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首页> 外文期刊>IEEE Transactions on Neural Networks >Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition
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Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition

机译：使用Bezier-Bernstein多项式函数和加性分解的广义神经模糊网络建模算法

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摘要

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bezier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bezier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.
机译：本文介绍了一种基于Bezier-Bernstein多项式基函数的非线性动力学系统的神经模糊模型构造新算法。本文的概括之处在于，它通过利用加法分解构造来克服与高n相关的维数诅咒，从而应对n维输入。这种新的构造算法还引入了单变量Bezier-Bernstein多项式函数，以实现广义过程的完整性。与基于B样条展开的神经模糊系统一样，基于Bezier-Bernstein多项式函数的神经模糊网络具有理想的属性，例如基本函数的非负性，支持的统一性以及基本函数作为模糊隶属函数的可解释性，以及结构的其他优点。简约和Delaunay输入空间分区，从根本上克服了与常规模糊和RBF网络相关的维数诅咒。这个新的建模网络基于加法分解方法，以及用于模型构建中的单变量和双变量Bezier-Bernstein多项式函数的两种单独的基函数形成方法。然后，使用常规的最小二乘法来学习整个网络的权重。包括数值示例，以证明这种基于数据的新建模方法的有效性。

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