Comparison of Polynomial and Radial Basis Kernel Functions based SVR and MLR in Modeling Mass Transfer by Vertical and Inclined Multiple Plunging Jets

Presently various computational techniques are used in modeling and analyzing environmental engineering data. In the present study, an intra-comparison of polynomial and radial basis kernel functions based on Support Vector Regression and, in turn, an inter-comparison with Multi Linear Regression has been attempted in modeling mass transfer capacity of vertical (θ = 90O) and inclined (θ multiple plunging jets (varying from 1 to 16 numbers). The data set used in this study consists of four input parameters with a total of eighty eight cases, forty four each for vertical and inclined multiple plunging jets. For testing, tenfold cross validation was used. Correlation coefficient values of 0.971 and 0.981 along with corresponding root mean square error values of 0.0025 and 0.0020 were achieved by using polynomial and radial basis kernel functions based Support Vector Regression respectively. An intra-comparison suggests improved performance by radial basis function in comparison to polynomial kernel based Support Vector Regression. Further, an inter-comparison with Multi Linear Regression (correlation coefficient = 0.973 and root mean square error = 0.0024) reveals that radial basis kernel functions based Support Vector Regression performs better in modeling and estimating mass transfer by multiple plunging jets.

Authors:

• S. Deswal
• M. Pal

Keywords:

• Mass transfer
• multiple plunging jets
• polynomial and radial basis kernel functions
• Support Vector Regression.

References:

[1] A. K. Bin, “Gas entrainment by plunging liquid jets”, Chem. Eng. Sci. J.
Great Britain, vol. 48, pp. 3585-3630, 1993.
[2] P. D. Cummings, and H. Chanson, “Air entrainment in the developing
flow region of plunging jets-part 1: theoretical development”, Fluids
Eng. J. ASME, vol. 119, pp. 597-602, 1997.
[3] H. Chanson, S. Aoki, and A. Hoque, “Similitude of air entrainment at
vertical circular plunging jets”, in Proc. ASME FEDSM’02, Montreal,
Quebec, 2002, pp. 1-6.
[4] H. Chanson, S. Aoki, and A. Hoque, “Physical modelling and similitude
of air bubble entrainment at vertical circular plunging jets”, Chem. Eng.
Sc., vol. 59, pp. 747-758, 2004.
[5] S. M. Leung, J. C. Little, T. Hoist, and N.G. Love, “Air/water oxygen
transfer in a biological aerated filter”, J. Environmental Eng., vol. 132,
pp. 181-189, 2006.
[6] S. Deswal, D. V. S. Verma, and M. Pal, “Multiple plunging jet aeration
system and parameter modelling by neural network and support vector
machines”, in Proc. Water Pollution VIII: Modelling, Monitoring and
Management, Italy, 2006, vol. 95, pp. 595-604.
[7] S. Deswal, and D. V. S. Verma, “Performance evaluation and modeling
of a conical plunging jets aerator”, Int. J. of Mathematical, Physical and
Engineering Sciences, vol. 2, pp. 33-37, 2008.
[8] D. Kusabiraki, H. Niki K. Yamagiwa, and A. Ohkawa, “Gas entrainment
rate and flow pattern of vertical plunging liquid jets”, The Canadian J.
Chem. Eng., vol. 68, pp. 893-903, 1990.
[9] M. E. Emiroglu, and A. Baylar, “Study of the influence of air holes
along length of convergent-divergent passage of a venture device on
aeration”, J. Hyd. Res., vol. 41, pp. 513-520, 2003.
[10] K. Tojo, N. Naruko, and K. Miyanami, “Oxygen transfer and liquid
mixing characteristics of plunging jet reactors”, Chem. Eng. J.
Netherlands, vol. 25, pp. 107-109, 1982.
[11] A. Ahmed, “Aeration by plunging liquid jet”, Ph.D. thesis,
Loughborough Univ. of Tech. UK, 1974.
[12] E. van de Sande, and J. .M. Smith, “Mass transfer from plunging water
jets”, Chem. Eng. J. Netherlands, vol. 10, pp. 225-233, 1975.
[13] J. A. C. van de Donk, “Water aeration with plunging jets”, Ph.D. thesis,
Technische Hogeschool Delft, Netherlands, 1981.
[14] K. Tojo, and K. Miyanami, “Oxygen transfer in jet mixers”, Chem. Eng.
J. Netherlands, vol. 24, pp. 89-97, 1982.
[15] A. K. Bin, and J. M. Smith, “Mass transfer in a plunging liquid jet
absorber”, Chem. Engng. Commun, vol. 15, pp. 367-383, 1982.
[16] D. Bonsignore, G. Volpicelli, A. Campanile, L. Santoro, and R.
Valentino, “Mass transfer in plunging jet absorbers”, Chem. Eng.
Process, vol. 19, pp. 85-94, 1985.
[17] A. Ohkawa, D. Kusabiraki, Y. Shiokawa, M. Sakal, and M. Fujii, “Flow
and oxygen transfer in a plunging water system using inclined short
nozzles in performance characteristics of its system in aerobic treatment
of wastewater”, Biotech. Bioeng., vol. 28, pp. 1845-1856, 1986.
[18] K. Funatsu, Y. Ch. Hsu, M. Noda, and S. Sugawa, “Oxygen transfer in
the water jet vessel”, Chem. Eng. Commun., vol. 73. pp. 121-139, 1988.
[19] A. Ahmed, and J. Glover, Conf. on Farm Wastes Disposal, Glasgow,
Sept. 1972. In E. van de Sande, and J. M. Smith, “Mass transfer from
plunging water jets”, Chem. Eng. J. Netherlands, vol. 10, pp.225-233,
1975.
[20] S. Deswal, and D. V. S. Verma, “Air-water oxygen transfer with
multiple plunging jets”, Water Qual. Res. J. Canada; vol. 42, pp. 295-
302, 2007. [21] S. Deswal, “Oxygen transfer by multiple inclined plunging water jets”,
International Journal of Mathematical, Physical and Engineering
Sciences, vol. 2, pp. 170-176, 2008.
[22] M. Ide, H. Uchiyama, and T. Ishikura, "Performance of multi-plunging
jet absorbers using liquid jets containing small solute bubbles",
Canadian J. Chemical Engineering; vol. 81(3-4), pp. 613-620, 2008.
[23] S. Deswal, and M. Pal, ""Multi-linear regression based prediction of
mass transfer by multiple plunging jets", Int. J. of Mathematical,
Computational, Physical, Electrical and Computer Engineering, vol. 8
(3), pp.493-496, 2014.
[24] M. Pal, and S. Deswal, “Modeling pile capacity using support vector
machines and generalized regression neural network” J. of Geotechnical
and Geoenvironmental Engineering ASCE, vol. 134, pp. 1021-1024,
2008.
[25] S. Deswal, and M. Pal, “Artificial neural network based modeling of
evaporation losses in reservoirs”, Int. J. of Mathematical, Physical and
Engineering Sciences, vol. 2, pp. 177-181, 2008.
[26] M. Pal, and S. Deswal, "Support vector regression based shear strength
modelling of deep beams", Computers & Structures, vol. 89(13), pp.
1430-1439, 2011.
[27] Y. K. Chow, W. T. Chan, I. F., Liu, and S. L. Lee, “Predication of pile
capacity from stress-wave measurements: a neural network approach”
Int. J. Numer. Analyt. Meth. Geomech., vol. 19, pp. 107–126, 1995.
[28] M. Pal, and P. M. Mather, “Support vector classifiers for land cover
classification”, in Proc. Map India 2003. Available:
www.gisdevelopment.net/ technology/rs/pdf/23.pdf>.
[29] M. Pal, “Support vector machines-based modelling of seismic
liquefaction potential”, Int. J. Numer. Analyt. Meth. Geomech., vol. 30,
pp. 983–996, 2006.
[30] S. Deswal, "Computational techniques and their potential in predicting
oxygen transfer by multiple oblique jets", Int. J. of Environmental
Science, vol. 1(5), pp. 986-999, 2011.
[31] S. Deswal, "Modeling Oxygen-transfer by Multiple Plunging Jets using
Support Vector Machines and Gaussian Process Regression
Techniques", Int. J. of Civil and Environmental Engineering, vol. 3(1);
pp. 28-33, 2011.
[32] T. Bagatur, and F. Onen, "A predictive model on air entrainment by
plunging water jets using GEP and ANN", KSCE J. of Civil
Engineering, vol. 18(1); pp. 304-314, 2014.
[33] V. N. Vapnik, The Nature of Statistical Learning Theory. New York:
Springer, 1995.
[34] A. J. Smola, and B. Schölkopf, A Tutorial on Support Vector
Regression. NeuroCOLT Technical Rep. No. NC-TR-98-030, Royal
Holloway College, Univ. of London, London, 1998.
[35] D. Leunberger, Linear and Nonlinear Programming. Addison-Wesley,
1984.
[36] I.H. Witten, and E. Frank, Data Mining: Practical Machines Learning
Tools and Techniques. San Francisco: Morgan Kaufmann, 2005.