Research and Application on Improved BP Neural Network Algorithm Rong Xie School of Automation Northwestern Polytechnical University Xi an China xierong2005 Xinmin Wang School of Automation Northwestern Polytechnical University Xi an China wxmin Yan Li School of Automation Northwestern Polytechnical University Xi an China liyan Kairui Zhao School of Automation Northwestern Polytechnical University Xi an China zhaokairui Abstract As the iterations are much and the adjustment speed is slow the improvements are made to the standard BP neural network algorithm The momentum term of the weight adjustment rule is improved make the weight adjustment speed more quicker and the weight adjustment process more smoother The simulation of a concrete example shows that the iterations of the improved BP neural network algorithm can be calculated and compared Finally choosing a certain type of airplane as the controlled object the improved BP neural network algorithm is used to design the control law for control command tracking the simulation results show that the improved BP neural network algorithm can realize quicker convergence rate and better tracking accuracy Keywords improved BP neural networ weight adjustment learning rate convergence rate momentum term I INTRODUCTION Artificial neural network ANN is developed under the basis of researching on complex biological neural networks The human brain is constituted by about 1011 highly interconnected units these units called neurons and each neuron has about 104 connections 1 Imitating the biological neurons neurons can be expressed mathematically the concept of artificial neural network is introduced and the types can be defined by the different interconnection of neurons It is an important area of the intelligent control by using the artificial neural network According to the different types of the neuron connections the neural networks can be divided into several types This paper studies feed forward neural network as the feed forward neural network using the error back propagation function in the weight training process it is also known as back propagation neural network or BP network for short 2 3 BP neural network is a core part of the feed forward neural network which can realize a special non linear transformation transform the input space to the output space Although the BP neural network has mature theory and wide application it still has many problems such as the convergence rate is slow the iterations are much and the real time performance is not so good It is necessary to improve the standard BP neural network algorithm to solve there problems and achieve optimal performance II STUCTURE AND ALGORITHM OF THE STANDARD BP NEURAL NETWORK A Structure of the BP neural network The standard structure of a typical three layer feed forward network is shown as follows 1 n 2 n 1 y 1 x 2 x 1 n x 1 o 2 o 2n o m 2 y 3 y m y 11 w 12 w 1m w 2m w 1n m w 11 v 12 v 2 1n v 2 3n v 2 mn v Figure 1 The standard structure of a typical three layer feed forward network B Algorithm of the BP neural network The flow chart of the standard BP neural network algorithm is as follows 4 1 iiii og netgg net 2 1 2 kik EEe 0 1 2 r p k r 1kkk 1jjj vvv max EE kijk wv Figure 2 Flow chart of the standard BP neural network algorithm 1462978 1 4244 5046 6 10 26 00 c 2010 IEEE III IMPROVEMENT OF THE STANDARD BP NEURAL NETWORK ALGORITHM The convergence rate of the standard BP algorithm is slow and the iterations of the standard BP algorithm are much they all have negative influences on the rapidity of the control system In this paper improvement has been made to the learning rate of the standard BP algorithm to accelerate the training speed of the neural network For the standard BP algorithm the formula to calculate the weight adjustment is as follows W W n E n 1 In formula 1 represents the learning rate W n represents the weight adjustment value of the nthiterations E n represents the error of the nthiterations W n represents the connection weight of the nthiterations From formula 1 the learning rate influences the weight adjustment value W n and then influences the convergence rate of the network If the learning rate is too small the convergence rate will become very slow If the learning rate is too big the excessive weight adjustment will cause the convergence process oscillates around the minimum point In order to solve the problem the momentum term is added behind the formula 1 WW1 W nn E n 2 In formula 2 W1n represents the momentum term W n 1 represents the weight adjustment value which generated by the 1 nth iterations represents the smoothing coefficient its value is from 0 to 1 Formula 2 is a improvement of formula 1 which can improve the convergence rate of the neural network in a certain degree but the effect is not obvious In order to accelerate the convergence speed of the neural networks the weight adjustment formula needs to be further improved sign function BP algorithm multiply the mome