Browse > Article
http://dx.doi.org/10.3741/JKWRA.2021.54.12.1305

Development of empirical formula for imbalanced transverse dispersion coefficient data set using SMOTE  

Lee, Sunmi (Department of Civil Engineering, Seoul National University of Science and Technology)
Yoon, Taewon (Department of Civil Engineering, Seoul National University of Science and Technology)
Park, Inhwan (Department of Civil Engineering, Seoul National University of Science and Technology)
Publication Information
Journal of Korea Water Resources Association / v.54, no.12, 2021 , pp. 1305-1316 More about this Journal
Abstract
In this study, a new empirical formula for 2D transverse dispersion coefficient was developed using the results of previous tracer test studies, and the performance of the formula was evaluated. Since many tracer test studies have been conducted under the conditions where the width-to-depth ratio is less than 50, the existing empirical formulas developed using these imbalanced tracer test results have limitations in applying to rivers with a width-to-depth ratio greater than 50. Therefore, in order to develop an empirical formula for transverse dispersion coefficient using the imbalanced tracer test data, the Synthetic Minority Oversampling TEchnique (SMOTE) was used to oversample new data representing the properties of the existing tracer test data. The hydraulic data and the transverse dispersion coefficients in conditions of width-to-depth ratio greater than 50 were oversampled using the SMOTE. The reliability of the oversampled data was evaluated using the ROC (Receiver Operating Characteristic) curve. The empirical formula of transverse dispersion coefficient was developed including the oversampled data, and the performance of the results were compared with the empirical formulas suggested in previous studies using R2. From the comparison results, the value of R2 was 0.81 for the range of W/H < 50 and 0.92 for 50 < W/H, which were improved accuracy compared to the previous studies.
Keywords
Transverse dispersion coefficient; SMOTE (Synthetic Minority Oversampling TEchnique); Empirical formula; Imbalanced data;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Baek, K.O., Seo, I.W., and Jung, S.J. (2006). "Evaluation of transverse dispersion coefficient in meandering channel from transient tracer tests." Journal of Hydraulic Engineering, Vol. 132, No. 10, pp. 1021-1032.   DOI
2 Barus, S., Islam, M.M., Yao,X., and Murase, K. (2014). "MWMOTE - Majority weighted minority oversampling technique for imbalanced data set learning." IEEE Transactions on Knowledge and Data Engineering, Vol. 26, No. 2, pp. 405-425.   DOI
3 Boxall, J.B., Guymer, I., and Mariion, A. (2003). "Transverse mixing in sinuous natural open channel flows." Journal of Hydraulic Research, IAHR, Vol. 41, No. 2, pp. 153-165.   DOI
4 Chawla, N.V., Bowyer, K.W., Hall, L.O., and Kegelmeyer, W.P. (2002). "SMOTE : Synthetic minority over-sampling technique." Journal of Artificial Intelligence Research, Vol. 16, pp. 321-357.   DOI
5 Douzas, G., Bacao, F., and Last, F. (2018). "Improving imbalanced learning through a heuristic oversampling method based on k-means and SMOTE." Information Sciences, Vol. 465, pp. 1-20.   DOI
6 Han, E.J., Kim, Y.D., Baek, K.O., and Seo, I.W. (2017). "Analytical and experimental study on dispersion and diffusion by tracer test." Water for Future, Vol. 50, No. 6, pp. 58-65.
7 Jeon, T.M., Baek, K.O., and Seo, I.W. (2007). "Development of an empirical equation for the transverse dispersion coefficient in natural streams." Environmental Fluid Mechanics, Vol. 7, pp. 317-329.   DOI
8 Lau, Y.L., and Krishnappan, B.G. (1981). "Modeling transverse mixing in natural streams." Journal of the Hydraulic Division, ASCE, Vol. 107, No. HY2, pp. 209-226.   DOI
9 Nitesh, V.C., Kevin W.B., Lawrence, O.H., and Philip, W.K. (2002). "SMOTE: synthetic minority over-sampling technique." Journal of Artificial Intelligence Research, Vol. 16, pp. 321-357.   DOI
10 Mahamud, K.R.K., Zorkeflee, M., and Din, A.M. (2016). "Fuzzy distance-based undersampling technique for imbalanced flood data." Proceedings of the Knowledge Management International Conference, UUM, Chiang Mai, Thailand, pp. 509-513.
11 Nokes, R.I., and Wood, I.R. (1988). "Vertical and lateral turbulent dispersion: Some experimental results." Journal of Fluid Mechanics, Vol. 187, pp. 373-394.   DOI
12 Noori, R., Karbassi, A., Farokhnia, A., and Dehghani, M. (2009). "Predicting the longitudinal dispersion coefficient using support vector machine and adaptive neuro-fuzzy inference system techniques." Environmental Engineering Science, Vol. 26, No.10, pp.1503-1510.   DOI
13 Sayre, W.W. (1979). "Shore-attached thermal plumes in rivers." Modelling in rivers, Edited by Shen, H.W., Wiley-Interscience, London, UK, pp.15.1-15.44.
14 Sayre, W.W., and Chang, F.M. (1968) A laboratory investigation of open channel dispersion processes for dissolved, suspended, and floating dispersants. Professional Paper, No. 433-E. US Geological Survey, U.S., pp. 1-71.
15 Seo, I.W., Choi, H.J., Kim, Y.D., and Han, E.J. (2016). "Analysis of two-dimensional mixing in natural streams based on transient tracer tests." Journal of Hydraulic Engineering, Vol. 142, No. 8, pp. 1-16.
16 Wu, Y., Ding, Y., and Feng, J. (2020). "SMOTE-Boost-based sparse Bayesian model for flood prediction." EURASIP Journal on Wireless Communications and Networking, Vol. 78, pp.1-12.
17 Snieder, E., Abogadil, K., and Khan, U.T. (2021). "Resampling and ensemble techniques for improving ANN-based high-flow forecast accuracy." Hydrology and Earth System Sciences, Vol. 25, pp. 2543-2566.   DOI
18 Swets, J.A. (1988). "Measuring the accuracy of diagnostic systems." American Association for the Advancement of Science, Vol. 240, No. 4857, pp.1285-1293.   DOI
19 Webel, G., and Schatzmann, M. (1984). "Transverse mixing in open channel flow." Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 4, pp. 423-435.   DOI
20 Yotsukura, N., and Cobb, E.D. (1972). Transverse diffusion of solutes in natural streams, Professional Paper, No.582-C, U.S. Geological Survey, U.S., pp. 1-19.
21 Yotsukura, N., and Sayre, W.W. (1976). "Transverse mixing in natural channels." Water Resources Reseach, Vol. 12, No. 4, pp. 695-704.   DOI
22 Bansal, M.K. (1971). "Dispersion in natural streams." Journal of the Hydraulics Division, ASCE, Vol. 97, No. 11, pp. 1867-1886.   DOI
23 Baek, K.O., and Seo, I.W. (2017). "Estimation of transverse dispersion coefficient for two-dimensional mixing in natural streams." Journal of Hydro-environment Research, Vol. 15, pp. 67-74.   DOI
24 Baek, K.O., Seo, I.W., and Jung, S.J. (2005). "2-D mixing of instantaneous pollutants in meandering channels : II. Determination and analysis of dispersion coefficients." Journal of the Korean Society of Civil Engineers B, KSCE, Vol. 25, No. 6B, pp. 463-471.
25 Bansal, M.K. (1970). Dispersion and reaeration in natural stream. Ph. D. dissertation, Univesite de Kansas Laurence, KS, U.S.
26 Beltaos, S. (1980). "Transverse mixing tests in natural streams." Journal of the Hydraulics Division, ASCE, Vol. 106, No. HY10, pp. 1607-1625.   DOI
27 Beltaos, S., and Day, T.J. (1978). "A field study of longitudinal dispersion." Canadian Journal of Civil Engineering, Vol. 5, pp. 572-585.   DOI
28 Bradley, A.P. (1997). "The use of the area under the ROC curve in theevaluation of machine learning algorithms." Pattern Recognition, Vol. 30, No. 7, pp. 1145-1159.   DOI
29 Zhu, F., Lin, Y., and Liu, Y. (2017). "Synthetic minority oversampling technique for multiclass imbalance problems." Pattern Recognition, Vol. 72, pp. 327-340.   DOI
30 Yotsukura, N., Sayre, W.W., and Alsaffar, A.M. (1968). "Discussion of The mechanics of dispersion in natural streams by HB Fischer." Journal of the Hydraulics Division, Vol. 95, pp. 1009-1038.
31 Holley, E.R., and Abraham, G. (1973). "Field tests on transverse mixing in rivers." Journal of Hydraulic Division, ASCE, Vol. 99, No. HY12, pp. 313-2331.
32 Fischer, H.B. (1973). "Longitudinal dispersion and turbulent mixing in open- channel flow." Annual Review of Fluid Mechanics, Vol. 5, pp.59-78.   DOI
33 Gharbi, S., and Verrette, J. (1998). "Relation between longitudinal and transversal mixing coefficients in natural streams." Journal of Hydraulic Research, IAHR, Vol. 36, No. 1, pp. 43-53.   DOI
34 Seo, I.W., Jeon, T.M., and Baek, K.O. (2005). "Development of empirical equation of transverse dispersion coefficient for analysis of 2-D mixing in natural streams." Journal of the Korean Society of Civil Engineers B, KSCE, Vol. 25, No. 4B, pp. 247-255.
35 Shin, J., Seo, I.W., and Baek, D. (2020). "Longitudinal and transverse dispersion coefficients of 2D contaminant transport model for mixing analysis in open channels." Journal of Hydrology, Vol. 583, pp. 1-15.
36 Fischer, H.B. (1969). "The effect of bends on dispersion coefficients in streams." Water Resources Research, Vol. 5, pp. 496-506.   DOI
37 Deng, Z., Singh, V.P., and Bengtsson, L. (2001). "Longitudinal dispersion coefficient in straight rivers." Journal of Hydraulic Engineering, Vol. 127, No. 11, pp. 919-927.   DOI
38 Holley, F.M.Jr., and Nerat, G. (1983). "Field calibration of stream-tube dispersion model." Journal of Hydraulic Engineering, ASCE, Vol. 109, No. 11, pp. 1455-1470.   DOI
39 Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J., and Brooks, N.H. (1979). Mixing in inland and coastal waters. Academic Press, NY, U.S.
40 Engmann, J.E.O., and Kellerhals, R. (1974). "Transverse mixing in an ice-covered river." Water Resources Research, Vol. 10, pp. 775-784.   DOI
41 Krishnappan, B.G., and Lau, Y.L. (1977). "Transverse mixing in meandering channels with varying bottom topography." Journal of Hydraulic Research, IAHR, Vol. 15, No. 4, pp. 351-371.   DOI
42 Rutherford, J.C. (1994). River mixing, John Wiley and Sons, Chichester, UK.
43 Jurafsky, D., and Martin J.M. (2017). Speech and language processing: An introduction to natural language processing, computational linguistics, and speech recognition, 3rd ed, Pearson Eucation, London, UK, p. 67.
44 Almquist, C.W., and Holley, E.R. (1985). Transverse mixing in meandering laboratory channels with rectangular and naturally varying cross sections. Technical Report CRWR-205, University of Texas, Austin, TX, U.S.
45 Baek, K.O., and Seo, I.W. (2007). "Evaluating coefficient of transverse dispersion induced by shear flow." Journal of the Korean Society of Civil Engineers B, KSCE, Vol. 27, No. 1B, pp. 21-28.
46 Seo, I.W., Baek, K.O., and Jeon, T.M. (2006). "Analysis of transverse mixing in natural streams under slug tests." Journal of Hydraulic Research, Vol. 44, No. 3, pp. 350-362.   DOI
47 Baek, K.O., and Seo, I.W. (2013). "Empirical equation for transverse dispersion coefficient based on theoretical background in river bends." Environmental Fluid Mechanics, Vol. 13, No. 5, pp. 465-477.   DOI
48 Holley, E.R. (1971). Transverse mixing in rivers. Laboratory Report, No. S-132, Delft Hydraulics Lab, Netherlands.
49 Yotsukura, N. Fischer, H.B., and Sayre, W.W. (1970). Measurement of mixing characteristics of the Missouri River between Sioux City, Iowa and Plattsmouth, Nebraska. U.S. Geological Survey Water-Supply Paper, Washington D.C, U.S.