Journal of Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회논문집)

Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회)
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Development of a Stability Formula for Tetrapod by Using M5' Model Tree

M5' Model Tree를 이용한 Tetrapod 안정식 개발

  • Kim, Seung-Woo (Coastal and Hydraulics Laboratory, US Army Engineer Research and Development Center (US Army ERDC)) ;
  • Suh, Kyung-Duck (Department of Civil and Environmental Engineering & Engineering Research Institute, Seoul National University)
  • Received : 2013.02.16
  • Accepted : 2013.06.10
  • Published : 2013.06.29
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Abstract

Tetrapod, one of the famous armor blocks for rubble mound breakwaters, has been widely used in the world. In order to evaluate the required weight of Tetrapod, many researchers have proposed various stability formulas. Since the stability formulas were proposed by curve-fitting the experimental data, some uncertainties are included in the formulas. The main uncertainties are associated with experimental data, derivation of the formula, and variability of the design variables. In this study, a new stability formula is developed by using M5' model tree, which reduces the uncertainty in the derivation of the formula. The index of agreement is used to evaluate the performance of the developed formula. The index of agreement for the new formula is higher by about 0.1 than the previous formula. The performance of the previous formula was not good when the predicted stability number is greater than about 3.0. However. the new formula is accurate regardless of the magnitude of stability number. As a result, the new formula performs better than the previous formula, while expressed in the form of a tree but still in an explicit form.

Tetrapod는 국내외에서 널리 사용되는 경사식 방파제의 대표적인 피복재이다. Tetrapod의 소요중량을 산정하기 위해 많은 연구자들이 다양한 안정식을 제안하였다. 기존 안정식은 수리실험자료를 곡선맞춤하여 산정하기 때문에 많은 불확실성을 포함하고 있다. 대표적인 불확실성은 실험자료의 불확실성, 안정식 산정방법의 불확실성, 그리고 확률변수의 불확실성이다. 본 연구에서는 안정식 산정 방법의 불확실성을 낮추기 위해 M5' model tree를 사용하여 Tetrapod의 안정식을 개발하였다. 개발된 안정식의 예측능력을 평가하기 위해 일치지수를 사용하였으며, 새 안정식은 여러 가지 모델에서 기존 안정식보다 약 0.1 정도 큰 일치지수를 보였다. 또한 기존 안정식은 안정수 3.0 이상에서 예측능력이 현격히 감소하는데 반해 새 안정식은 안정수의 크기에 관계없이 일정한 예측능력을 보였다. 결과적으로 새로 개발된 안정식은 예측능력이 우수할 뿐 아니라 기존 안정식과 유사하게 명시적인 공식으로 표현된다.

Keywords

References

  1. 김승우, 서경덕 (2011). 인공신경망과 M5' model tree를 이용한 Tetrapod 피복블록 의 안정수 예측. 한국해안.해양공학회논문집, 23(1), 109-117.
  2. 김승우, 서경덕, 이동영, 전기천 (2012). 극치파고분포의 형상모수에 따른 Tetrapod 피복블록의 부분안전계수 산정. 대한토목학회논문집, 32(1B), 59-69.
  3. 해양연구원 (2001). 경사식 방파제의 최적설계 기술개발 (I)
  4. Bonakdar L. and Etemad-Shahidi, A. (2011). Predicting wave runup on rubble mound structures using M5 model tree. Ocean Eng., 38, 111-118. https://doi.org/10.1016/j.oceaneng.2010.09.015
  5. Breiman, L., Friedman, J.H., Olshen, R.A., and Stone, C.J. (1984). Classification and regression trees, Wadsworth, Belmont, CA.
  6. De Jong, R.J. (1996). Wave transmission at low-crested structures. Stability of tetrapods at front, crest and rear of a low-crested breakwater. MSc-thesis, Delft University of Technology.
  7. Etemad-Shahidi, A. and Bonakdar, L. (2009). Design of rubble-mound breakwaters using M5' machine learning method. Applied Ocean Research, 31, 197-201. https://doi.org/10.1016/j.apor.2009.08.003
  8. Etemad-Shahidi, A. and Mahjoobi, J. (2009). Comparison between M5' model tree and neural networks for prediction of significant wave height in Lake Superior. Ocean Eng., 36, 1175-1181. https://doi.org/10.1016/j.oceaneng.2009.08.008
  9. Günaydin K. (2008). The estimation of monthly mean significant wave heights by using artificial neural network and regression methods. Ocean Eng., 35, 1406-1415. https://doi.org/10.1016/j.oceaneng.2008.07.008
  10. Hanzawa, M., Sato, H., Takahashi, S., Shimosako, K., Takayama, T., and Tanimoto, K. (1996). New stability formula for wave-dissipating concrete blocks covering horizontally composite breakwaters. Proc. 25th Int. Conf. Coast. Eng., 1665-1678.
  11. Hudson, R.Y. (1959). Laboratory investigation of rubble-mound breakwaters. J. Waterw. Harbors Div., 85(WW3), 93-121.
  12. Jekabsons G. (2010). M5' regression tree and model tree toolbox for Matlab, 2010, available at http://www.cs.rtu.lv/jekabsons, M5PrimeLab.
  13. Kim, D.H. and Park, W.S. (2005). Neural network for design and reliability analysis of rubble mound breakwaters. Ocean Eng., 32. 1332-1349.
  14. Quinlan J.R. (1992). Learning with continuous classes. In: Adams, Sterling, editors. Proceedings of AI'92. World Scientific, 343-348
  15. Singh, S., Bhatti, T.S., and Kothari, D.P. (2007). Wind power estimation using artificial neural network. J. Energy Eng., 133(1), 46-52. https://doi.org/10.1061/(ASCE)0733-9402(2007)133:1(46)
  16. Suh, K.-D. and Kang, J.S. (2012a). Stability formula for Tetrapods. J. Waterw., Port, Coast. and Ocean Eng., 138(3), 261-266. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000124
  17. Suh, K.-D. and Kang, J.S. (2012b). Stability formula for Tetrapod incorporating slope effect. Proc. 33rd Int. Conf. Coast. Eng., ASCE, Santander, Spain.
  18. U.S. Army Corps of Engineers (USACE) (1987). Shore Protection Manual, U.S. Army Corps of Engineers.
  19. Van der Meer, J.W. (1988). Stability of Cubes, Tetrapods and Accropods. Proc. of the Breakwaters '88 Conference; Design of Breakwaters, Institution of Civil Engineering, Thomas Telford, London, UK, 71-80.
  20. Van der Meer, J.W. (2000). Design of concrete armour layers. Proc. Coastal Structures '99, Balkema, Rotterdam, Netherlands, 213-221.
  21. Van Gent, M.R.A., Van den Boogaard, H.F.P., Pozueta, B., and Medina, J.R. (2007). Neural network modeling of wave overtopping at coastal structures. Coastal Eng., 54, 586-593. https://doi.org/10.1016/j.coastaleng.2006.12.001
  22. Wang, Y. and Witten, I.H. (1997). Induction of model trees for predicting continuous classes. In: Proceeding of the Poster Papers of the European Conference on Machine Learning, University of Economics, Faculty of Informatics and Statistics, Prague, 128-137.
  23. Willmott, C.J. (1981). On the validation of models. Phys. Geogr., 2(2), 184-194.
  24. Yoon, H.-D., Cox, D.T., and Kim, M. (2013). Prediction of timedependent sediment suspension in the surf zone using artificial neural network. Coastal Eng., 71, 78-86. https://doi.org/10.1016/j.coastaleng.2012.08.005