Implementation of Stochastic Optimization Method-Assisted Radial Basis Neural Network for Transport Phenomenon in Non-Newtonian Third-Grade Fluids: Assessment of Five Optimization Tools

Abstract

Implementation of radial basis neural network is demonstrated by considering a test case of non-Newtonian third-grade fluid flow and heat transfer through two parallel plates. Five commonly used stochastic optimization methods: genetic algorithm, global search algorithm, multiple starting point algorithm, simulated annealing algorithm, and pattern search algorithm, are employed to optimize the RBNN. Flow of a non-Newtonian third-grade fluid through two parallel plates, subjected to uniform heat flux, is considered. At first, governing equations, describing the flow and heat transfer problem, are solved by the least-square method, a semi-analytical tool. The velocity and the temperature profiles are obtained for different values of third-grade fluid parameter ‘A’, which are then used for training different stochastic optimization method-assisted RBNNs (SOMARBNNs). For proper functioning of RBNN, a suitable value for an important attribute called ‘spread’ is required. Deciding the value for ‘spread’ requires experience and knowledge of neural networks. The present approach makes the selection of proper value of ‘spread’ very easy, and beginners can use the RBNN for problem-solving. With the help of different stochastic optimization methods, the value of spread for the RBNN is determined. Once all SOMARBNNs are trained, the temperature profile and the corresponding third-grade fluid parameter ‘A’ are obtained as output, corresponding to any new velocity profile fed as input. Further, the data for training are perturbed by different levels of noise, and different SOMARBNNs are successfully employed to get the output. The performance evaluation of different SOMARBNNs is carried out in terms of CPU time and error in result. The results indicate that PSAARBNN is better than other SOMARBNNs, as it is able to generate results with high accuracy for both low noise data and high noise data. Moreover, the CPU time requirement by PSAARBNN is lowest.