Abstract
Air pollution prevention and control is an important way to eliminate haze, and air quality prediction can provide predictive information for air pollution prevention and people’s health. Therefore, it is of great practical usefulness to establish a scientific and effective air quality prediction model. Combined forecasting is a popular statistical method for air pollution forecasting, which generally includes two steps of individual model selection and weight determination. This research introduces LASSO for individual models selection, and ELM to establish a nonlinear combined forecasting model, named CEEMD-LASSO-ELM. LASSO can not only select individual models, but also avoids the possible collinearity between the selected individual models. Daily air quality index (AQI) series of Guangzhou, Kunming, Lanzhou and Hulunbuir are selected to verify the feasibility and effectiveness of the proposed CEEMD-LASSO-ELM model. Combined with CEEMD, seven comparative models are Random-ELM, Rank-ELM, Random-LR, Rank-LR, LASSO-GRNN, LASSO-PSOGSASVR and LASSO-LR. The data analysis shows that the proposed CEEMD-LASSO-ELM model has better prediction accuracy and stronger generalization ability. Taking Lanzhou as an example, the MAPE of CEEMD-LASSO-ELM model is 1.813% lower than that of the seven comparative models on average.
Graphical abstract
Similar content being viewed by others
References
Bates JM, Granger CWJ (1969) The combination of forecasts. J Oper Res Soc 20(4):451–468. https://doi.org/10.1057/jors.1969.103
Breiman L (1996) Stacked regressions. Machine Learning 24: 49–64.https://doi.org/10.1023/A:1018046112532
Bunn DW (1975) A Bayesian approach to the linear combination of forecasts. J Oper Res Soc 26(2):325–329. https://doi.org/10.1057/jors.1975.67
Chattopadhyay S, Bandyopadhyay G (2007) Artificial neural network with backpropagation learning to predict mean monthly total ozone in Arosa. Switzerland Int J Remote Sens 28(20):4471–4482. https://doi.org/10.1080/01431160701250440
Che JX (2015) Optimal sub-models selection algorithm for combination forecasting model. Neurocomputing 151:364–375. https://doi.org/10.1016/j.neucom.2014.09.028
Chen KY (2011) Combining linear and nonlinear model in forecasting tourism demand. Expert Syst Appl 38(8):10368–10376. https://doi.org/10.1016/j.eswa.2011.02.049
Chen GJ, Li KK, Chung TS, Sun HB, Tang GQ (2001) Application of an innovative combined forecasting method in power system load forecasting. Elect Power Syst Res 59(2):131–137. https://doi.org/10.1016/S0378-7796(01)00137-7
Clemen RT, Winkler RL (1986) Combining economic forecasts. J Bus Econ Stat 4(1):39–46. https://doi.org/10.1080/07350015.1986.10509492
Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297. https://doi.org/10.1023/A:1022627411411
Du P, Wang JZ, Hao Y, Niu T, Yang WD (2020) A novel hybrid model based on multi-objective Harris hawks optimization algorithm for daily PM2.5 and PM10 forecasting. Applied Soft Computing 96:106620. https://doi.org/10.1016/j.asoc.2020.106620
Durao RM, Mendes MT, Pereira MJ (2016) Forecasting O3 levels in industrial area surroundings up to 24h in advance, combining classification trees and MLP models. Atmos Pollut Res 7(6):961–970. https://doi.org/10.1016/j.apr.2016.05.008
Granger CWJ (1989) Invited review combining forecasts—twenty years later. J Forecast 8(3):167–173. https://doi.org/10.1002/for.3980080303
Granger CWJ, Ramanathan R (1984) Improved methods of combining forecasts. J Forecast 3(2):197–204. https://doi.org/10.1002/for.3980030207
Gupta S, Wilton PC (1987) Combination of forecasts: an extension. Manage Sci 33(3):356–372. https://doi.org/10.1287/mnsc.33.3.356
Huang GB, Zhu QY, Siew CK (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No. 04CH37541). IEEE 2: 985–990. https://doi.org/10.1109/IJCNN.2004.1380068
Karmy JP, Maldonado S (2019) Hierarchical time series forecasting via support vector regression in the European travel retail industry. Expert Syst Appl 137:59–73. https://doi.org/10.1016/j.eswa.2019.06.060
Kennedy J, Eberhart R (1995) Particle swarm optimization. Proceedings of ICNN'95—International Conference on Neural Networks. IEEE 4: 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
Lai YC, Dzombak DA (2020) Use of the autoregressive integrated moving average (ARIMA) model to forecast near-term regional temperature and precipitation. Weather Forecast 35(3):959–976. https://doi.org/10.1175/WAF-D-19-0158.1
Lecun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324. https://doi.org/10.1109/5.726791
Lemke C, Gabrys B (2010) Meta-learning for time series forecasting and forecast combination. Neurocomputing 73(10–12):2006–2016. https://doi.org/10.1016/j.neucom.2009.09.020
Li HM, Wang JZ, Li RR, Lu HY (2019) Novel analysis–forecast system based on multi-objective optimization for air quality index. J Clean Prod 208:1365–1383. https://doi.org/10.1016/j.jclepro.2018.10.129
Liu DJ, Li L (2015) Application study of comprehensive forecasting model based on entropy weighting method on trend of PM25 concentration in Guangzhou, China. Int J Environ Res Public Health 12(6):7085–7099. https://doi.org/10.3390/ijerph120607085
Liu XL, Moreno B, García AS (2016) A grey neural network and input-output combined forecasting model. Primary energy consumption forecasts in Spanish economic sectors. Energy 115:1042–1054. https://doi.org/10.1016/j.energy.2016.09.017
Mirjalili S, Hashim SZM (2010) A new hybrid PSOGSA algorithm for function optimization. 2010 International Conference on Computer and Information Application. IEEE 374–377. https://doi.org/10.1109/ICCIA.2010.6141614.
Mo LL, Xie L, Jiang XY, Teng G, Xu LX, Xiao J (2018) GMDH-based hybrid model for container throughput forecasting: Selective combination forecasting in nonlinear subseries. Appl Soft Comput 62:478–490. https://doi.org/10.1016/j.asoc.2017.10.033
Mu B, Li S, Yuan S (2017) An improved effective approach for urban air quality forecast. 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD). IEEE 935–942. https://doi.org/10.1109/FSKD.2017.8393403
Niu DX, Ma TN, Liu BY (2017) Power load forecasting by wavelet least squares support vector machine with improved fruit fly optimization algorithm. J Comb Optim 33(3):1122–1143. https://doi.org/10.1007/s10878-016-0027-7
Rashedi E, Nezamabadi PH, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248. https://doi.org/10.1016/j.ins.2009.03.004
Shen SJ, Li G, Song HY (2011) Combination forecasts of international tourism demand. Ann Tour Res 38(1):72–89. https://doi.org/10.1016/j.annals.2010.05.003
Shi SM, Xu LD, Liu B (1996) Applications of artificial neural networks to the nonlinear combination of forecasts. Expert Syst 13(3):195–201. https://doi.org/10.1111/j.1468-0394.1996.tb00119.x
Song C, Fu XS (2020) Research on different weight combination in air quality forecasting models. J Clean Prod 261:1211. https://doi.org/10.1016/j.jclepro.2020.121169
Specht DF (1991) A general regression neural network. IEEE Trans Neural Netw 2(6):568–576. https://doi.org/10.1109/72.97934
Tibshirani R (1996) Regression shrinkage and selection via the LASSO. J Roy Stat Soc: Ser B (Methodol) 58(1):267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
Wang B, Jiang QC, Jiang P (2019a) A combined forecasting structure based on the L1 norm: application to the air quality. J Environ Manage 246:299–313. https://doi.org/10.1016/j.jenvman.2019.05.124
Wang Q, Li SY, Li RR (2019b) Will Trump’s coal revival plan work? -comparison of results based on the optimal combined forecasting technique and an extended IPAT forecasting technique. Energy 169:762–775. https://doi.org/10.1016/j.energy.2018.12.045
Wu ZH, Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv Adapt Data Anal 1(01):1–41. https://doi.org/10.1142/S1793536909000047
Wu QL, Lin HX (2019) Daily urban air quality index forecasting based on variational mode decomposition, sample entropy and LSTM neural network. Sustain Cities Soc 50:101657. https://doi.org/10.1016/j.scs.2019.101657
Xiao L, Wang JZ, Dong Y, Wu J (2015) Combined forecasting models for wind energy forecasting: a case study in China. Renew Sustain Energy Rev 44:271–288. https://doi.org/10.1016/j.rser.2014.12.012
Yang ZS, Wang J (2017) A new air quality monitoring and early warning system: air quality assessment and air pollutant concentration prediction. Environ Res 158:105–117. https://doi.org/10.1016/j.envres.2017.06.002
Yang ZS, Wang J (2018) A combination forecasting approach applied in multistep wind speed forecasting based on a data processing strategy and an optimized artificial intelligence algorithm. Appl Energy 230:1108–1125. https://doi.org/10.1016/j.apenergy.2018.09.037
Yang AL, Li WD, Yang X (2019) Short-term electricity load forecasting based on feature selection and least squares support vector machines. Knowl-Based Syst 163:159–173. https://doi.org/10.1016/j.knosys.2018.08.027
Yao SJ, Song YH, Zhang LZ, Cheng XY (2000) Wavelet transform and neural networks for short-term electrical load forecasting. Energy Convers Manage 41(18):1975–1988. https://doi.org/10.1016/S0196-8904(00)00035-2
Yeh JR, Shieh JS, Huang NE (2010) Complementary ensemble empirical mode decomposition: A novel noise enhanced data analysis method. Adv Adapt Data Anal 2(02):135–156. https://doi.org/10.1142/S1793536910000422
Zhang GP (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175. https://doi.org/10.1016/S0925-2312(01)00702-0
Zhang H, Mu JH (2021) A back propagation neural network-based method for intelligent decision-making. Complexity 2021:1–11. https://doi.org/10.1155/2021/6610797
Zhang SH, Wang JY, Guo ZH (2019) Research on combined model based on multi-objective optimization and application in time series forecast. Soft Comput 23(22):11493–11521. https://doi.org/10.1007/s00500-018-03690-w
Zhu SL, Wang JZ, Zhao WG, Wang JJ (2011) A seasonal hybrid procedure for electricity demand forecasting in China. Appl Energy 88(11):3807–3815. https://doi.org/10.1016/j.apenergy.2011.05.005
Zhu SL, Yang L, Wang WN, Liu XR, Lu MM, Shen XP (2018) Optimal-combined model for air quality index forecasting: 5 cities in North China. Environ Pollut 243:842–850. https://doi.org/10.1016/j.envpol.2018.09.025
Zhu SL, Wang X, Shi NY, Lu MM (2020) CEEMD-subset-OASVR-GRNN for ozone forecasting: Xiamen and Harbin as cases. Atmos Pollut Res 11(4):744–754. https://doi.org/10.1016/j.apr.2020.01.003
Zhu Y, Zhou X (2019) Prediction of air quality index based on wavelet transform combination model. 2019 11th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC). IEEE. 1:157–160. https://doi.org/10.1109/IHMSC.2019.00044
Acknowledgements
The work is partially supported by Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2022-16), 2022 Gansu Province Outstanding Graduate Student "Innovation Star" Project (Grant No. 2022CXZX-055), and National Natural Science Foundation of China (Grant No. 71971105). In this research, Suling Zhu, Peiqi Wang and Ruyi Wang are the co-first authors.
Author information
Authors and Affiliations
Contributions
SZ: conceived and designed the study. SZ and PW: designed the algorithms, preliminary experiment, optimized the proposed model through the experimental results, and completed the writing of the manuscript. RW: analyzed and checked the data. RW, PW, ML, XW, and JC: reviewed and edited the manuscript. All authors read and approved the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors have no competing interests to declare that are relevant to the content of this article.
Additional information
Handling Editor: Luiz Duczmal.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhu, S., Wang, P., Wang, R. et al. CEEMD-LASSO-ELM nonlinear combined model of air quality index prediction for four cities in China. Environ Ecol Stat 30, 309–334 (2023). https://doi.org/10.1007/s10651-023-00562-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10651-023-00562-x