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Improved Harmony Search Methods to Replace Variational Principle in Geotechnical Problems

Published online by Cambridge University Press:  31 March 2011

Y. M. Cheng ,
L. Li  and
S. S. Fang
Y. M. Cheng*
Affiliation:
Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Hong Kong
L. Li
Affiliation:
School of Civil Engineering, Qingdao Technological University, China
S. S. Fang
Affiliation:
Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Hong Kong
*
* Associate Professor, corresponding author
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Abstract

Variational principle is an important principle in engineering discipline. This principle is suitable for simple problems where an analytical expression can be determined, but there are many practical problems where the classical variational principle is practically impossible to be applied. In this paper, the authors will try to demonstrate that the variational principle can be replaced by the use of modern artificial intelligence based optimization method (harmony search method) which can be applied to much more complicated problems. Two different improved harmony search algorithms are proposed in this paper. The new algorithms differ from the original algorithm in that: (1) The harmonies are rearranged into several pairs and the better pairs are used to develop several new harmonies; (2) Different probabilities are assigned to different harmonies. The robustness of the proposed methods is demonstrated by using three difficult examples, and the sensitivities of the related optimization parameters are investigated through statistical orthogonal analysis.

Keywords

Variational principleSlope stability analysisHarmony search algorithmMinimum factor of safetyRandom number
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 1 , March 2011 , pp. 107 - 119
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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References

REFERENCES

1.Lanczos, C., The Variational Principles of Mechanics, Dover Publications (1986).Google Scholar
2.Maupertuis, P. L. N., “Accord De Différentes Lois De La Nature Qui Avaient Jusqu'ici Paru Incompatibles,” Mém. As. Sc. Paris p. 417 (1744).Google Scholar
3.Euler, L., Methodus Inveniendi Lineas Curvas Maximi Minive Proprietate Gaudentes, Bousquet, Lausanne & Geneva (1744).Google Scholar
4.Lagrange, J. L., Personal communication with Euler (1760).Google Scholar
5.Hamilton, W. R., “On a General Method in Dynamics,” Philosophical Transaction of the Royal Society, I, pp. 247–308 (1834).Google Scholar
6.Hamilton, W. R., “On a General Method in Dynamics,” Philosophical Transaction of the Royal Society, II, pp. 95–144 (1835).Google Scholar
7.Jacobi, C. G. J., Vorlesungen über Dynamik, gehalten an der Universität Königsberg im Wintersemester (1842).Google Scholar
8.Baker, R. and Garber, M., “Theoretical Analysis of the Stability of Slopes,” Geotechnique, 28, pp. 395–341 (1978).CrossRefGoogle Scholar
9.Baker, R., “Determination of the Critical Slip Surface in Slope Stability Computations,” International Journal of Numerical and Analytical Methods in Geomechanics, 4, pp. 333–359 (1980).CrossRefGoogle Scholar
10.Revilla, J. and Castillo, E., “The Calculus of Variations applied to Stability of Slopes,” Geotechnique, 27, pp. 1–11 (1977).CrossRefGoogle Scholar
11.De Josseline De Jong, G., “Application of Calculus of Variation to the Vertical Cut-Off in Cohesive Frictionless Soil,” Geotechnique, 30, pp. 1–16 (1980).CrossRefGoogle Scholar
12.De Josseline De Jong, G, “Variational Fallacy,” Geotechnique, 31, pp. 289–290 (1981).CrossRefGoogle Scholar
13.Castilo, E. and Luceno, A., “Evaluation of Variational Methods in Slope Analysis,” Proceedings of International Symposium on Landslides, New-Delhi, India, 1, pp. 255–258 (1980).Google Scholar
14.Castilo, E. and Luceno, A., “A Critical Analysis of Some Variational Methods in Slope Stability Analysis,” International Journal for Numerical and Analytical Methods in Geomechanics, 6, pp. 195–209(1982).CrossRefGoogle Scholar
15.Baker, R., “Sufficient Conditions for Existence of Physically Significant Solutions in Limiting Equilibrium Slope Stability Analysis,” International Journal of Solids and Structures, 40, pp. 3717–3735 (2003).CrossRefGoogle Scholar
16.Nguyen, V. U., “Determination of Critical Slope Failure Surfaces,” Journal of Geotechnical Engineering, ASCE. 111, pp. 238–250(1985).CrossRefGoogle Scholar
17.Celestino, T. B. and Duncan, J. M., “Simplified Search for Non-circular Slip Surface,” Proceeding 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, pp. 391–394 (1981).Google Scholar
18.Arai, K. and Tagyo, K., “Determination of Noncir-cular Slip Surfaces Giving the Minimum Factor of Safety in Slope Stability Analysis,” 21, pp. 43–51 (1985).Google Scholar
19.Yamagami, T. and Jiang, J. C., “A Search for the Critical Slip Surface in Three-Dimensional Slope Stability Analysis,” Soils and Foundations, 37, pp. 1–16 (1997).CrossRefGoogle Scholar
20.Chen, Z. and Shao, C., “Evaluation of Minimum Factor of Safety in Slope Stability Analysis,” Canadian Geotechnical Journal, 25, pp. 735–748 (1983).CrossRefGoogle Scholar
21.Greco, V. R., “Efficient Monte Carlo Technique for Locating Critical Slip Surface,” Journal of Geotechnical Engineering, ASCE. 122, pp. 517–525 (1996).CrossRefGoogle Scholar
22.Malkawi, A. I. H., Hassan, W. F. and Sarma, S. K., “Global Search Method for Locating General Slip Surface Using Monte Carlo Techniques,” Journal of Geotechnical and Geoenvironmental Engineering, 127, pp. 688–698 (2001).CrossRefGoogle Scholar
23.Zolfaghari, A. R., Heath, A. C. and McCombie, P. F., “Simple Genetic Algorithm Search for Critical Non-Circular Failure Surface in Slope Stability Analysis,” Computers and Geotechnics, 32, pp. 139–152 (2005).CrossRefGoogle Scholar
24.Bolton, , Hermanus, P. J., Heymann, G. and Groen-wold, A., “Global Search for Critical Failure Surface in Slope Stability Analysis,” Engineering Optimization, 35, pp. 51–65 (2003).CrossRefGoogle Scholar
25.Cheng, Y. M., “Locations of Critical Failure Surface and some Further Studies on Slope Stability Analysis,” Computers and Geotechnics, 30, pp. 255–267 (2003).CrossRefGoogle Scholar
26.Cheng, Y. M., Li, L., Chi, S. C. and Wei, W. B., “Particle Swarm Optimization Algorithm for Location of Critical Non-Circular Failure Surface in Two Dimensional Slope Stability Analysis,” Computers and Geotechnics, 34, pp. 92–103 (2007a).CrossRefGoogle Scholar
27.Cheng, Y. M., Li, L. and Chi, S. C., “Performance Studies on Six Heuristic Global Optimization Methods in the Location of Critical Failure Surface,” Computers and Geotechnics, 34, pp. 462–484 (2007b).CrossRefGoogle Scholar
28.Cheng, Y. M., “Global Optimization Analysis of Slope Stability by Simulated Annealing with Dynamic Bounds and Dirac Function,” Engineering Optimization, 39, pp. 17–32 (2007c).CrossRefGoogle Scholar
29.Wu, L. Y. and Tsai, Y. F., “Variational Stability Analysis of Cohesive Slope by Applying Boundary Integral Equation Method,” Journal of Mechanics, 21, pp. 187–195 (2005).CrossRefGoogle Scholar
30.Janbu, N., Bjerrum, L. and Kjaernsli, B., “Soil Mechanics Applied to some Engineering Problems,” Norwegian Geotechnical Institute, Publ., 16 (1956).Google Scholar
31.Chen, Z., “Random Trials used in Determining Global Minimum Factors of Safety of Slopes,” Canadian Geotechnical Journal, 29, pp. 225–233 (1992).CrossRefGoogle Scholar
32.Geem, Z. W., Kim, J. H. and Loganathan, G. V., “A New Heuristic Optimization Algorithm: Harmony Search,” Simulation, 76, pp. 60–68 (2001).CrossRefGoogle Scholar
33.Lee, K. S. and Geem, Z. W., “A New Meta-Heuristic Algorithm for Continuous Engineering Optimization: Harmony Search Theory and Practice,” Computer Methods in Applied Mechanics and Engineering, 194, pp. 3902–3933 (2005).CrossRefGoogle Scholar
34.Fisher, R. A., J. Royal Statistical Society, 126A, pp. 159–170 (1963).Google Scholar