Industrial Applications of Genetic Algorithms:Space Shuttle Main Engine Condition Monitoring Using Genetic Algorithms and Radial Basis Function Neural Network

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GA/RBFNN TESTING AND RESULTS

The parameters typically predicted from spectral scans are the plume temperature, the number densities for the metallic species present, and the broadening parameter. Number density and broadening parameter can be used to obtain the metallic species concentration. To test the viability of the GA hybrid approach to the plume emission problem, spectral data was generated for the element Chromium. The data represented example input (spectra) to output (temperature, number density, and broadening parameter) RBFNN variables. Three scenarios were investigated: 1) Training the RBFNN using the random RBF center selection method; 2) Training with the Bayesian Information Criterion (BIC) selection method; and 3) Using the GA RBF center, basis function, and width evolution method. Having trained three separate RBFNNs using the aforementioned methods, a separate data set was created for the purpose of testing. This data was not seen by the RBFNNs during training and should provide an excellent measure of the RBFNN’s generalization ability. Table 10.1 below shows the resulting performance of the three methods. The mean percentage error on the test data is given as well as the standard deviation error for the RBFNN predictions.

Note, the same test data was used in all three cases. Preprocessing and scaling of this data could improve or degrade each of the networks performances. However, by using sound preprocessing schemes and maintaining the same data set it is hoped that this bias can be removed, thereby allowing comparisons between the methods to be stated. Table 10.1 reveals that the GA hybrid approach is much better than the random scheme and at least as good as the BIC scheme. The BIC scheme is an excellent selection method for nonlinear problems so, considering the results, it is apparent that the GA hybrid is just as effective at finding good solutions.

A problem was noted with the particular fitness function detailed earlier. The performance of the RBFNN after GA center evolution was extremely sensitive to the weighting factors. Moreover, during the GA center, evolution the RBFNN performance error oscillated between suitable and unsuitable values. This was most likely caused by the method in which fitness sharing was implemented. To this end, more work will need to be done.

Finally, the goal was to evolve RBF basis functions that competed, yet cooperated, to approximate the mapping between the spectrum and the plume physical parameters. Thus, it was hoped that the average population fitness would increase and eventually match the fitness of the best performer. Figure 10.5 below shows the fitness performances versus the generation number for one particular GA run. Note, on the average, the fitness continues to increase for both plots, but the average population fitness doesn’t approach the best fitness like it should. Once again, this is most likely caused by the niching function and its establishment. Notwithstanding this reservation, the GA thus established was able to match the performance of the BIC scheme. This certainly reveals promise in the method and further research would most likely prove fruitful.

Figure 10.5 Fitness performance versus generation number.

CONCLUSIONS

A hybrid RBFNN and GA was developed that allowed for the evolution of the internal RBF parameters in such a fashion that contributed to the overall reduction of RBFNN mapping error. Considering the physical nature of the RBFNN, a fitness function was established that implemented both competition and cooperation between population members. The hybrid GA/RBFNN was tested on actual SSME plume spectral data. The results showed that the hybrid scheme is much better than the random scheme and just as good as the current BIC scheme in use. Improvements can be made to the niching implementation that may attenuate the undesirable sensitivity and oscillations seen in the evolution. Finally, it should be noted that this functional mapping is highly nonlinear and the performance of the GA is very encouraging.

REFERENCES

  1 Benzing, D. A., Whitaker, K. W., & Krishnakumar, K. (1997). Experimental verification of neural network-based SSME anomaly detection. Proceedings of the 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA-97-2903, Seattle, WA, July 6-9.
  2 Whitehead, B. A. & Choate, T. D. (1996). Cooperative-competitive genetic evolution of the radial basis function centers and widths for time series prediction. IEEE Transactions On Neural Networks, 7(4).
  3 Mackey, M. C. & Glass, L. (1977). Oscillation and chaos in physiological control systems. Science, 197, 287-289.
  4 Moody, J. & Darken, C. J. (1989). Fast learning in networks of locally-tuned processing units. Neural Computation, 1, 281-294.
  5 Orr, M. J. L. (1996). Regularisation in the selection of radial basis function centres, Centre for Cognitive Science, University of Edinburgh, 2, Buccleuch Place, Edinburgh EH8 9LW, UK.
  6 Orr, M. J. L. (1996). MATLAB routines for subset selection and ridge regression in linear neural networks. Centre for Cognitive Science, Edinburgh University, Scotland, UK, April.
  7 Musavi, M. T., Ahmed, W., Chan, K. H., Faris, K. B., & Hummels, D. M. (1992). On the training of radial basis function classifiers. Neural Networks, 5, 595-603.
  8 Fahlman, A. E. & Lebiere, C. (1991). The cascade-correlation learning architechure. Advances in neural processing systems 2, (Eds.)R.P. Lippmann, J.E. Moody, & D.S. Touretzky, San Francisco: Morgan Kauffmann Publishers, 524-532.
  9 Powers, W. T., Cooper, A. E., & Wallace, T. L. (1992). OPAD status report: Investigation of SSME component erosion. SAE Paper 92-1030.
  10 Cikanek, H. A. III (1987). Failure characteristics of space shuttle main engine failures. Proceedings of the Joint \Propulsion Conference, June.
  11 Powers, W. T., Cooper, A. E., & Wallace, T. L. (1995). Validation of UV-VIS atomic spectral model for quantitative prediction of number density, temperature, and broadening parameter. 1995 JANNAF Propulsion Systems Hazards Subcommittee, Marshall Space Flight Center, AL, October.
  12 Wallace, T. L., Powers, W. T., & Cooper, A.E. (1993). Simulation of UV atomic radiation for application in exhaust plume spectrometry. Proceedings of the 29th Joint Propulsion Conference and Exhibit, AIAA Paper 93-2512, Monterey, CA.

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