北京航空航天大学出版社,1994
[15]孙增圻.智能控制理论及应用[M].北京:清华大学出版社,1997
[16]BARTELS R H,SAMAVATI F F.Reversing subdivision rules:local linear conditions and observations on inner products[J].Journal of Computational and Applied Mathematics,2000,119(5):29-67
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