Improved Support Vector Regression, Its Application In Process Modeling And Control

Support vector machine has become a general method for machine learning in the framework of the statistical learning theory. That is, it shows the advantage of capability in dealing with small samples, overfitting, high dimensions and local minimum, and exhibits good generalization. Thus, it has been widely used for pattern recognition, regression estimation, density estimation, system identification, process modeling and control. From the perspective of theory and application, this paper made systematic study on the main aspects of large scale samples, model selection, process modeling and predictive control for support vector regression. Main contents are listed as follows.(1) Effective data reduction algorithms were proposed to improve large-scale learning problem. For large dataset learning problem of regression estimation, sample reduction approach based on boundary vector extraction was presented. It shifted all target outputs up and down by introducingε'band, and then regression problem can be converted to a two-class classification problem in the high dimensional space. It adjustedε'band and enabled all the training data to be just separable linearly in the feature space, and then extracted boundary vectors in terms of adaptive projective algorithm to realize sample reduction of the regression problem. Dimension reduction based on quantum clustering technique is proposed to solve high dimension learning problem. It introduced inertia threshold into quantum clustering, and thus selected the optimal feature subsets with best generalization ability.(2) Three optimization algorithms were modified to optimize model parameters for support vector regression. Parameter selection has a direct effect on the generalization of support vector regression approach. Thus, adaptive particle swarm algorithm was developed to select model parameters for support vector regression. It adjusted inertia weight for each particle in each iteration to enhance the speed of convergence. Meanwhile, fuzzy cultural algorithm was proposed by fuzzy acceptance and fuzzy influence to optimize the model parameters for support vector regression and improve the optimization process. Weighted support vector regression on the penalized parameter C was presented to assign different weight according to sample training error. The generalization accuracy of support vector regression was improved in terms of numerical simulation.(3) Improved conformal mapping kernel function and multi-scale wavelet kernel function were given. A new factor function was determined to decrease the volume of the data points far away from support vectors in feature space, and then improved conformal mapping kernel was presented to verify the validity of the generalization precision for support vector regression by the simulation of standard regression dataset and ethylene concentration data. Multi-scale morlet wavelet was developed to solve the problem of complex and multi-peak function estimation. The simulations of standard regression datasets and propylene concentration in bottom products of propylene distillation column verified the feasibility of this method.(4) Dynamic modeling approach for support vector regression was presented to design the model of nonlinear multivariable system. For time varying characteristics in industrial process, dynamic modeling approach for multi-input and multi-output system based on linear programming support vector regression was proposed, in order to establish accurate model for controlled object in industrial process. It provided non-linear mapping of original input variables and history output variables, respectively, carried on linear superposition, and employed support vector regression to solve the problem. Then it is applied to construct dynamic model for complex industrial process. The simulation of the poly ethylene terephthalate production and second-order difference nonlinear multivariable system verified the validity.(5) Nonlinear predictive control for support vector regression was given based on the above-mentioned dynamic modeling. Support vector regression can approach arbitrary nonlinear system by arbitrary accuracy. Therefore, nonlinear predictive control method based on linear programming support vector regression with Gaussian kernel function was presented. It did nonlinear mapping of the original input and output, regarded dynamic model based on linear programming support vector regression as predictive model for predictive control system, and then expanded this model by Taylor's formula to make the model linearization, and obtained the optimal control law of predictive control system. The experiments of weakly and strongly nonlinear system depicted that this approach exhibited excellent disturbance-rejection ability.