Response surface methodology: A neural network approach

Abstract Response surface methodology is used to optimize the parameters of a process when the function that describes it is unknown. The procedure involves fitting a function to the given data and then using optimization techniques to obtain the optimal parameters. This procedure is usually difficult due to the fact that obtaining the right model may not be possible or at best very time consuming. In this paper, a two-stage procedure for obtaining the best parameters for a process with an unknown model is developed. The procedure is based on implementing response surface methodology via neural networks. Two neural networks are trained: one for the unknown function and the other for derivatives of this function which are computed using the first neural network. These neural networks are then used iteratively to compute parameters for an equation which is ultimately used for optimizing the function. Results of some simulation studies are also presented.

[1]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[2]  Daniel Sbarbaro,et al.  Neural Networks for Nonlinear Internal Model Control , 1991 .

[3]  Jack P. C. Kleijnen,et al.  Simulation: A Statistical Perspective , 1992 .

[4]  Douglas C. Montgomery,et al.  Multiple response surface methods in computer simulation , 1977 .

[5]  P J Webros.  BACKPROPAGATION THROUGH TIME: WHAT IT DOES AND HOW TO DO IT , 1990 .

[6]  R. H. Myers,et al.  Variance dispersion properties of second-order response surface designs , 1992 .

[7]  Abdel-Moez E. Bayoumi,et al.  Prediction of flank wear and engagements from force measurements in end milling operations , 1993 .

[8]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[9]  André I. Khuri,et al.  Response surface methodology: 1966–1988 , 1989 .

[10]  H. Su,et al.  Yield optimization of analog MOS integrated circuits including transistor mismatch , 1993, 1993 IEEE International Symposium on Circuits and Systems.

[11]  H. B. Dharmappa,et al.  Optimization of granular bed filtration treating polydispersed suspension , 1992 .

[12]  Bahram Shafai,et al.  Interval Identification of Nonlinear Systems using Neural Networks , 1993, 1993 American Control Conference.

[13]  Douglas C. Montgomery,et al.  Applied Statistics and Probability for Engineers, Third edition , 1994 .

[14]  John W. Bandler,et al.  Yield-driven electromagnetic optimization via multilevel multidimensional models , 1993 .

[15]  Geoffrey E. Hinton,et al.  How neural networks learn from experience. , 1992, Scientific American.

[16]  G. Geoffrey Vining,et al.  Combining Taguchi and Response Surface Philosophies: A Dual Response Approach , 1990 .

[17]  Pandu R. Tadikamalla,et al.  Output maximization of a CIM system: simulation and statistical approach , 1993 .

[18]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[19]  Jeffrey D. Tew,et al.  Simulation metamodel estimation using a combined correlation-based variance reduction technique for first and higher-order metamodels , 1995 .

[20]  M. S. Hewidy,et al.  Electrochemical cutting using tubular cathodes: response surface approach , 1989 .

[21]  Imran A. Tasadduq,et al.  Neural-net controller for nonlinear plants: design approach through linearisation , 1994 .

[22]  Wanzhu Tu,et al.  Dual response surface optimization , 1995 .

[23]  Douglas C. Montgomery,et al.  A Nonlinear Programming Solution to the Dual Response Problem , 1993 .