Abstract
This study aims to build an artificial intelligence (AI)-based inference model to predict the coefficient of performance (COP) for refrigeration equipment under various R404A refrigerant conditions. The proposed model, the evolutionary multivariate adaptive regression splines (EMARS), is a hybrid of the multivariate adaptive regression splines (MARS) and the artificial bee colony (ABC). In the EMARS, the MARS primarily addresses the learning and curve fitting and the ABC carries out optimization to determine the fittest parameter settings with minimal prediction error. A tenfold cross-validation method was used to compare the performance of the EMARS against four other AI techniques, including the back-propagation neural network, classification and regression tree, genetic programming, and support vector machine. An analysis of comparison results supports EMARS as the best model for predicting the COP, with an MAPE value \(<\)1%. In addition to performing significantly better than the four benchmark models, EMARS is unique in being able to: operate automatically without human intervention or domain knowledge; explore the approximate function of the input–output relationship; and identify the relative importance of various factors of influence automatically.
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References
Andalib A, Atry F (2009) Multi-step ahead forecasts for electricity prices using NARX: a new approach, a critical analysis of one-step ahead forecasts. Energy Convers Manag 50:739–747. doi:10.1016/j.enconman.2008.09.040
Arcaklioǧlu E, Erişen A, Yilmaz R (2004) Artificial neural network analysis of heat pumps using refrigerant mixtures. Energy Convers Manag 45:1917–1929. doi:10.1016/j.enconman.2003.09.028
Ayan K, Kılıç U (2012) Artificial bee colony algorithm solution for optimal reactive power flow. Appl Soft Comput 12:1477–1482. doi:10.1016/j.asoc.2012.01.006
Bechtler H, Browne MW, Bansal PK, Kecman V (2001) New approach to dynamic modelling of vapour-compression liquid chillers: artificial neural networks. Appl Thermal Eng 21:941–953. doi:10.1016/S1359-4311(00)00093-4
Bishop CM (2006) Pattern recognition and machine learning (information science and statistics). Springer, New York
Chen X, Zhou Y, Yu J (2011) A theoretical study of an innovative ejector enhanced vapor compression heat pump cycle for water heating application. Energy Build 43:3331–3336. doi:10.1016/j.enbuild.2011.08.037
Chengmin C, Yufeng Z, Lijun M (2012) Assessment for central heating systems with different heat sources: a case study. Energy Build 48:168–174. doi:10.1016/j.enbuild.2012.01.025
Chou J-S, Hsu Y-C, Lin L-T (2014) Smart meter monitoring and data mining techniques for predicting refrigeration system performance. Expert Syst Appl 41:2144–2156. doi:10.1016/j.eswa.2013.09.013
Esen H, Inalli M, Sengur A, Esen M (2008a) Artificial neural networks and adaptive neuro-fuzzy assessments for ground-coupled heat pump system. Energy Build 40:1074–1083. doi:10.1016/j.enbuild.2007.10.002
Esen H, Inalli M, Sengur A, Esen M (2008b) Modeling a ground-coupled heat pump system by a support vector machine. Renew Energy 33:1814–1823. doi:10.1016/j.renene.2007.09.025
Esen H, Inalli M, Sengur A, Esen M (2008c) Modelling a ground-coupled heat pump system using adaptive neuro-fuzzy inference systems. Int J Refrig 31:65–74. doi:10.1016/j.ijrefrig.2007.06.007
Esen H, Inalli M, Sengur A, Esen M (2008d) Performance prediction of a ground-coupled heat pump system using artificial neural networks. Expert Syst Appl 35:1940–1948. doi:10.1016/j.eswa.2007.08.081
Esen H, Inalli M, Sengur A, Esen M (2008) Predicting performance of a ground-source heat pump system using fuzzy weighted pre-processing-based ANFIS. Build Environ 43:2178–2187. doi:10.1016/j.buildenv.2008.01.002
Fernando SL, de Andrés J, Lorca P, de Cos Juez FJ (2012) A hybrid device for the solution of sampling bias problems in the forecasting of firms’ bankruptcy. Expert Syst Appl 39:7512–7523. doi:10.1016/j.eswa.2012.01.135
Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat 19:1–67. doi:10.2307/2241837
Friedman JH, Roosen CB (1995) An introduction to multivariate adaptive regression splines. Stat Method Med Res 4:197–217. doi:10.1177/096228029500400303
Gao W, Liu S (2011) Improved artificial bee colony algorithm for global optimization. Inform Process Lett 111:871–882. doi:10.1016/j.ipl.2011.06.002
García NPJ, Martínez TJ, de Cos Juez FJ, Sánchez LF (2012) Using multivariate adaptive regression splines and multilayer perceptron networks to evaluate paper manufactured using eucalyptus globulus. Appl Math Comput 219:755–763. doi:10.1016/j.amc.2012.07.001
Heil MT, Selden TM (2001) Carbon emissions and economic development: future trajectories based on historical experience. Environ Develop Econ 6:63–83
Hong W-C (2011) Electric load forecasting by seasonal recurrent SVR (support vector regression) with chaotic artificial bee colony algorithm. Energy 36:5568–5578. doi:10.1016/j.energy.2011.07.015
International Energy Agency (2009) Gadgets and gigawatts : policies for energy efficient electronics. OECD, IEA, Paris
Küçüksille EU, Selbaş R, Şencan A (2009) Data mining techniques for thermophysical properties of refrigerants. Energy Convers Manag 50:399–412. doi:10.1016/j.enconman.2008.09.002
Küçüksille EU, Selbaş R, Şencan A (2011) Prediction of thermodynamic properties of refrigerants using data mining. Energy Convers Manag 52:836–848. doi:10.1016/j.enconman.2010.08.009
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Erciyes University, Engineering Faculty, Computer Engineering Department (citeulike-article-id:6592152)
Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214:108–132. doi:10.1016/j.amc.2009.03.090
Kıran MS, Özceylan E, Gündüz M, Paksoy T (2012) Swarm intelligence approaches to estimate electricity energy demand in Turkey. Knowl Based Syst 36:93–103. doi:10.1016/j.knosys.2012.06.009
Kriner M (2007) Survival analysis with multivariate adaptive regression splines. Muchen University
Lee DG, Lee BW, Chang SH (1997) Genetic programming model for long-term forecasting of electric power demand. Electr Power Syst Res 40:17–22. doi:10.1016/S0378-7796(96)01125-X
Lee T-S, Chiu C-C, Chou Y-C, Lu C-J (2006) Mining the customer credit using classification and regression tree and multivariate adaptive regression splines. Comput Stat Data Anal 50:1113–1130. doi:10.1016/j.csda.2004.11.006
Li H, Liu K, Li X (2010) A comparative study of artificial bee colony, bees algorithms and differential evolution on numerical benchmark problems. In: Cai Z, Tong H, Kang Z, Liu Y (eds) Computational intelligence and intelligent systems, vol 107. Communications in computer and information science. Springer, Berlin, pp 198–207. doi:10.1007/978-3-642-16388-3_22
Li J-Q, Pan Q-K, Gao K-Z (2011) Pareto-based discrete artificial bee colony algorithm for multi-objective flexible job shop scheduling problems. Int J Adv Manuf Technol 55:1159–1169. doi:10.1007/s00170-010-3140-2
Lu C-J, Lee T-S, Lian C-M (2012) Sales forecasting for computer wholesalers: a comparison of multivariate adaptive regression splines and artificial neural networks. Decis Support Syst 54:584–596. doi:10.1016/j.dss.2012.08.006
Meesad P, Unger H, Boonkrong S (2013) The 9th international conference on computing and information technology (IC2IT2013): 9th–10th May 2013. King Mongkut’s University of Technology, North Bangkok. Springer
Orenstein T, Kohavi Z, Pomeranz I (1995) An optimal algorithm for cycle breaking in directed graphs. J Electron Test 7:71–81. doi:10.1007/BF00993315
Ozgoren M, Bilgili M, Babayigit O (2012) Hourly performance prediction of ammonia-water solar absorption refrigeration. Appl Therm Eng 40:80–90. doi:10.1016/j.applthermaleng.2012.01.058
Ren C, An N, Wang J, Li L, Hu B, Shang D (2014) Optimal parameters selection for BP neural network based on particle swarm optimization: a case study of wind speed forecasting. Knowl Based Syst 56:226–239. doi:10.1016/j.knosys.2013.11.015
Schmalensee R, Stoker TM, Judson RA (1995) World energy consumption and carbon dioxide emission: 1950–2050 Sloan school of management. Massachusetts Institute of Technology, Cambridge
Sekulic S, Kowalski BR (1992) MARS: a tutorial. J Chemom 6:199–216. doi:10.1002/cem.1180060405
Şahin A, Kılıç B, Kılıç U (2011) Design and economic optimization of shell and tube heat exchangers using artificial bee colony (ABC) algorithm. Energy Convers Manag 52:3356–3362. doi:10.1016/j.enconman.2011.07.003
Taylan P, Weber G-W, Özkurt FY (2010) A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization. TOP 18:377–395. doi:10.1007/s11750-010-0155-7
Vidoli F (2011) Evaluating the water sector in Italy through a two stage method using the conditional robust nonparametric frontier and multivariate adaptive regression splines. Eur J Oper Res 212:583–595. doi:10.1016/j.ejor.2011.02.003
Wada K, Akimoto K, Sano F, Oda J, Homma T (2012) Energy efficiency opportunities in the residential sector and their feasibility. Energy 48:5–10. doi:10.1016/j.energy.2012.01.046
Wang E, Fung AS, Qi C, Leong WH (2012) Performance prediction of a hybrid solar ground-source heat pump system. Energy Build 47:600–611. doi:10.1016/j.enbuild.2011.12.035
Yu Z, Haghighat F, Fung BCM, Yoshino H (2010) A decision tree method for building energy demand modeling. Energy Build 42:1637–1646. doi:10.1016/j.enbuild.2010.04.006
Zhou Y, Leung H (2007) Predicting object-oriented software maintainability using multivariate adaptive regression splines. J Syst Softw 80:1349–1361. doi:10.1016/j.jss.2006.10.049
Acknowledgments
The authors would like to thank San Der Saving Energy Technology, Ltd., for providing technical and experiment support at the Taoyuan Bureau of Employment and Vocational Training. Gratitude is further extended to the National Science Council, Taiwan, for their financial support of this research under Grant No. NSC100-2628-E-011-022-MY3.
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Cheng, MY., Chou, JS. & Cao, MT. Nature-inspired metaheuristic multivariate adaptive regression splines for predicting refrigeration system performance. Soft Comput 21, 477–489 (2017). https://doi.org/10.1007/s00500-015-1798-y
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DOI: https://doi.org/10.1007/s00500-015-1798-y