Abstract: According to the NARX identification problems, it constructs a more sparser NARX models using the radial basis function models with the nonorthogonal kernels. Compared with the traditional radial basis or other kernel models who use a common scale, it uses multiscales and selects the center and scale parameters by minimizing the training error. In the learning phase, it constructs models incrementally by the nonorthogonal kernel method. Using the k-means clustering train the data set to obtain the centers which will be selected, set multiscales, and get the corresponding weights with the least squares, then find the best kernel function that make the smallest model error using the forward selection. Experiments show that the proposed method is feasible in generalization and the sparse.

Key words: NARX models, radial basis function, forward selection, k-means clustering

摘要： 针对非线性自回归模型（Nonlinear Auto-Regressive with extrainput，NARX）系统辨识问题，利用非正交的方法来构造较为稀疏的逼近NARX模型的径向基函数模型。与已有的径向基或其他的核模型只采用同一固定的尺度不同，采用多个尺度，通过最小化当前训练误差，选择最佳的核中心和尺度参数。在学习过程中，采用非正交核函数的方法进行模型逐步回归。对样本数据利用k均值聚类算法得到核函数中心参数备选项，同时设置多个备选尺度，并通过最小二乘法求得相应核函数的权值，利用前向选择方法从中找出使模型误差最小的最优核函数。仿真实验验证了方法在泛化性能和稀疏性方面的可行性。

关键词: NARX模型, 径向基函数, 前向选择, k均值聚类