Nonlinear System Identification Using Levenberg-Marquardt Combined With Differential Evolution And Biogeography-Based Optimization Trained BP Neural Network

System identification is always the difficulty and the focus control theory study. There are lots of the shortcomings of traditional identification methods for nonlinear system identification,but the neural network is parallel processing, self-learning, self-adapting, and can approximate any nonlinear function with any precision. Therefore it is more applicable to the identification of nonlinear systems.BP neural network, as an artificial intelligence technique, develops rapidly in the recent fifty years, and attains compelling production. Recently many researchers have applied it to nonlinear system identification, and utilize the function approach capacity of BP neural network for nonlinear system identification, attained excellent effect. But during the using of BP neural network in nonlinear system identification, we find there are many localizations, such as the convergence to local least value, unable convergence to the given error; the studying period is long,the time of iteration is more and the speed of convergence is slow; the choice of the first connecting value is blind and without overall situation and. Those shortages will depress the effect of system identification, so we must adopt some corresponding methods to improve the simulating effect and forecasting precision.Point to the above problems of BP network, in this paper, BP network based on differential evolution algorithm and Levenberg-Marquardt algorithm is introduced. Differential evolution algorithm is a population-based global optimization algorithm, and its advantages are simple structure, robustness, and easy of use. Levenberg-Marquardt algorithm is a rapid algorithm using the standard numeric optimizing technique. And this new algorithm provides the compromise of the fast speed of Newton's method and the convergence of gradient descent algorithm. It can solve the convergence to local least value and accelerate the speed of convergence. Then BP neural network based on Differential Evolution algorithm and Levenberg-Marquardt algorithm is used in nonlinear system identification, the differential evolution algorithm for training the BP neural network to calculate the initial weights of the network, and Levenberg-Marquardt algorithm is used to train the BP network to convergence. After comparing with the literature [47], simulation results show that the new algorithm has higher speed of convergence and identification accuracy.However, in order to further improve the identification accuracy and the convergence rate, a new hybrid evolution algorithm is introduced, namely DEBBO, which combines differential evolution algorithm with biogeography optimization algorithm for the differential evolution algorithm lack of local search ability. DEBBO combines the exploration of DE with the exploitation of BBO effectively, and hence it can generate the promising candidate solutions. Using DEBBO to calculate the initial weights of BP network can speed up the rate of convergence and obtain better robustness. Therefore, BP neural network based on DEBBO and LM algorithm used in nonlinear system identification is proposed, and simulation results show that the proposed algorithm has better recognition results and faster convergence.Finally, the DEBBO-LM is used in short time traffic flow prediction. By comparing with the literature [60], the proposed algorithm has good prediction accuracy and popularization value.