The objective of this study is to show how a multi-layer perceptron (MLP) neural network can be used to model a CMM measuring process. To date, most MLP-based process models have been established for process mean only. An innovative approach is proposed to model simultaneously the mean and the variation of a CMM process using one integrated MLP architecture. Therefore, the MLP-based model obtained captures not only the process mean but also the process variation information. Selected issues related to neural network training are also discussed. Specifically, the guideline that was proposed by Mirchandani and Cao (1989) for selecting a number of hidden neurons is tested to determine the effects of the number of hidden neurons. The performances of two different learning algorithms - back-propagation with momentum factor (BPM) and the Fletcher-Reeves (FR) algorithm - are studied in terms of CPU time, training error, and generalization error.
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References
Davis, W. (1992) Process variation analysis employing artificial neural network. IJCNN, II, 260–265.
Dennis, J. E. Jr and Schnabel, R. B. (1983) Numerical Methods for Unconstrained Optimization and Non-linear Equations, Prentice-Hall, Englewood Cliffs, NJ.
Hornik, K., Stinchcombe, M. and White, H. (1989)Multilayer feedforward networks are universal approximators. Neural Networks, 2, 359–366.
Huang, T., Zhang, C., Lee, S. and Wang, H.-P. (1993) Implementation and comparison of three neural network learning algorithms. Kybernetes, 22(1), 22–38.
Liao, T. W. and Chen, L. J. (1994)A neural network approach for grinding processes: modeling and optimization. International Journal of Machine Tools and Manufacturing, 34(7), 917–937.
Lippmann, R. P. (1987) An introduction to computing with neural nets. IEEE ASSP Magazine, April, pp.4–22.
Luo, Y.-L., Kim, T.-S., Liao, T. W. and Tang, K. (in press) An investigation into the influences of operating parameters on CMM performances, Engineering Design and Automation.
McClelland, J. L. andRumelhart, D. E. (1988) Explorations in Parallel Distributed Processing, MIT Press, Cambridge, MA.
Mirchandani, F. and Cao, W. (1989) On hidden nodes for neural nets. IEEE Transactions on Circuits and Systems, 36(5), 661–664.
Nix, D. A. and Weigend, A. S. (1994) Estimating the mean and variance of the target probability distribution, in Proceedings of 1994 IEEE ICNN, Orlando, June.
Phansalkar, V V and Sastry, P. S. (1994)Analysis of the backpropagation algorithm with momentum. IEEE Transactions on Neural Networks, 5(3), 505–506.
Porta, C. and Waeldele, F. (1986) Testing of Three Coordinate Measuring Machine Evaluation Algorithms, Commission of the European Communities, Physikalish-Technische Bundesanstalt.
Rangwala, S. S. and Dornfeld, D. A. (1989) Learning and optimization of machining operations using computing abilities of neural networks. IEEE Transactions on Systems, Man, and Cybernetics, 19(2), 299–314.
Reklaitis, G. V, Ravindran, A. and Ragsdell, K. M. (1983) Engineering Optimization: Methods and Applications, Wiley, New York.
Rumelhart, D. E., Hilton, G. E. and Williams, R. J. (1986) Learning internal representation by error propagation, in Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1: Foundations, Rumelhart, D. E. and McClelland, J. L.(eds), Chapter 8, MIT Press, Cambridge, MA.
Schaffer, G. H. (1982) Taking the measure of CMMs. Special Report 749, American Machinist, 145–160.
Smith, A. E. (1993) Predicting product quality with backpropagation: a thermoplastic injection molding case study. International Journal of Advanced Manufacturing Technology, 8, 252–257.
Tannock, J. D. T., Lee, H., Cox, D. R., and Sims Williams, J. H. (1993) Intelligent inspection planning and computer aided inspection. Proceedings of the Institution of Mechanical Engineeers, 207, 99–104.
Tao, L. G. and Davies, B. J. (1992)Knowledge-based 21/2D prismatic component inspection planning. International Journal of Advanced Manufacturing Technology, 7, 339–347.
Zelen, M. and Severo, N. C. (1964) Probability Functions. No. 26in Handbook of Mathematical Functions, Abramowitz, M. and Stegun, I. A. (eds), National Bureau of Standards, Applied Mathematics Series, 55, US Government Printing Office, Washington DC.
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Warren Liao, T. MLP neural network models of CMM measuring processes. J Intell Manuf 7, 413–425 (1996). https://doi.org/10.1007/BF00122832
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DOI: https://doi.org/10.1007/BF00122832