Modeling Oxygen-transfer by Multiple Plunging Jets using Support Vector Machines and Gaussian Process Regression Techniques

Authors: Surinder Deswal

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333774

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, "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.