Over the past several decades, several air pollution prevention measures have been developed in response to the growing concern over air pollution. Using models to anticipate air pollution accurately aids in the timely prevention and management of air pollution. However, the spatial-temporal air quality aspects were not properly taken into account during the prior model construction. In this study, the distance correlation coefficient (DC) between measurements made in various monitoring stations is used to identify appropriate correlated monitoring stations. To derive spatial-temporal correlations for modeling, the causality relationship between measurements made in various monitoring stations is analyzed using Transfer Entropy (TE). This work explores the process of identifying a piecewise affine (PWA) model using a larger dataset and suggests a unique hierarchical clustering-based identification technique with model structure selection. This work improves the BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies) by introducing Kullback-Leibler (KL) Divergence as the dissimilarity between clusters for handling clusters with arbitrary shapes. The number of clusters is automatically determined using a cluster validity metric. The task is formulated as a sparse optimization problem, and the model structure is selected using parameter estimations. Beijing air quality data is used to demonstrate the method, and the results show that the proposed strategy may produce acceptable forecast performance.
YazdiM.D., et al. The effect of long-term exposure to air pollution and seasonal temperature on hospital admissions with cardiovascular and respiratory disease in the United States: A difference-in-differences analysis, The Science of the Total Environment (2022), 156855.
2.
AtkinsonR.W., KangS., AndersonH.R., MillsI.C. and WaltonH., Epidemiological time series studies of PM2.5 and daily mortality and hospital admissions: a systematic review and meta-analysis, Thorax69 (2014), 660–665.
3.
WangJ. and SongG., A deep spatial-temporal ensemble model for air quality prediction, Neurocomputing314 (2018), 198–206.
4.
ZhangT., RamakrishnanR. and LivnyM., BIRCH: A new data clustering algorithm and its applications, Data Mining and Knowledge Discovery1 (1997), 141–182.
5.
WanL. and YangJ., Advanced split BIRCH algorithm in reconfigurable network, J Networks8 (2013), 2050–2056.
6.
RenZ.X. and JiX.X., On prediction of air pollutants with Takagi-Sugeno models based on a hierarchical clustering identification method, 31. Art. no, Atmospheric Pollution Research14(4) (1017), 101731.
7.
RangelM.G.L., HenríquezJ.R., CostaJ.A.M. and JúniorJ.C.d.L., An assessment of dispersing pollutants from the pre-harvest burning of sugarcane in rural areas in the northeast of Brazil, Atmospheric Environment178 (2018), 265–281.
8.
YangZ., et al. Modification and validation of the Gaussian plume model (GPM) to predict ammonia and particulate matter dispersion, Atmospheric Pollution Research11 (2020), 1063–1072.
9.
BrayC.D., et al. Evaluating ammonia (NH 3) predictions in the NOAA National Air Quality Forecast Capability (NAQFC) using in-situ aircraft and satellite measurements from the CalNexcampaign, Atmospheric Environment163 (2017), 65–76.
10.
Lago KitagawaY.K., et al. Source apportionment modelling of PM2.5 using CMAQ-ISAM over a tropical coastal-urban area, Atmospheric Pollution Research, 2021.
11.
ThongthammachartT., ArakiS., ShimaderaH., EtoS., MatsuoT. and KondoA., An integrated model combining random forests and WRF/CMAQ model for high accuracy spatiotemporal PM2.5 predictions in the Kansai region of Japan, Atmospheric Environment262 (2021), 118620.
12.
KooY.-S., ChoiD.-R., KwonH.Y., JangY.-K. and HanJ.-S., Improvement of PM10 prediction in East Asia using inverse modeling, Atmospheric Environment106 (2015), 318–328.
13.
SaideP.E., et al. Forecasting urban PM10 and PM2.5 pollution episodes in very stable nocturnal conditions and complex terrain using WRF–Chem CO tracer model, Atmospheric Environment45 (2011), 2769–2780.
14.
ZhouG., et al. Numerical air quality forecasting over eastern China: An operational application of WRF-Chem, Atmospheric Environment153 (2017), 94–108.
15.
García NietoP.J., Sánchez LasherasF., García–GonzaloE. and de Cos JuezF.J., PM10 concentration forecasting in the metropolitan area of Oviedo (Northern Spain) using models based on SVM, MLP, VARMA and ARIMA: A case study, The Science of the Total Environment621 (2018), 753–761.
16.
ElbayoumiM., RamliN.A. and YusofN.F.F.M., Development and comparison of regression models and feedforward backpropagation neural network models to predict seasonal indoor PM2.5–10 and PM2.5 concentrations in naturally ventilated schools, Atmospheric Pollution Research6 (2015), 1013–1023.
17.
DomanskaD. and WojtylakM., Application of fuzzy time series models for forecasting pollution concentrations, Expert Syst Appl39 (2012), 7673–7679.
18.
YangH., ZhuZ., LiC. and LiR., A novel combined forecasting system for air pollutants concentration based on fuzzy theory and optimization of aggregation weight, Appl Soft Comput87 (2020), 105972.
19.
KaboodvandpourS., AmanollahiJ., QhavamiS. and MohammadiB., Assessing the accuracy of multiple regressions, ANFIS and ANN models in predicting dust storm occurrences in Sanandaj, Iran, Natural Hazards78 (2015), 879–893.
20.
LiY., JiangP., SheQ. and LinG., Research on air pollutant concentration prediction method based on self-adaptive neuro-fuzzy weighted extreme learning machine, Environmental Pollution241 (2018), 1115–1127.
21.
LinY.-C., LeeS.-J., OuyangC.-S. and WuC.-H., Air quality prediction by neuro-fuzzy modeling approach, Appl Soft Comput86 (2020).
22.
Nabavi-PelesaraeiA., RafieeS., MohtasebiS.S., Hosseinzadeh-BandbafhaH., ChauK.-W.Comprehensive model of energy, environmental impacts and economic in rice milling factories by coupling adaptive neuro-fuzzy inference system and life cycle assessment, Journal of Cleaner Production, 2019.
23.
XieQ., NiJ.-Q. and SuZ., A prediction model of ammonia emission from a fattening pig room based on the indoor concentration using adaptive neuro fuzzy inference system, Journal of Hazardous Materials325 (2017), 301–309.
24.
ZeinalnezhadM., ChofrehA.G., GoniF.A. and KlemesJ.J., Air pollution prediction using semi-experimental regression model and adaptive neuro-fuzzy inference system, Journal of Cleaner Production261 (2020), 121218.
25.
LeongW.C., KelaniR.O., AhmadZ.A.Prediction of air pollution index (API) using support vector machine (SVM), Journal of Environmental Chemical Engineering, 2020.
26.
SuX., AnJ., ZhangY., ZhuP. and ZhuB., Prediction of ozone hourly concentrations by support vector machine and kernel extreme learning machine using wavelet transformation and partial least squares methods, Atmospheric Pollution Research11 (2020), 51–60.
27.
SuleimanA., TightM.R., QuinnA.Applying machine learning methods in managing urban concentrations of traffic-related particulate matter (PM10 and PM2.5), Atmospheric Pollution Research, 2019.
28.
ShamsoddiniA., AboodiM., KaramiJ.Tehran air pollutants prediction based on random forest feature selection method, ISPRS –International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (2017), 483–488.
29.
YangW., DengM., XuF. and WangH., Prediction of hourly PM 2.5 using a space-time support vector regression model, Atmospheric Environment181 (2018), 12–19.
30.
AlimissisA., PhilippopoulosK., TzanisC.G., DeligiorgiD.Spatial estimation of urban air pollution with the use of artificial neural network models, Atmospheric Environment, 2018.
31.
FengX., LiQ., ZhuY., HouJ., JinL. and WangJ., Artificial neural networks forecasting of PM2.5 pollution using air mass trajectory based geographic model and wavelet transformation, Atmospheric Environment107 (2015), 118–128.
32.
ParkS., et al. Predicting PM10 concentration in Seoul metropolitan subway stations using artificial neural network (ANN), Journal of Hazardous Materials341 (2018), 75–82.
33.
SayeedA., ChoiY., EslamiE., LopsY., RoyA. and JungJ., Using a deep convolutional neural network to predict ozone concentrations, 24 hours in advance, Neural Networks: The Official Journal of the International Neural Network Society121 (2020), 396–408.
34.
QiY., LiQ., KarimianH. and LiuD., A hybrid model for spatiotemporal forecasting of PM2.5 based on graph convolutional neural network and long short-term memory, The Science of the Total Environment664 (2019), 1–10.
35.
Chang-HoiH., et al. Development of a PM2.5 prediction model using a recurrent neural network algorithm for the Seoul metropolitan area, Republic of Korea, Atmospheric Environment245 (2021), 118021.
36.
FanJ., LiQ., HouJ., FengX.D., KarimianH., LinS.A spatiotemporal prediction framework for air pollution based on deep RNN, ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences (2017), 15–22.
37.
HuangY., YingJ.J.-C. and TsengV.S., Spatio-attention embedded recurrent neural network for air quality prediction, Knowl Based Syst233 (2021), 107416.
38.
Becerra-RicoJ., Aceves-FernándezM.A., Esquivel-EscalanteK., OrtegaJ.C.P.Airborne particle pollution predictive model using Gated Recurrent Unit (GRU) deep neural networks, Earth Science Informatics (2020), 1–14.
39.
HuL., WangC., YeZ. and WangS., Estimating gaseous pollutants from bus emissions: A hybrid model based on GRU and XGBoost, The Science of the Total Environment783 (2021), 146870.
40.
XuR., DengX., WanH.S., CaiY., PanX.A deep learning method to repair atmospheric environmental quality data based on Gaussian diffusion, Journal of Cleaner Production, 2021.
41.
LuX., et al. Development and application of a hybrid long-short term memory –three dimensional variational technique for the improvement of PM2.5 forecasting, The Science of the Total Environment770 (2021), 144221.
42.
MaJ., DingY., ChengJ.C.P., JiangF., WanZ.A temporal-spatial interpolation and extrapolation method based on geographic Long Short-Term Memory neural network for PM2.5, Journal of Cleaner Production, 2019.
43.
WuC.-l., HeH.-D., SongR.-F., PengZ.-R.Prediction of air pollutants on roadside of the elevated roads with combination of pollutants periodicity and deep learning method, Building and Environment, 2021.
44.
ZhaoJ., DengF., CaiY. and ChenJ., Long short-term memory –Fully connected (LSTM-FC) neural network for PM2.5 concentration prediction, Chemosphere220 (2019), 486–492.
45.
MaJ., LiZ., ChengJ.C.P., DingY., LinC. and XuZ., Air quality prediction at new stations using spatially transferred bi-directional long short-term memory network, The Science of the Total Environment705 (2020), 135771.
46.
ZhangB., ZhangH., ZhaoG. and LianJ., Constructing a PM2.5 concentration prediction model by combining auto-encoder with Bi-LSTM neural networks, Environ Model Softw124 (2020), 104600.
47.
PakU., et al. Deep learning-based PM2.5 prediction considering the spatiotemporal correlations: A case study of Beijing, China, The Science of the Total Environment699 (2020), 133561.
48.
ZhuJ., DengF., ZhaoJ. and ZhengH., Attention-based parallel networks (APNet) for PM2.5 spatiotemporal prediction, The Science of the Total Environment769 (2021), 145082.
49.
ZhangB., ZouG., QinD., NiQ., MaoH. and LiM., RCL-Learning: ResNet and convolutional long short-term memory-based spatiotemporal air pollutant concentration prediction model, Expert Syst Appl207 (2022), 118017.
50.
ZhangB., et al. Deep learning for air pollutant concentration prediction: A review, Atmospheric Environment, 2022.
51.
YanR., LiaoJ., YangJ., SunW., NongM. and LiF., Multi-hour and multi-site air quality index forecasting in Beijing using CNN, LSTM, CNN-LSTM, and spatiotemporal clustering, Expert Syst Appl169 (2021), 114513.
52.
LeCunY., BengioY. and HintonG., Deep Learning, Nature521 (2015), 436–444.
53.
BartlettP.L., MontanariA. and RakhlinA., Deep learning: a statistical viewpoint, Acta Numerica30 (2021), 87–201.
54.
RenZ., An optimized excitation signal design for identification of PWA model and application to automotive throttles, Measurement and Control56(3-4) (2023), 844–856.
55.
WangJ., SongC., ZhaoJ. and XuZ., A PWA model identification method for nonlinear systems using hierarchical clustering based on the gap metric, Comput Chem Eng138 (2020), 106838.
56.
DuY., LiuF., QiuJ. and BussM., Online Identification of Piecewise Affine Systems Using Integral Concurrent Learning, IEEE Transactions on Circuits and Systems I: Regular Papers68 (2021), 4324–4336.
57.
VaeziM. and IzadianA., Piecewise Affine System Identification of a Hydraulic Wind Power Transfer System, IEEE Transactions on Control Systems Technology23 (2015), 2077–2086.
58.
BreschiV., PigaD. and BemporadA., Piecewise affine regression via recursive multiple least squares and multicategory discrimination, Autom73 (2016), 155–162.
59.
Sindareh-EsfahaniP. and PieperJ.K., Machine learning–based piecewise affine model of wind turbines during maximum power point tracking, Wind Energy23 (2020), 404–422.
60.
YangY., XiangC., GaoS. and LeeT.H., Data-driven identification and control of nonlinear systems using multiple NARMA-L2 models, International Journal of Robust and Nonlinear Control28 (2018), 3806–3833.
61.
LauerF.On the complexity of piecewise affine system identification, ArXiv, vol. abs/1509.02348, 2015.
62.
SunX., HuW., CaiY., WongP.K. and ChenL., Identification of a piecewise affine model for the tire cornering characteristics based on experimental data, Nonlinear Dynamics101(2) (2020), 857–874.
63.
SongC., WangJ., MaX. and ZhaoJ., A PWA model identification method based on optimal operating region partition with the output-error minimization for nonlinear systems, Journal of Process Control88 (2020), 1–9.
64.
ZhangQ., JingH., LiuZ., JiangY. and GuM., A novel PWA lateral dynamics modeling method and switched T-S observer design for vehicle sideslip angle estimation, IEEE Transactions on Industrial Electronics69(2) (2022), 1847–1857.
65.
SzekelyG.J., RizzoM.L. and BakirovN.K., Measuring and testing dependence by correlation of distances, Annals of Statistics35(6) (2007), 2769–2794.
66.
SchreiberT., Measuring information transfer, Physical Review Letters85(2) (2000), 461–464.
67.
RodgersJ.L. and NicewanderW.A., Thirteen ways to look at the correlation coefficient, The American Statistician42 (1988), 59–66.
68.
RenZ., KrollA., SofskyM. and LaubensteinF., On physical and data-driven modeling of systems with friction: methods and application to automotive throttles, At-Automatisierungstechnik61(3) (2013), 155–171.
69.
TibshiraniR., Regression Shrinkage and Selection via the Lasso, Journal of the Royal Statistical Society Series b-Methodological58 (1996), 267–288.
70.
HastieT.J., TibshiraniR., FriedmanJ.H.The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition, in Springer Series in Statistics, 2005.
71.
Saberi-MovahedF., NajafzadehM. and MehrpooyaA., receiving more accurate predictions for longitudinal dispersion coefficients in water pipelines: Training group method of data handling using extreme learning machine conceptions, Water Resources Management34 (2020), 529–561.
72.
NajafzadehM. and AnvariS., Long-lead streamflow forecasting using computational intelligence methods while considering uncertainty issue, Environmental Science and Pollution Research30 (2023), 84474–84490.
