Asymmetric Error Functions for Reducing the Underestimation of Local Scour around Bridge Piers: Application to Neural Networks Models
Publication: Journal of Hydraulic Engineering
Volume 141, Issue 7
Abstract
Many of the empirical formulas used for the prediction of the expected scour depth at piers are excessively conservative, providing substantial overestimations. On the other hand, the recently proposed neural networks methods generally issue accurate predictions but also high percentages of underpredictions, due to the use of a symmetric error function for their parameterization. A novel error function is proposed in this paper for optimizing neural networks, giving more weight to underestimation than to overestimation discrepancies, in order to obtain safer design predictions. The performances of the proposed model on independent field records are compared with those of a conventionally trained neural network and with those of a set of widely used formulas. The asymmetric error function (that might be applied to parameterize any other model or equation, as a proficient alternative to least-square errors or envelope curves) allows researchers to obtain predictions closer to the measurements than those issued by traditional formulas, substantially reducing the extent of unnecessary overdesign and at the same time the percentage of severe underestimations is comparable with those of the safest formulas.
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References
Ansari, S. A., and Qadar, A. (1994). Ultimate depth of scour around bridge piers, ASCE, New York, 51–55.
Azamathulla, H. Md., Ghani, A., Zakaria, N., and Guven, A. (2010). “Genetic programming to predict bridge pier scour.” J. Hydraul. Eng., 165–169.
Ballio, F., Radice, A., and Dey, S. (2010). “Temporal scales for live-bed scour at abutments.” J. Hydraul. Eng., 395–402.
Bateni, S. M., Jeng, D.-S., and Melville, B. W. (2007). “Bayesian neural networks for prediction of equilibrium and time-dependent scour depth around bridge piers.” Adv. Eng. Softw., 38(2), 102–111.
Brandimarte, L., Montanari, A., Briaud, J.-L., and D’Odorico, P. (2006). “Stochastic flow analysis for predicting river scour of cohesive soils.” J. Hydraul. Eng., 493–500.
Brandimarte, L., Paron, P., and Di Baldassarre, G. (2012). “Bridge pier scour: A review of processes, measurements and estimates.” Environ. Eng. Manage. J., 11(5), 975–989.
Breusers, H. N. C., Nicollet, G., and Shen, H. W. (1977). “Local scour around cylindrical piers.” J. Hydraul. Res., 15(3), 211–252.
Briaud, J.-L. (2006). “Bridge scour.” Geotechnical News, Vol. 24, BiTech Publishers.
Briaud, J.-L., Ting, F. C. K., Chen, H. C., Guadavalli, R., Perugu, S., and Wei, G. (1999). “SRICOS: Prediction of scour rate in cohesive soils at bridge piers.” J. Geotech. Geoenviron. Eng., 237–246.
Carpenter, D. D., and Miller, C. (2011). “A critical evaluation of bridge scour for Michigan specific conditions.”, Michigan DOT, Lansing, MI.
Chabert, J., and Engeldinger, P. (1956). Study of scour at bridge piers, Laboratoire d’Hydraulique, Chatou, France (in French).
Chase, K. J., and Holnbeck, S. R. (2004). “Evaluation of pier scour equations for coarse-bed streams.”, USGS, Reston, VA.
Chee, R. K. W. (1982). “Live-bed scour at bridge piers.”, School of Engineering, Univ. of Auckland, Auckland, New Zealand.
Chiew, Y. M. (1984). “Local scour at bridge piers.”, Dept. of Civil Engineering, Univ. of Auckland, Auckland, New Zealand.
Choi, S.-U., and Cheong, S. (2006). “Prediction of local scour around bridge piers using artificial neural networks.” J. Am. Water Resour. Assoc., 42(2), 487–494.
Christodoulakis, G., Lee, E., Stathopoulos, K., and Tessaromatis, N. (2008). “On the term structure of loss preference asymmetry in earnings forecasts.” Proc., European Financial Management Association 2008 Annual Meeting, 30.
Christoffersen, P. F., and Diebold, F. X. (1996). “Further results on forecasting and model selection under asymmetric loss.” J. App. Econom., 11(5), 561–571.
Coulibaly, P., Anctil, F., and Bobee, B. (2000). “Daily reservoir inflow forecasting using artificial neural networks with stopped training approach.” J. Hydrol., 230(3–4), 244–257.
Crone, S. F. (2002). “Training artificial neural networks using asymmetric cost functions.” Computational intelligence for the E-age, L. Wang, J. C. Rajapakse, K. Fukushima, and X. Y. S.-Y. Lee, eds., IEEE, New York, 2374–2380.
Crone, S. F., Lessmann, S., and Stahlbock, R. (2005). “Utility based data mining for time series analysis–Cost sensitive learning for neural network predictors.” Proc., Int. Workshop on Utility-Based Data Mining, Association for Computing Machinery (ACM) Conf. on Knowledge Discovery in Data, New York, 59–68.
Dey, S., Bose, S. K., and Sastry, G. L. N. (1995). “Clear-water scour at circular piers: A model.” J. Hydraul. Eng., 869–876.
Diebold, F. X., and Lopez, J. A. (1996). “Forecast evaluation and combination.” G. S. Maddala and C. R. Rao, eds., Handbook of statistics, Vol. 14, North-Holland Publishing, Amsterdam, Netherlands, 241–268.
Elliott, G., Komunjer, I., and Timmermann, A. (2005). “Estimation and testing of forecast rationality under flexible loss.” Rev. Econ. Stud., 72(4), 1107–1125.
Ettema, R. (1980). “Scour at bridge piers.”, School of Engineering, Univ. of Auckland, Auckland, New Zealand.
Froelich, D. C. (1988). “Analysis of onsite measurements of scour at piers.” Proc., ASCE National Conf. on Hydraulic Engineering, Reston, VA, 534–539.
Gao, D., Posada, G. L., and Nordin, C. F. (1993). “Pier scour equations used in the People’s Republic of China.”, Washington, DC.
Govindasamy, A. V., Briaud, J.-L., Kim, D., Olivera, F., Gardoni, P., and Delphia, J. (2010). “Observational method for estimating future scour depth at existing bridges.” Proc., Int. Conf. on Scour and Erosion 2010 (ICSE-5), 41–65.
Granger, C. W. J. (1999). “Outline of forecast theory using generalized cost functions.” Spanish Econ. Rev., 1(2), 161–173.
Granger, C. W. J., and Pesaran, M. H. (2000). “A decision theoretic approach to forecast evaluation.” Statistics and finance: An interface, W. S. Chan, W. K. Li, and H. Tong, eds., Imperial College Press, London, 261–278.
Hagan, M. T., and Menhaj, M. (1994). “Training feedforward networks with the Marquardt algorithm.” IEEE Trans. Neural Netw., 5(6), 989–993.
Hancu, S. (1971). “On the estimation of local scour in the bridge piers zone.” Proc., 14th Int. Association for Hydraulic Research (IAHR) Congress, Vol. 3, Delft, Netherlands, 299–313 (in French).
Haykin, S. (1998). Neural networks: A comprehensive foundation, Prentice Hall, Upper Saddle River, NJ.
Hong, J., Chiew, Y., Lu, J., Lai, J., and Lin, Y. (2012a). “Houfeng Bridge failure in Taiwan.” J. Hydraul. Eng., 186–198.
Hong, J., Goyal, M. K., Chiew, Y., and Chua, L. H. C. (2012b). “Predicting time-dependent pier scour depth with support vector regression.” J. Hydrol., 468–469(1), 241–248.
Hopkins, G. R., Vance, R. W., and Kasraie, B. (1980). “Scour around bridge piers.”, Washington, DC.
Jain, S. C. (1981). “Maximum clear-water scour around circular piers.” J. Hydraul. Div., 107(HY5), 611–626.
Jeng, D.-S., Bateni, S. M., and Lockett, E. (2005). “Neural network assessment for scour depth around bridge piers.”, Dept. of Civil Engineering, Univ. of Sydney, Sydney, NSW, Australia.
Johnson, P. A. (1995). “Comparison of pier-scour equations using field data.” J. Hydraul. Eng., 626–629.
Johnson, P. A., and Whittington, R. M. (2011). “Vulnerability-based risk assessment for stream instability at bridges.” J. Hydraul. Eng., 1248–1256.
Jones, J. S. (1984). “Comparison of prediction equations for bridge pier and abutment scour.”, Transportation Research Board, Washington, DC, 202–209.
Kothyari, U. C. (1989). “Scour around bridge piers.” Ph.D. thesis, Univ. of Roorkee, Roorkee, India.
Kothyari, U. C., Garde, R. J., and Ranga Raju, K. G. (1992). “Temporal variation of scour around circular bridge piers.” J. Hydraul. Eng., 1091–1106.
Kothyari, U. C., Hager, W. H., and Oliveto, G. (2007). “Generalized approach for clear-water scour at bridge foundation elements.” J. Hydraul. Eng., 1229–1240.
Kothyari, U. C., and Kumar, A. (2012). “Temporal variation of scour around circular compound piers.” J. Hydraul. Eng., 945–957.
Lagasse, P. F., and Richardson, E. V. (2001). “ASCE compendium of stream scour papers.” J. Hydraul. Eng., 531–533.
Lança, R., Fael, C., Maia, R., Pêgo, J., and Cardoso, A. (2013). “Clear-water scour at comparatively large cylindrical piers.” J. Hydraul. Eng., 1117–1125.
Laursen, E. M., and Toch, A. (1956). “Scour around bridge piers and abutments.”, Iowa Highway Research Board, Ames, IA.
Lee, S. O., and Sturm, T. W. (2009). “Effect of sediment size scaling on physical modeling of bridge scour.” J. Hydraul. Eng., 793–802.
Lee, T. L., Jeng, D. S., Zhang, G. H., and Hong, J. H. (2007). “Neural network modelling for estimation of scour depth around bridge piers.” J. Hydrodyn., 19(3), 378–386.
Lu, J., Hong, J., Su, C., Wang, C., and Lai, J. (2008). “Field measurements and simulation of bridge scour depth variations during floods.” J. Hydraul. Eng., 810–821.
Melville, B. W. (1997). “Pier and abutment scour: Integrated approach.” J. Hydraul. Eng., 125–136.
Melville, B. W., and Chiew, Y.-M. (1999). “Time scale for local scour at bridge piers.” J. Hydraul. Eng., 59–65.
Melville, B. W., and Coleman, S. E. (2000). Bridge scour, Water Resources Publications, Highlands Ranch, CO.
Mia, M. F., and Nago, H. (2003). “Design method of time-dependent local scour at circular bridge pier.” J. Hydraul. Eng., 420–427.
Miller, M. C., McCave, I. N., and Komar, P. D. (1977). “Threshold of sediment motion under unidirectional currents.” Sedimentology, 24(4), 507–527.
Mueller, D. S. (1996). “Local scour at bridge piers in nonuniform sediment under dynamic conditions.” Ph.D. thesis, Colorado State Univ., Fort Collins, CO.
Mueller, D. S., and Wagner, C. R. (2005). “Field observations and evaluations of streambed scour at bridges.”, Washington, DC.
Neill, C. R. (1973). Guide to bridge hydraulics, University of Toronto Press, Toronto.
Oliveto, G., and Hager, W. H. (2002). “Temporal evolution of clear-water pier and abutment scour.” J. Hydraul. Eng., 811–820.
Pagan-Ortiz, J. E. (1998). “Status of the scour evaluation of bridges over waterways in the United States.” Proc., Water Resources Engineering ‘98, ASCE, Reston, VA, 2–4.
Parola, A. C., Hagerty, D. G., Mueller, D. S., Melville, B. W., Parker, G., and Usher, J. S. (1997). “The need of research on scour at bridge crossings.” Proc., 27th Int. Association for Hydraulic Research (IAHR) Congress, Delft, Netherlands, 124–129.
Pesaran, M. H., and Skouras, S. (2002). “Decision-based methods for forecast evaluation.” A companion to economic forecasting, M. P. Clements and D. F. Hendry, eds., Blackwell, Malden, MA, 241–267.
Radice, A., Porta, G., and Franzetti, S. (2009). “Analysis of the time-averaged properties of sediment motion in a local scour process.” Water Resour. Res., 45, W03401.
Rhodes, J., and Trent, R. (1993). “Economics of floods, scour, and bridge failures.” Proc., Hydraulic Engineering ’93, H. W. Shen, S. T. Su, and F. Wen, eds., ASCE, Reston, VA, 928–933.
Richardson, E. V., and Davis, S. R. (1995). “Evaluating scour at bridges.”, Washington, DC.
Richardson, E. V., and Davis, S. R. (2001). “Evaluating scour at bridges.”, Washington, DC.
Rumelhart, D. E., Widrow, B, and Lehr, M. A. (1994). “The basic ideas in neural networks.” Commun. ACM, 37(3), 87–92.
Shen, H. W., Schneider, V. R., and Karaki, S. (1969). “Local scour around bridge piers.” J. Hydraul. Div., 95(6), 1919–1940.
Sheppard, D. M, Demir, H., and Melville, B. (2011). “Scour at wide piers and long skewed piers.”, Transportation Research Board, Washington, DC.
Sheppard, D. M., Melville, B., and Demir, H. (2014). “Evaluation of existing equations for local scour at bridge piers.” J. Hydraul. Eng., 14–23.
Sheppard, D. M., and Miller, W. Jr. (2006). “Live-bed local pier scour experiments.” J. Hydraul. Eng., 635–642.
Sheppard, D. M., Odeh, M., and Glasser, T. (2004). “Large-scale clear-water local pier scour experiments.” J. Hydraul. Eng., 957–963.
Silva, D. G. E., Jino, M., and de Abreu, B. T. (2010). “Machine learning methods and asymmetric cost function to estimate execution effort of software testing.” Proc., 3rd Int. Conf. on Software Testing, Verification and Validation (ICST), IEEE, New York, 275–284.
Toth, E., and Brandimarte, L. (2011). “Prediction of local scour depth at bridge piers under clear-water and live-bed conditions: Comparison of literature formulae and artificial neural networks.” J. Hydroinf., 13(4), 812–824.
Wardhana, K., and Hadipriono, F. C. (2003). “Analysis of recent bridge failures in the United States.” J. Perform. Constr. Facil., 144–150.
Yousefpour, N., et al. (2011). “Determination of unknown foundation of bridges for scour evaluation using artificial neural networks.”, ASCE, Reston, VA, 1514–1523.
Zhuravlyov, M. M. (1978). New method for estimation of local scour due to bridge piers and its substantiation, State All Union Scientific Research Institute on Roads, Moscow, Russia.
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Published In
Journal of Hydraulic Engineering
Volume 141 • Issue 7 • July 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jan 31, 2014
Accepted: Oct 23, 2014
Published online: Mar 20, 2015
Published in print: Jul 1, 2015
Discussion open until: Aug 20, 2015
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