Modeling Oxygen-transfer by Multiple Plunging Jets using Support Vector Machines and Gaussian Process Regression Techniques
The paper investigates the potential of support vector
machines and Gaussian process based regression approaches to
model the oxygen–transfer capacity from experimental data of
multiple plunging jets oxygenation systems. The results suggest the
utility of both the modeling techniques in the prediction of the
overall volumetric oxygen transfer coefficient (KLa) from operational
parameters of multiple plunging jets oxygenation system. The
correlation coefficient root mean square error and coefficient of
determination values of 0.971, 0.002 and 0.945 respectively were
achieved by support vector machine in comparison to values of
0.960, 0.002 and 0.920 respectively achieved by Gaussian process
regression. Further, the performances of both these regression
approaches in predicting the overall volumetric oxygen transfer
coefficient was compared with the empirical relationship for multiple
plunging jets. A comparison of results suggests that support vector
machines approach works well in comparison to both empirical
relationship and Gaussian process approaches, and could successfully
be employed in modeling oxygen-transfer.
[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, "Oxygen transfer by multiple inclined plunging water jets",
International Journal of Mathematical, Physical and Engineering
Sciences, vol. 2, pp. 170-176, 2008.
[8] 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.
[9] 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.
[10] 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.
[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] W. T. Chan, Y. K. Chow, and I. F. Liu, "Neural networks: an alternative
to the pile driving formulas" Comput. Geotech., vol. 17, pp. 135-156,
1995.
[22] 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.
[23] Y. B. Dibike, S. Velickov, D. P. Solomatine, and M. B. Abbott, "Model
induction with support vector machines: Introduction and applications"
J. Comput. Civ. Eng., vol. 15, pp. 208-216, 2001.
[24] M. Pal, and P. M. Mather, "Support vector classifiers for land cover
classification" Proc. Map India 2003. Available:
www.gisdevelopment.net/ technology/rs/pdf/23.pdf>.
[25] M. K. Gill, T. Asefa, M. W. Kemblowski, and M. Makee, "Soil moisture
prediction using support vector machines" Environ. Urbanization, vol.
42, pp. 1033-1046, 2006.
[26] M. Pal, "Support vector machines-based modelling of seismic
liquefaction potential" Int. J. Numer. Analyt. Meth. Geomech., vol. 30,
pp. 983-996, 2006.
[27] M. Pal, and A. Goel, "Prediction of the end depth ratio and discharge in
semicircular and circular shaped channels using support vector
machines" Flow Meas. Instrum., vol. 17, pp. 50-57, 2006.
[28] M. Pal, and S. Deswal S, "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.
[29] S. Deswal, and D. V. S. Verma, "Performance evaluation and modeling
of a conical plunging jets aerator", International Journal of
Mathematical, Physical and Engineering Sciences, vol. 2, pp. 33-37,
2008.
[30] S. Deswal, and M. Pal, "Artificial neural network based modeling of
evaporation losses in reservoirs", International Journal of Mathematical,
Physical and Engineering Sciences, vol. 2, pp. 177-181, 2008.
[31] M. Pal, and S. Deswal, "Modelling pile capacity using Gaussian process
Regression", Computers and Geotechnics, 2010. (accepted).
[32] C. E. Rasmussen, and C. K. I. Williams, Gaussian Processes for
Machine Learning. The MIT Press, Cambridge, MA, 2006.
[33] M. Kuss, "Gaussian process models for robust regression, classification,
and reinforcement learning", PhD thesis, Technischen Universität
Darmstadt, 2006.
[34] V. N. Vapnik, The Nature of Statistical Learning Theory. Springer, New
York, 1995.
[35] 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.
[36] D. Leunberger, Linear and Nonlinear Programming. Addison-Wesley,
1984.
[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, "Oxygen transfer by multiple inclined plunging water jets",
International Journal of Mathematical, Physical and Engineering
Sciences, vol. 2, pp. 170-176, 2008.
[8] 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.
[9] 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.
[10] 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.
[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] W. T. Chan, Y. K. Chow, and I. F. Liu, "Neural networks: an alternative
to the pile driving formulas" Comput. Geotech., vol. 17, pp. 135-156,
1995.
[22] 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.
[23] Y. B. Dibike, S. Velickov, D. P. Solomatine, and M. B. Abbott, "Model
induction with support vector machines: Introduction and applications"
J. Comput. Civ. Eng., vol. 15, pp. 208-216, 2001.
[24] M. Pal, and P. M. Mather, "Support vector classifiers for land cover
classification" Proc. Map India 2003. Available:
www.gisdevelopment.net/ technology/rs/pdf/23.pdf>.
[25] M. K. Gill, T. Asefa, M. W. Kemblowski, and M. Makee, "Soil moisture
prediction using support vector machines" Environ. Urbanization, vol.
42, pp. 1033-1046, 2006.
[26] M. Pal, "Support vector machines-based modelling of seismic
liquefaction potential" Int. J. Numer. Analyt. Meth. Geomech., vol. 30,
pp. 983-996, 2006.
[27] M. Pal, and A. Goel, "Prediction of the end depth ratio and discharge in
semicircular and circular shaped channels using support vector
machines" Flow Meas. Instrum., vol. 17, pp. 50-57, 2006.
[28] M. Pal, and S. Deswal S, "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.
[29] S. Deswal, and D. V. S. Verma, "Performance evaluation and modeling
of a conical plunging jets aerator", International Journal of
Mathematical, Physical and Engineering Sciences, vol. 2, pp. 33-37,
2008.
[30] S. Deswal, and M. Pal, "Artificial neural network based modeling of
evaporation losses in reservoirs", International Journal of Mathematical,
Physical and Engineering Sciences, vol. 2, pp. 177-181, 2008.
[31] M. Pal, and S. Deswal, "Modelling pile capacity using Gaussian process
Regression", Computers and Geotechnics, 2010. (accepted).
[32] C. E. Rasmussen, and C. K. I. Williams, Gaussian Processes for
Machine Learning. The MIT Press, Cambridge, MA, 2006.
[33] M. Kuss, "Gaussian process models for robust regression, classification,
and reinforcement learning", PhD thesis, Technischen Universität
Darmstadt, 2006.
[34] V. N. Vapnik, The Nature of Statistical Learning Theory. Springer, New
York, 1995.
[35] 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.
[36] D. Leunberger, Linear and Nonlinear Programming. Addison-Wesley,
1984.
@article{"International Journal of Architectural, Civil and Construction Sciences:56503", author = "Surinder Deswal", title = "Modeling Oxygen-transfer by Multiple Plunging Jets using Support Vector Machines and Gaussian Process Regression Techniques", abstract = "The paper investigates the potential of support vector
machines and Gaussian process based regression approaches to
model the oxygen–transfer capacity from experimental data of
multiple plunging jets oxygenation systems. The results suggest the
utility of both the modeling techniques in the prediction of the
overall volumetric oxygen transfer coefficient (KLa) from operational
parameters of multiple plunging jets oxygenation system. The
correlation coefficient root mean square error and coefficient of
determination values of 0.971, 0.002 and 0.945 respectively were
achieved by support vector machine in comparison to values of
0.960, 0.002 and 0.920 respectively achieved by Gaussian process
regression. Further, the performances of both these regression
approaches in predicting the overall volumetric oxygen transfer
coefficient was compared with the empirical relationship for multiple
plunging jets. A comparison of results suggests that support vector
machines approach works well in comparison to both empirical
relationship and Gaussian process approaches, and could successfully
be employed in modeling oxygen-transfer.", keywords = "Oxygen-transfer, multiple plunging jets, support
vector machines, Gaussian process.", volume = "5", number = "1", pages = "38-6", }
