Applications Of Particle Swarm Optimization And Support Vector Machine In Simulating And Predicting Stream Water Quality

Simulation and prediction of water quality is the basis of successfully accomplishing the tasks about water environment, such as river basin planning and water pollution comprehensive cure. The mechanism water quality model takes into account the factors that have impact on change of water quality, so the concept of model is clear. But parameter estimation of these models is usually very hard, which makes them have some limits to application for many river systems. However, water quality models without considering mechanism often acquire satisfactory simulating and predicting results because they built models aiming at specific water quality system by using statistical method or other mathematical methods.Particle Swarm Optimization (PSO), which has obvious ties with both evolutionary computation and swarm intelligence, was developed by Kennedy and Eberhart in 1995. The underlying motivation for the development of PSO was social behavior of animals such as bird flocking and fish schooling. Due to its simplicity in coding and consistency in performance, PSO technique has been used to solve various optimization problems. PSO is similar to Genetic Algorithm (GA) in that the system is initialized with a population of random solutions. Each individual (named agent or particle), flies in the problem space with a velocity which is dynamically adjusted according to the flying experience of its own and its colleagues. Modification of the agent position is realized by the position and velocity information. PSO is simple in application and quick in convergence, but also has the shortcomings of low degree of convergence and frequent trapping in local optima. So an Adaptive Particle Swarm Optimization (APSO) based on the variance of swarm population's fitness and the changing error of optimal fitness value is proposed, and tested on several benchmark functions. The test results indicate that the new algorithm has better advantage of convergence property than standard PSO, and can avoid the premature convergence problem effectively. Parameter estimation is an important issue when the existing mechanism water quality model is applied in water quality simulation and prediction. In most cases, parameter estimation is transformed into optimization problem which minimizes the total error summation between measured data and simulated data of water quality index. Such optimization problem usually has many local optima, and has the property of high-order nonlinearity, so it is difficult for traditional optimization methods to solve. In this paper, the APSO method is applied in solving parameter estimation problem. The test results of four examples indicate that the method proposed has high accuracy, and is easy to program and calculate.Support Vector Machine (SVM) is a new kind of machine learning algorithm proposed recently which is based on VC dimension theory and structural risk minimization of statistical learning theory. SVM can obtain the optimum result from the gained information which is not the optimum result only when the samples are infinite. SVM has much stronger theory foundation and better generalization than neural network which is based on empirical risk minimization. Least Squares Support Vector Machine (LS-SVM) is an improved algorithm to standard support vector machines. It simplifies the model parameters and speeds the computation by solving a set of linear equations instead of quadratic programming for standard SVM. As for innovatory methods without considering mechanism, the paper adopts SVM, which establishes the input-output relationship between upstream water quality impact factor and downstream section dissolved oxygen. The simulating results of training data fit well, and predicting results are acceptable. The grid search method based on k fold cross validation error for selecting the model parameters of SVM is also presented.