Sensitivity Analysis On The Second Kind Of Rational Spline Weight Function Neural Network With Cubic Numerator And Quadratic Denominator And Its Application

When the trained neural network is interfered by noise, its weight will be changed. The sensitivity of neural network can use to judge and measure the performance of network. and it also can reflect the resistance to interference. Therefore, the analysis and study of the sensitivity of neural network has important role and significance. This article is based on the theory of spline weight function neural network. Main contributions of this thesis are summarized as follows:Firstly, through the relevant knowledge of numerical analysis and numerical approximation, combine Peano kernel theorem derive the error calculation formula of the second kind of rational spline weight function neural network with cubic numerator and quadratic denominator(shorted as 3/2). The theoretical analysis and the simulations show that the neural network of rational spline weight function has the fast training speed, the small error and the stronger generalization ability, etc.Secondly, combining with the definition of statistic sensitivity, we derive the calculation formula of the sensitivity of the second kind SWF neural network. The theoretical analysis and the simulations show that if not very big noise is in the input layer, the output error is relatively small and relative stabilization. It reflects that the network has strong ability of anti-interference.Finally, base on the theory of the second of 3/2 spline weight function neural network, the PM2.5 concentration prediction model has been built. The main computing workload of this model is to solve the linear algebra equations. At the same time, the model solved the problems that The higher the PM2.5 concentration fluctuate is, the larger the forecasting errors will be. Through the simulation experiments, we know this algorithm has little prediction error, simple structure, compare with the BP neural network and SVM network.