Identification of piecewise affine systems based on statistical clustering technique
Identification of piecewise affine systems based on statistical clustering technique
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DOI：
10.1016/j.automatica.2004.12.005
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发表时间：
2005-05-01
期刊：
影响因子：
6.4
通讯作者：
Katayama, T
中科院分区：
文献类型：
--
作者：
Nakada, H;Takaba, K;Katayama, T
研究了一类分段仿射自回归外生（PWARX）模型的辨识问题。PWARX模型由ARX子模型组成，每个子模型对应于回归空间的多面体区域。在子模型个数先验已知的临时假设下，利用统计聚类算法将输入输出数据分成若干类。我们利用支持向量分类器来估计回归空间中两个相邻区域之间的边界超平面。在每个聚类中，子模型的参数向量由最小二乘法获得。事实证明，目前的统计聚类方法，使我们能够估计子模型的数量的基础上的信息标准，如CAIC和MDL。在将子模型的数量固定为不同的值之后，通过将识别过程应用于相同的数据集若干次来执行子模型的数量的估计。最后，我们通过一个Hammerstein模型的数值例子验证了本识别方法的适用性。(c)2005爱思唯尔有限公司保留所有权利。
This paper is concerned with the identification of a class of piecewise affine, systems called a piecewise affine autoregressive exogenous (PWARX) model. The PWARX model is composed of ARX sub-models each of which corresponds to a polyhedral region of the regression space. Under the temporary assumption that the number of sub-models is known a priori, the input-output data are collected into several clusters by using a statistical clustering algorithm. We utilize support vector classifiers to estimate the boundary hyperplane between two adjacent regions in the regression space. In each cluster, the parameter vector of the sub-model is obtained by the least squares method. It turns out that the present statistical clustering approach enables us to estimate the number of sub-models based on the information criteria such as CAIC and MDL. The estimate of the number of sub-models is performed by applying the identification procedure several times to the same data set, after having fixed the number of sub-models to different values. Finally, we verify the applicability of the present identification method through a numerical example of a Hammerstein model. (c) 2005 Elsevier Ltd. All rights reserved.