CSTR Identification With Improved Support Vector Machine

Considering the wide-spreadness of nonlinear systems in practical engineering, nonlinear system identification becomes strongly connected with engineering applications and thus a hot and challenging field in research area. SVM is a perfect tool with good generalization for small-scaled problems under nonlinear conditions, which can be an effective method for nonlinear identification.In real world, data acquisition is often accompanied by various noise and some other uncertain factors, which leads to decrease in accuracy of identification models with noisy data. To solve this problem, this paper focuses on the performance in nonlinear system identification and anti-noise ability of the proposed algorithms, namely, weighted support vector (W-SVM) machines and wavelet-based support vector machines (Wa-SVM).In this paper, our main works are as follows:We give the complete flow of modeling with SVM, and discussed in details that the influence of parameters selection (C, epsilon, kernel function) on performance, and eventually applied SVM to CSTR identification issue, in which we build a model for reaction time (T) and reaction density (Ca), repectively.To overcome the over-sensitivity to data outliers, we present a weighted SVM algorithm based on support vector data descriptions (SVDD). The proposed method maps data to a feature space and gives each sample a weight by calculating their distance to the center of the minimal hyper-ball. Simulation with data outliers shows that the proposed method is in good performance compared to standard SVM.For the outlier problem, we present another method called wavelet-based SVM. The method makes fully use of the advantage of wavelet transformation over outliers. First, we do 3-level wavelet decomposition on the noisy data, which is followed by a wavelet threshold de-noising. Then, we train SVM with each de-noised component, and thus obtain 4 SVM sub-models. Finally, the predictive outputs of all sub-models are reconstructed to demonstrate real output of the method. By comparison with standard SVM, the proposed method shows good performance in simulation.