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Received July 19, 2020
Accepted March 16, 2021
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This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits
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Approximate solution of non-linear dynamic energy model for multiple effect evaporator using fourier series and metaheuristics
1Faculty of Informatics, Technische Universität Wien, 1040, Vienna, Austria 2Department of Instrumentation and Control Engineering, Dr. B. R. Ambedkar National Institute of Technology Jalandhar, India 3Department of Electrical Engineering, Indian Institute of Technology Roorkee, India 4School of Electrical and Electronics, SASTRA University, Thanjavur, Tamilnadu-613401, India 5Department of Industrial and Production Engineering, Dr. B. R. Ambedkar National Institute of Technology Jalandhar, India
vermaop@nitj.ac.in
Korean Journal of Chemical Engineering, May 2021, 38(5), 906-923(18), 10.1007/s11814-021-0787-3
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Abstract
This article presents the approximate solution of non-linear dynamic energy model of multiple effect evaporator (MEE) using Fourier series and metaheuristics. The dynamic model of MEE involves first-order simultaneous ordinary differential equations (SODEs). Prior to solving the dynamic model, the non-linear steady-state model is solved to obtain the optimum steady-state process parameters. These process parameters serve as the initial conditions (constraints) for the SODEs. The SODEs are exemplified as an optimization problem by the weighted residual function to produce their approximate solutions. The optimization task is to find the best estimates of unknown coefficients in the Fourier series expansion using two preeminent metaheuristic approaches: Particle swarm optimization and harmony search. Besides, the influence of the number of approximation terms in Fourier series expansion on the accuracy of the approximate solutions has been investigated. The solution of the dynamic model assists in the investigation of open-loop dynamics of the MEE. Moreover, the acquired results may assist in designing suitable controllers to ensure energy-efficient performance of MEE and to monitor the product quality. The optimization results reveal that both the metaheuristic approaches offer minimum violation of the constraints and, therefore, validate their efficiency in solving such complex non-linear energy models.
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References
Verma OP, Manik G, Sethi SK, Renew. Sust. Energ. Rev., 100, 90 (2019)
Verma OP, Manik G, Mohammed TH, Korean J. Chem. Eng., 4, 2570 (2017)
Bhargava R, Khanam S, Mohanty B, Ray AK, Comput. Chem. Eng., 32(12), 3213 (2008)
Verma OP, Mohammed TH, Mangal S, Manik G, In: Adv. Intell. Syst. Comput., 437, 1011, Springer (2016).
Kaya D, Sarac HI, Energy, 32(8), 1536 (2007)
Gautami G, Khanam S, Desalination, 288, 16 (2012)
Verma OP, Mohammed TH, Mangal S, Manik G, Int. J. Syst. Assur. Eng. Manag., 9, 111 (2018)
Bhargava R, Khanam S, Mohanty B, Ray AK, Comput. Chem. Eng., 32(10), 2203 (2008)
Verma OP, Mohammed TH, Mangal S, Manik G, Energy, 129, 148 (2017)
Verma OP, Suryakant, Manik G, Int. J. Syst. Assur. Eng. Manag., 8, 63 (2017)
Verma DP, Manik G, Suryakant, Jain VK, Jain DK, Wang H, Sustain. Comput. Informatics Syst., 20, 130 (2018)
Pati S, Yadav D, Verma OP, Hybridization of Neural Computing with Nature Inspired Algorithms, 1 (2020).
Yadav D, Verma OP, Heliyon, 6, e04349 (2020)
Olsson A, Particle swarm optimization: theory, techniques and applications, Nova Science Publishers, Inc., US (2010).
Jaberipour M, Khorram E, Karimi B, Comput. Math. Appl., 62, 566 (2011)
Geem ZW, Kim JH, Loganathan GV, Simulation, 76, 60 (2001)
Geem ZW, Music-inspired harmony search algorithm, Springer, Berlin Heidelberg (2009).
Yang XS, Stud. Comput. Intell, 191, 1 (2009)
Ingram G, Zhang T, Stud. Comput. Intell, 191, 15 (2009)
Verma OP, Manik G, Jain VK, J. Comput. Sci., 25, 238 (2018)
Verma OP, Mohammed TH, Mangal S, Manik G, Trans. Inst. Meas. Control., 40, 2278 (2018)
Sadollah A, Eskandar H, Yoo DG, Kim JH, Eng. Appl. Artif. Intell, 40, 117 (2015)
Babaei M, Appl. Soft Comput. J., 13, 3354 (2013)
Osman IH, Laporte G, Ann. Oper. Res., 63, 513 (1996)
Glover F, Kochenberger G, Handbook of metaheuristics, Springer US (2006).
Yang XS, Engineering optimization an introduction with metaheuristic applications,Inc., Hoboken, New Jersey (2010).
Yang XS, Nature-inspired metaheuristic algorithms second edition, Luniver Press, UK (2010).
Belendez A, Arribas E, Ortuno M, Gallego S, Marquez A, Pascual I, Comput. Math. Appl., 64, 1602 (2012)
Lee ZY, Appl. Math. Comput., 179, 779 (2006)
Mateescu GD, Romanian J. Econ. Forecasting, 3, 5 (2006)
Mastorakis N, Mastorakis NE, WSEAS Trans. on Mathematics 5, 1276 (2006).
Cao H, Kang L, Chen Y, Yu J, Genet. Program. Evolvable Mach., 1, 309 (2000)
Karr CL, Wilson E, Appl. Intell, 19, 147 (2003)
Reich C, In: Proc. ACM Symp. Appl. Comput., USA, 1, 428 (2000).
Bansal JC, Evolutionary and swarm intelligence algorithms, Springer International Publishing, Switzerland (2019).
Zhang T, Geem ZW, Swarm Evol. Comput., 48, 31 (2019)
Sadollah A, Choi Y, Yoo DG, Kim JH, Appl. Soft Comput. J., 33, 360 (2015)
Verma OP, Manik G, Mohammed TH, Korean J. Chem. Eng., 4, 2570 (2017)
Bhargava R, Khanam S, Mohanty B, Ray AK, Comput. Chem. Eng., 32(12), 3213 (2008)
Verma OP, Mohammed TH, Mangal S, Manik G, In: Adv. Intell. Syst. Comput., 437, 1011, Springer (2016).
Kaya D, Sarac HI, Energy, 32(8), 1536 (2007)
Gautami G, Khanam S, Desalination, 288, 16 (2012)
Verma OP, Mohammed TH, Mangal S, Manik G, Int. J. Syst. Assur. Eng. Manag., 9, 111 (2018)
Bhargava R, Khanam S, Mohanty B, Ray AK, Comput. Chem. Eng., 32(10), 2203 (2008)
Verma OP, Mohammed TH, Mangal S, Manik G, Energy, 129, 148 (2017)
Verma OP, Suryakant, Manik G, Int. J. Syst. Assur. Eng. Manag., 8, 63 (2017)
Verma DP, Manik G, Suryakant, Jain VK, Jain DK, Wang H, Sustain. Comput. Informatics Syst., 20, 130 (2018)
Pati S, Yadav D, Verma OP, Hybridization of Neural Computing with Nature Inspired Algorithms, 1 (2020).
Yadav D, Verma OP, Heliyon, 6, e04349 (2020)
Olsson A, Particle swarm optimization: theory, techniques and applications, Nova Science Publishers, Inc., US (2010).
Jaberipour M, Khorram E, Karimi B, Comput. Math. Appl., 62, 566 (2011)
Geem ZW, Kim JH, Loganathan GV, Simulation, 76, 60 (2001)
Geem ZW, Music-inspired harmony search algorithm, Springer, Berlin Heidelberg (2009).
Yang XS, Stud. Comput. Intell, 191, 1 (2009)
Ingram G, Zhang T, Stud. Comput. Intell, 191, 15 (2009)
Verma OP, Manik G, Jain VK, J. Comput. Sci., 25, 238 (2018)
Verma OP, Mohammed TH, Mangal S, Manik G, Trans. Inst. Meas. Control., 40, 2278 (2018)
Sadollah A, Eskandar H, Yoo DG, Kim JH, Eng. Appl. Artif. Intell, 40, 117 (2015)
Babaei M, Appl. Soft Comput. J., 13, 3354 (2013)
Osman IH, Laporte G, Ann. Oper. Res., 63, 513 (1996)
Glover F, Kochenberger G, Handbook of metaheuristics, Springer US (2006).
Yang XS, Engineering optimization an introduction with metaheuristic applications,Inc., Hoboken, New Jersey (2010).
Yang XS, Nature-inspired metaheuristic algorithms second edition, Luniver Press, UK (2010).
Belendez A, Arribas E, Ortuno M, Gallego S, Marquez A, Pascual I, Comput. Math. Appl., 64, 1602 (2012)
Lee ZY, Appl. Math. Comput., 179, 779 (2006)
Mateescu GD, Romanian J. Econ. Forecasting, 3, 5 (2006)
Mastorakis N, Mastorakis NE, WSEAS Trans. on Mathematics 5, 1276 (2006).
Cao H, Kang L, Chen Y, Yu J, Genet. Program. Evolvable Mach., 1, 309 (2000)
Karr CL, Wilson E, Appl. Intell, 19, 147 (2003)
Reich C, In: Proc. ACM Symp. Appl. Comput., USA, 1, 428 (2000).
Bansal JC, Evolutionary and swarm intelligence algorithms, Springer International Publishing, Switzerland (2019).
Zhang T, Geem ZW, Swarm Evol. Comput., 48, 31 (2019)
Sadollah A, Choi Y, Yoo DG, Kim JH, Appl. Soft Comput. J., 33, 360 (2015)
