| Summary: | 博士 === 雲林科技大學 === 工程科技研究所博士班 === 97 === Since traditional radial basis function networks (RBFNs) have only one hidden layer and have fast convergence speeds, they are widely used for various applications. When the traditional RBFNs are used, the number of hidden nodes, the initial parameters of the kernel, and the initial weights of the network must be determined first. Therefore, a support vector regression (SVR) approach is proposed to solve the initial problem of the traditional RBFNs. That is, the SVR uses the quadratic programming optimization to determine the initial structure of the traditional RBFNs.
In this dissertation, we introduce two different SVR ( -SVR and -SVR) methods with Gaussian kernel functions. The -SVR approach with the insensitive loss function can make use of a small subset of the training data, called the support vectors (SVs), to approximate the desired outputs within a tolerance band. The -SVR approach with a new parameter can control the number of support vectors and training errors, to approximate the desired outputs.
When the proposed RBFNs is used for identification of a nonlinear multi-input multi-output (MIMO) system, a systematic way that integrates the SVR and the least squares regression (LSR) is proposed to construct the initial structure of the RBFNs. The first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the SVR method. Then the weights of the RBFNs are determined by solving a simple minimization problem based on the concept of LSR. After initialization, an annealing robust learning algorithm (ARLA) is then applied to train the RBFNs.
In general, for the scientific and engineering applications, the obtained training data are always subject to outliers. Outliers may occur due to various reasons, such as erroneous measurements or noisy data from the tail of noise distribution functions. When there are outliers, there still exist some problems in the traditional RBFNs approaches.
The proposed annealing robust radial basis function networks (ARRBFNs) with SVR are trained by the ARLA, which uses the annealing concept in the cost function of the robust back-propagation learning algorithm and can overcome the error measurement caused by the outliers. Hence, the proposed method has (i) the same capability of universal approximator with the traditional RBFNs, (ii) a faster learning speed than the traditional RBFNs, and (iii) outlier noise rejection with the proposed ARRBFNs.
In the simulation examples, the proposed method with different SVRs for identification of a nonlinear MIMO system is studied. Meanwhile, the identification of nonlinear dynamic systems with outliers, the prediction of chaotic time series with outliers such as the Mackey–Glass time series and the Lorenz chaotic system are also studied. Finally, we show how to apply the proposed method for nonlinear inverse system identification with outliers.
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