Sensitivity Analysis On Rational Spline Weight Function Neural Network With Cubic Numerator And Linear Denominator And Its Application

Sensitivity is an important tool, which can measure the performance of neural networks. And it can be used to measure the ability of the trained neural network, when disturbed by some external factors. Therefore, sensitivity analysis of neural networks has an important significance.The spline weight function neural network is a new kind of neural network, which overcomes the shorting of traditional neural network that weight is difficult to reflect training sample information. Based on the theory of spline weight function neural network and cubic numerator and linear denominator of rational spline function, topological structure and learning algorithm of this kind of rational spline weight function neural network are studied. According to the knowledge of cubic spline, cubic spline and Peano kernel thoery, calculation formula of error and sensitivity are derived.Through the theoretical analysis, we conclude that this kind of neural network has good learning, generalization ability and the calculation formula of error and sensitivity.The simulation experiment demonstrates the advantage of the rational spline function neural network with cubic numerator and linear denominator in learning, generalization and anti-jamming capability. Variation of sensitivity is showed with the increase of sample disturbance.Combined with practical application, air quality assessment model based on cubic numerator and linear denominator of rational spline function neural network is established. Use MATLAB tools to simulate this application. Through the simulation experiments, we know this algorithm can accurately evaluate air quality. Compared with the traditional BP neural network, it has the advantages of simple structure, fast speed and high precision.