;In this thesis, first propose an Improved Particle Swarm Optimization Neural Network model (IPSONN), by changing the acceleration coefficient to balance the personal and social experience, let particles at the beginning and the end of the searching stage have bigger value to enhance the searching ability, also use the nonlinear characteristics to improve the disadvantage of particle swarm algorithm which easily fall into the local optimum, then use improved PSO algorithm to train neural network. In addition, propose (PSOHBNN) model which is improved based on social experience, make particles have chance to jump out of the valley and find the global optimum. Then, we combine these two method, named Improved Particle Swarm Optimization Hybrid Backpropagation Neural Network model (IPSOHBNN), take these three algorithms as the learning algorithm for training feedforward neural network and do the function approximation for benchmark functions. In the results, the proposed PSO algorithms in training neural network have good prediction value for most of functions. Finally, these models applied to forecast the concentration of air quality pollution index (PM2.5), from the figure of test data can see the proposed PSO algorithms effectively train good network model and forecast the concentration of PM2.5 accurately.
