International Journal of Knowledge-based and Intelligent Engineering Systems 14 (2010) 201–215 201 DOI 10.3233/KES-2010-0202 IOS Press Forward and reverse modeling of electron beam welding process using radial basis function neural networks Vidyut Dey, Dilip Kumar Pratihar * and G.L. Datta Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721 302, India Abstract. An attempt has been made in the present study to model input-output relationships of an electron beam welding process in both forward as well as reverse directions using radial basis function neural networks. The performance of this network is dependent on its architecture significantly, which, in turn, depends on the number of hidden neurons, as the number of input nodes and that of output neurons can be decided beforehand for modeling a particular process. Input-output data can be clustered based on their similarity among them. The number of hidden neurons of this network is generally kept equal to that of clusters made by the data-set. Two popular fuzzy clustering algorithms, namely fuzzy C-means and entropy-based fuzzy clustering have been used for grouping the data into some clusters. As both these algorithms have inherent limitations, a modified clustering algorithm has been proposed by eliminating their demerits and combining their advantages. Radial basis function neural network developed using the proposed clustering algorithm is found to perform better than that designed based on the above two well-known clustering algorithms. Keywords: Electron beam welding, Radial Basis Function Neural Networks, Forward Mapping, Reverse Mapping, Clustering List of symbols a: Constant in similarity-distance relationship a 1 , b 1 : Coordinates of point P 1 on bead profile a 2 , b 2 : Coordinates of point P 2 on bead profile C: Number of clusters d ij : Euclidean distance between i th data point and j th cluster center D ′ k : Deviation in prediction at k th output neurons E i : Entropy of a data point X i f : Fitness value of a GA-solution g: Level of cluster fuzziness G max : Maximum number of generations ∗ Corresponding author. Tel.: +91 3222 282992; Fax: +91 3222 282278; E-mail: dkpra@mech.iitkgp.ernet.in. L: Number of input nodes kept equal to the dimension of the data m: Number of hidden neurons M a : Marangoni number n: Number of output neurons N: Number of training scenarios or data points N ′ : Population size O okp : Calculated output of the k th output for p th training case N ′ : Population size p: A particular training scenario p c : Probability of crossover p m : Probability of mutation P e : Peclet number P r : Prandtl number S ij : Similarity between data points i and j t: Iteration number T okp : Target output of k th output for p th training case ISSN 1327-2314/10/$27.50  2010 – IOS Press and the authors. All rights reserved