Field dependent-shear stress prediction of magnetorheological fluid using an optimum extreme learning machine model

Abstract

Extreme learning machine (ELM) application to model the shear stress of magnetorheological (MR) fluids has superiority over the existing methods, such as Herschel-Bulkley. Although the shear stress has been successfully predicted, the hidden node numbers are too high reaching up to 10,000 that will hinder the application of the models. Furthermore, the existing works have tried to determine the hidden node number only by trial and error method. Therefore, this paper aims to reduce the hidden node number by employing the particle swarm optimization (PSO) considering the accuracy and the hidden node numbers. The ELM based-shear stress model was firstly defined by treating the magnetic field and shear rate as the inputs and shear stress as output. The objective function optimization method was then formulated to minimize the normalized error and the hidden node numbers. Finally, the proposed methods were tested at various ELM activation functions and samples. The results have shown that the platform has successfully reduced the hidden node numbers from 10,000 to 571 while maintaining the error of less than 1%. In summary, the proposed objective function for PSO optimization has successfully built the optimum shear stress model automatically.