A Novel Nonlinear Function Fitting Model Based on FOA and GRNN

Yongli Zhang,Sanggyun Na,Jianguang Niu

doi:10.1155/2019/2697317

Yongli Zhang, Sanggyun Na + Show 1 more

Open Access

https://doi.org/10.1155/2019/2697317

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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.

Highlights

In various fields of science and technology, the relationship between different variables is usually described by the function
In the most complex Griewank function, the prediction of fly optimization algorithm (FOA)-Generalized regression neural network (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 genetic algorithm (GA)-back propagation (BP), particle swarm optimization (PSO)-BP, and BP
FOA-GRNN model was further designed by Yongli Zhang et al in 2018, FOA-GRNN was only directly applied to the research issue of technological innovation, not compared with other algorithms or models to verify the its advantages in the algorithm performance such as nonlinear fitting ability and predictive stability [20]

Summary

A Novel Nonlinear Function Fitting Model Based on FOA and GRNN

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. 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 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.

Introduction

Generalized Regression Neural Network

Simulation Experiments

Conclusion and Discussion