A Novel Nonlinear Function Fitting Model Based on FOA and GRNN

Abstract

The nonlinear function fitting is an essential research issue. At present, the main function fitting methods are statistical methods and artificial neural network, but statistical methods have many inherent strict limits in application, and the back propagation (BP) neural network used widely has too many optimized parameters. For the gaps and lacks of existing researches, the FOA-GRNN was proposed and compared with the GRNN, GA-BP, PSO-BP, and BP through three nonlinear functions from simplicity to complexity for verifying the accuracy and robustness of the FOA-GRNN. The experiment results showed that the FOA-GRNN had the best fitting precision and fastest convergence speed; meanwhile the predictions were stable and reliable in the Mexican Hat function and Rastrgrin function. In the most complex Griewank function, the prediction of FOA-GRNN was becoming unstable and the model did not show better than GRNN model adopting equal step length searching method, but the performance of FOA-GRNN is superior to that of GA-BP, PSO-BP, and BP. The paper presents a new approach to optimize the parameter of GRNN and also provides a new nonlinear function fitting method, which has better fitting precision, faster calculation speed, more few adjusted parameters, and more powerful processing ability for small samples. The processing capacity of FOA for treating high complex nonlinear function needs to be further improved and developed in the future study.