The Research Of Least Squares Support Vector Regression And Its Application In Prediction Of Water Quality

In the water environmental amelioration planning, the prediction of river water quality is very important, and which have been researched widely. Because the diversity of water flowing, and coupled with the pollution of uncertain point source, the river flow is very complex.The water environment information that we usually get is not complete, and the water environment system structure parameters and boundary condition are changeable and complex,which made the prediction of water quality to be a difficult problem.Statistical learning methods can predict river water quality by the research of the relationship between the water quality and the effects, which based on the existing data.As a new machine learning method according to the statistical learning theory, support vector machines can solve the practical problems with the characters of small sample, nonlinear, high dimension and local minima.It has been successfully applied to the classification, regression and time series prediction fields, etc.Least squares support vector machines, which originated from support vector machines and proposed by Suykens, not only shows a higher modeling precision and good generalization ability in many problems, but also reduces the computational complexity.However, there are some problems have not been researched sufficient of the algorithm and its application in water quality prediction, such as input selection problem in regression prediction model, relatively high prediction error of peak samples,etc.Some problems, which related of least squares support vector regression, have been studied in this paper, and some proposed algorithms have been applied to predict the river water quality. The main research contents and results in the paper as follow:1) Input selection problem of regression prediction model is studied. An input selection algorithm based on partial mutual information is proposed based on the information entropy of information theory. The main idea of this algorithm as follow:Whether an alternative input is selected or not determined by the estimated value of relevant information between the alternative input and the output of the model in a given input variable condition.The simulation results of the linear and nonlinear test examples shows that the proposed input selection method can select the right input variables,and eliminate the redundancy input variables.The sequence of input selected reflect the importance of the input to the output.The application results show that the selected input variables based on the algorithm can reflect changes of the system.2) A least squares support vector regression algorithm, which can improve the prediction accuracy of peak samples, is proposed. The influence of samples distribution to the fitting error of least squares support vector regression is analyzed firstly. And then according to the weighted least square idea, the fitting errors is amended using the distribution density of the learning samples and the amplitude factor, which help to improve the fitting accuracy of peak samples in least square support vector regression algorithm. The proposed algorithm is tested and applied to prediction of water quality. The results show that the prediction accuracy of the proposed algorithm to the peak samples have been improved significantly with the holistic accuracy maintained simultaneously, and the algorithm can eliminate the influence of distribution density. It is more suited for peak prediction applications.Its prediction error of peak samples decreased more than27%to the the LS-SVR algorithm.3) Least squares support vector regression algorithm for a large sample is studied, and a fast regression algorithm is proposed to deal with large sample learning problem. The learning sample is clustered by an unsupervised hard clustering method in Hilbert space,according to the Euclidean distance which used to be a similarity measure. And then the clustering centers are selected as the support vectors. Nystrom algorithm is used to approximate the kernel Gram matrix based on the support vector set, so as to obtain an approximate solution of the original problem.The results of function fitting test and its application to predict chloride content in saltwater show that the computational efficiency is improved by more than50times,with unsignificant decrease of learning error.4) A multiple kernel least squares support vector regression with grouped features is proposed, which help to improve the performance and the flexibility of Least squares support vector regression algorithm. All of the input variables with homologous features are mapped into Hilbert space using a same basic mapping functions, and then modeling with regression method.The problem of the fitting optimization objective is transformed into semi infinite linear programming problem,and soluted by an exchange method.The results of function fitting test and its appication to predict CODMn demonstrate that its prediction errors declines more than17%to standard least squares support vector regression algorithm.