Soft Computing Applications in Air Quality Modeling: Past, Present, and Future

Abstract

Air quality models simulate the atmospheric environment systems and provide increased domain knowledge and reliable forecasting. They provide early warnings to the population and reduce the number of measuring stations. Due to the complexity and non-linear behavior associated with air quality data, soft computing models became popular in air quality modeling (AQM). This study critically investigates, analyses, and summarizes the existing soft computing modeling approaches. Among the many soft computing techniques in AQM, this article reviews and discusses artificial neural network (ANN), support vector machine (SVM), evolutionary ANN and SVM, the fuzzy logic model, neuro-fuzzy systems, the deep learning model, ensemble, and other hybrid models. Besides, it sheds light on employed input variables, data processing approaches, and targeted objective functions during modeling. It was observed that many advanced, reliable, and self-organized soft computing models like functional network, genetic programming, type-2 fuzzy logic, genetic fuzzy, genetic neuro-fuzzy, and case-based reasoning are rarely explored in AQM. Therefore, the partially explored and unexplored soft computing techniques can be appropriate choices for research in the field of air quality modeling. The discussion in this paper will help to determine the suitability and appropriateness of a particular model for a specific modeling context.

1. Introduction

Air pollutants cause widespread detrimental effects on physical, biological, and economic systems. The prominent and dangerous pollutants are carbon oxides (CO_x), nitrogen oxides (NO_x), Sulphur oxides (SO_x), ozone (O₃), lead (Pb), respirable suspended particles or particulate matters (PM_2.5 and PM₁₀), and total volatile organic compounds (TVOC) [1,2,3,4]. Exposure to such pollutants causes many diseases, including respiratory diseases, type 2 diabetes, asthma, allergies, and cancer [5,6,7,8,9]. Typically, the environmental regulatory agencies regulate the atmospheric quality against high air pollutant concentrations to protect human health by minimizing different detrimental effects. Air quality models play a vital role in assessing the quality of the atmosphere. They can stimulate the health of the atmosphere and provide increasing domain knowledge and reliable forecasting. Air pollutant prediction models can provide early warnings, and their effective utilization can reduce significant numbers of measuring and data acquisition stations [10,11,12]. Therefore, scientists and researchers have explored many predictive tools, such as autoregressive integrated moving average (ARIMA) [13], bias adjustment [14], linear unbiased estimator [15], principal component regression (PCR) [16], non-parametric regression [17], machine learning [18], and hybrid [19] techniques for AQM.

Artificial Intelligence-based (AI) models, especially artificial neural networks (ANN) or the universal approximation approach of any non-linear function, provide flexible, efficient, less assumption dependent, and adaptive modeling techniques for environmental systems. The capability of different forms of neural networks have been investigated for modeling many air pollutants, including CO_x [20], NO_x [20,21], O₃ [22], PM_2.5, and PM₁₀ [23], and SO_x [21] in different locations throughout the world. Another machine-learning tool, namely the support vector machine (SVM) follows the structural risk minimization principle. It performs better than the empirical risk minimization process in minimizing the error of the training data. It maps the training data into a high dimensional feature space (Hilbert space) and turns the nonlinear regression function into a linear one [24,25,26]. Researchers have also employed this tool for the prediction of air pollutant concentrations [27,28,29,30,31]. Besides, evolutionary computational algorithm-driven ANN and SVM models have also been explored in the field of AQM, for instance a genetic-algorithm-tuned ANN modeled the hourly PM₁₀ concentrations in Greece [31].

The fuzzy logic model (FLM) is a powerful tool to deal with the complex engineering problems that are difficult to solve using traditional mathematical models. It can capture the impreciseness of linguistic terms in statements of natural language [32,33,34]. Jorquera et al. [35] have illustrated the effectiveness of FLM in predicting daily maximum O₃ levels. Besides, the combination of neural networks and fuzzy logic models (neuro-fuzzy model) has also received widespread attention in AQM due to their adaptiveness and better generalization performance. For instance, the neuro-fuzzy systems and FLM were employed to model concentrations of O₃ and PM₁₀ [36] and short-term hydrocarbon (HC) concentrations [37]. Moreover, deep learning and deep multi-output long short-term memory (LSTM) neural networks (deep learning) modeled air pollutant concentrations in the work of [38] and [39], respectively. Likewise, the ensemble models are also popular for classification and regression problems that use few learning machines to learn partial solutions for a given problem and combine the solutions to obtain a more generalized but complete solution to the original problem. A model for nitrogen dioxide (NO₂) concentrations in Spain was developed using an ensemble technique [40]. Furthermore, hybrid models combining data processing techniques and various above-mentioned soft computing structures were also investigated for modeling air pollutant concentrations [41,42,43,44,45]. Other models, including GMDH [46], HMM [47], and random forest partitioned (RFP) technique [48], were also explored for AQM in a few cases.

Different kinds of soft computing approaches have been explored in air quality modeling throughout the world. The growing number of studies can create confusion in the selection of appropriate soft computing models amongst the available models. Therefore, there is a continuous need to review articles to guide decision-makers, academics, and researchers. However, only a few review articles are available that discuss soft computing techniques in air quality modeling [11,18,49,50,51]. They are mostly limited to either artificial neural networks or deep learning techniques. Articles covering the whole spectrum of the available soft computing techniques can rarely be found. Besides, in recent years, other AI-based models such as functional networks, genetic programming, type-2 fuzzy logic, genetic fuzzy, genetic neuro-fuzzy, and case-based reasoning models have been successfully used to solve many complex non-linear regression problems, including oil-yield [52], particle size in a fluidized bed reactor [53], flood flows [54], and power system stability [55]. However, such models have not yet been explored significantly in air quality modeling for the prediction of the air pollutant concentration levels. Besides, evolutionary optimization (EO) technique-driven ANN, SVM, extreme learning machines (ELM), and neuro-fuzzy models are also obtaining popularity for their accuracy in predicting problems without EO-driven models. Hence, similar EO-driven techniques can also be explored for air quality modeling. Moreover, the ELM, GMDH, HMM, and RFP models are rarely observed in the current literature for air quality prediction. Furthermore, different hybrid models can also be explored for AQM. Therefore, considering the importance of the AQM issue throughout the world, this study critically reviews and analyzes the existing soft computing models and provides guidelines for future research directions on the exploration of many soft computing models.

This paper is divided into five main sections. The second section will present the analysis of the input selection approaches for soft computing models in air quality modeling. The third section critically evaluates the proposed machine learning models in the literature. The fourth section investigates the potential soft computing models that are assumed to be suitable for air quality modeling. The fifth section reports the conclusions of this study.

2. Input and Output Selection Approaches

Researchers throughout the world mostly use meteorological and air pollutant data for modeling air quality, employing soft computing techniques as inputs. In a few cases, the influence of temporal data, traffic data, satellite data, and geographic data have also been employed. However, researchers rarely used direct industrial emission data, power plant emission data, and other types of data.

Table 1. Inputs and outputs of the soft computing models.

Inputs			Outputs
Meteorological data	Air pollutant data	Geographical data	API or AQI COx NOx O3 Pb PM2.5 PM10 (TSP/RSP) SOx TVOC
General weather condition Temperatures Wind speed Wind direction Wind bearing Atmospheric pressure Relative humidity Solar radiation Sunshine duration Precipitation/rain Air mass origin Moisture content Dew point Urban heat island Visibility Cloud cover Stability class Mixing height Planetary layer height Solar elevation Friction velocity	AQI COx NH3 NOx O3 Pb PM2.5 PM10 (TSP or RSP) SOx TVOC	Altitude Longitude Latitude
		Sustainability and economic parameters
		Gross domestic product Gross inland energy consumption Production of primary coal and lignite Paper and paperboard Round wood Sand wood Refined copper, aluminum, pig iron, crude steel, and fertilizers Incineration of wood Motorization rate
		Other data types
		Direct industrial and thermal power plant data Satellite data (aerosol optical depth) Daily fire pixel observations Drilling diameter Moisture and slit content Rock mass density Rebound hardness number
	Traffic data
	Vehicle movement Vehicle volume Vehicle emission Vehicle type (two- or three-wheelers, diesel- or gasoline-powered)
Temporal data
Hour of the day Day of the week and month Month of the year Weekday or weekend day Sine and cosine of the hour Sine of the weekday

provides the components of different types of data used as inputs for the soft computing techniques in AQM. It also includes the list of modeled air pollutants.

To reduce the volume of the input space by selecting most dominant variables, many different techniques, including cross-correlation analysis (CCA), principal component analysis (PCA), random forest (RF), learning vector quantization (LVQ), and rough set theory (RST), have been explored in literature. Among the mentioned techniques, CCA is the simplest in analyzing the relationship of the multiple time series data. This linear data analysis approach can also be employed to select the inputs of non-linear models [56]. The deployment of CCA reduced the number of input variables and provided better generalization performance while predicting O₃ and PM₁₀ concentrations in Milan, Italy [57]. The PCA is another modern and popular tool in data analysis for extracting relevant information from complex datasets [58,59,60]. This simple and non-parametric method reduces the dimensionality of a given complex dataset by identifying the meaningful underlying variables known as principal components. It provides the optimal information preserving transformations within the class of linear methods [61]. However, typical PCA is suitable for two-dimensional data collected from a steady-state process that contains linear relationships between the variables. Still, in reality, the data are multidimensional and contain nonlinearity [62]. To address such limitations, several extensions, including hierarchical PCA [63], dynamic PCA [64], nonlinear PCA [65], and online adaptive PCA [66], are often employed. Researchers have employed PCA techniques while predicting PM₁₀ and PM_2.5 [41], O₃ [42], RSP [67], an air quality index (AQI), or an air pollution index (API) [68].

The RF is a straightforward technique to compute the contributions of each variable to the decision-making in a high dimensional dataset. It creates multiple trees using classification and regression trees (CART) that grow fully without pruning [69,70,71]. Researchers have employed RF to model air pollutant concentrations including PM_2.5 [71], SO₂ [72,73], NO₂ [72], CO [72], PM₁₀ [72], and O₃ [72]. The RST is another easily understandable and mature mathematical tool that successfully determines the smallest attribute subset that represents similar knowledge of the original attribute set [74]. It has already made tremendous achievements in many fields, including pattern recognition, medical diagnostics, machine learning, and knowledge discovery in the database [75]. Lei et al. [76] simplified the sample structure by reducing unnecessary attributes using RST to improve the training speed of the wavelet neural network while modeling AQI. Besides, the LVQ is an adaptive nearest-neighbor pattern classifier technique. It consists of four layers (input, competitive, linear, and output) that are based on the competitive learning of training data. Details of the LVQ processes can be found in the work of [77]. Jiang et al. [78] employed the LVQ techniques to reduce the number of input variables while modeling PM_2.5 concentrations using a neuro-fuzzy system. Other data processing techniques including wavelet decomposition [47,79], complete ensemble empirical mode decomposition with adaptive noise and variational mode decomposition (CEEMD-ANVMD) [80], fuzzy k-means (FKM), fuzzy c-means (FCM) [81], and others (logarithmic, scaling, and normalization) [82], were also employed to select input variables. Furthermore, the normalization and standardization of the data is a regularly used data pre-processing technique [11].

However, missing data is a regularly encountered phenomenon in AQM that hampers the overall processes and accuracy of the modeling techniques. This can occur due to a wide range of factors, such as errors in the measurement processes, faults in data acquisition, and insufficient sampling. Researchers have recovered the missing data in several well-established techniques in AQM, including linear interpolation [40,47,81], multivariate imputation by chained equations [83], and the expectation maximization (EM) imputation method [47,84]. In many cases, they also followed list-wise and pair-wise deletion approaches in dealing with the missing data [11]. Finally, the accuracy and precision of the AQM techniques are justified using several statistical performance indices (SPI). The SPI includes bias ratio (BR), correlation coefficient (R), determination coefficient (R²), index of agreement (IA), mean absolute error (MAE), mean absolute percentage error (MAPE), mean bias error (MBE), the proportion of systematic error (PSE), root mean squared error (RMSE), time taken (tt), and variance ratio (VR) [85].

3. Analysis of Available Soft Computing Models

Primarily, artificial neural networks (ANN), support vector machines (SVM), evolutionary ANN and SVM, and fuzzy logic and neuro-fuzzy systems are widely used in AQM. Besides, the hybrid techniques combining several soft computing methods are also receiving widespread attention in AQM. The deep learning machine, ensemble model, and other types of soft computing techniques have been employed in a few cases for modeling purposes. An extensive number of papers that use soft computing approaches are summarized in

Table 2. Summary of the soft computing approaches employed for air quality modeling.

Year	Ref.	Study Region	Model Name	Outputs	Year	Ref.	Study Region	Model Name	Outputs
ANN Models					Fuzzy Logic and Neuro-Fuzzy Models
1993	[90]	Šoštanj, Slovenia	MLP-NN	SO2	1995	[91]	Japan	Neuro-fuzzy system	CO
1994	[92]	Mexico	ANN	O3	1998	[35]	Santiago, Chile	Fuzzy logic model	O3
1999	[93]	UK	MLP-NN	O3	2003	[37]	Villa San Giovanni, Italy	Neuro-fuzzy system	HC
1999	[94]	Central London, UK	MLP-NN	NOx	2004	[95]	Seoul, Korea	Neuro-fuzzy system	O3
2000	[96]	Santiago, Chile	MLP-NN	PM2.5	2006	[97]	Zonguldak, Turkey	ANFIS	SO2 and TSP
2001	[98]	Santiago, Chile	ANN	PM2.5	2007	[99]	Mexico City, Mexico	Genetic fuzzy System	O3
2002	[100]	Delhi, India	LM-NN	SO2	2009	[36]	Northern Italy	Neuro-fuzzy system	O3 and PM10
2002	[101]	Kuwait	ANN	O3	2010	[102]	Delhi, India	Neuro-fuzzy system	CO
2005	[103]	Belgium	ANN	PM10	2012	[104]	Dukla, Czech Republic	Fuzzy logic model	O3
2005	[57]	Milan, Italy	FF-NN	O3 and PM10	2012	[105]	Bogotá, Colombia	Genetic fuzzy System	PM10
2005	[106]	US–Mexico border	MLP-NN, RBF-NN, and SMLP-NN	PM2.5	2013	[107]	Johor Bahru, Malaysia	Fuzzy time series	API
2006	[108]	Carcaixent, Spain	MLP-NN	O3	2013	[109]	Tehran, Iran	ANFIS	O3
2006	[110]	Santiago, Chile	MLP-NN	PM10	2013	[111]	Bor, Serbia	ANFIS	SO2
2008	[112]	Ontario, Canada	FF-NN and B-NN	O3	2015	[113]	Delhi, India	Neuro-fuzzy system	PM2.5
2008	[114]	Istanbul, Turkey	FF-NN	SO2, PM10, and CO	2015	[115]	Romania	ANFIS	PM10
2009	[20]	Zagreb, Croatia	ANN	NO2, O3, CO, and PM10	2016	[116]	Howrah, India	ANFIS	SO2, NO2, CO, O3, and PM10
2010	[117]	Istanbul, Turkey	FF-NN	SO2, PM10, and CO	2017	[12]	Jeddah, Saudi Arabia	ANFIS	O3
2013	[118]	New South Wales, Australia	RBF-NN	O3	2017	[78]	China	Neuro-fuzzy system	PM2.5
2013	[109]	Tehran, Iran	ANN	O3	2017	[119]	Queensland, Australia	ANFIS	PM2.5
2013	[120]	Northeast Spain	MLP-NN	PM10	2018	[121]	Queensland, Australia	ANFIS	NO2
2013	[107]	Johor Bahru, Malaysia	MLP-NN	API	2019	[122]	Mid–southern Taiwan	Fuzzy inference system	PM2.5 and Pb
2014	[123]	Kocaeli, Turkey	ANN	PM10	2020	[124]	Delhi, India	ANFIS	PM2.5
2014	[125]	Athens, Greece	ANN	O3	2020	[126]	Tehran, Iran	ANFIS	CO, SO2, O3, and NO2
2014	[127]	Nagercoil, India	MPL and RBF NN	O3	Ensembles Models
2015	[128]	Australia	RBF-NN	O3	2012	[129]	Europe and North America	Ensemble model	O3
2015	[130]	Lisbon, Portugal	BP-NN	PM10	2015	[131]	Mexico City, Mexico	Two ensemble techniques	O3
2016	[132]	Beijing City, China	ANN	PM2.5	2016	[133]	Harbin and Chongqing, China	Decomposition-ensemble method	PM2.5
2016	[134]	Algiers, Algeria	ANN	PM10	2017	[135]	Guangzhou and Lanzhou, China	Decomposition-ensemble learning paradigm	PM2.5
2016	[136]	Santiago, Chile	FF-NN	PM2.5	2017	[137]	Shandong Province, China	Ensemble model	PM2.5
2016	[138]	Seoul, Korea	ANN	PM10	2018	[139]	Beijing, China	Deep spatial-temporal ensemble model	PM2.5
2017	[140]	Canada	MLP-NN and ELM	O3, PM2.5, and NO2	2018	[79]	Shenyang and Chengdu, China	Secondary-decomposition-ensemble	PM2.5
2017	[141]	Tabriz, Iran	MLP-NN	NOx	2018	[142]	Beijing, China	Stacked ensemble method	PM2.5
2018	[89]	Brescia, Italy	ANN	PM10	2019	[143]	Italy	Ensemble model	PM10 and PM2.5
2018	[144]	Northern China	ANN	O3	2019	[145]	China	Ensemble model	AQI
2019	[21]	Belgrade, Serbia	W-NN and GR-NN	SOx and NOx	2019	[146]	United States	Ensemble model	PM2.5
2019	[22]	Central Poland	ANN	O3	2019	[40]	Madrid, Spain	Ensemble neural networks	NO2
2019	[147]	Andalusia, Spain	BP-NN and RBF-NN	PM10	2019	[148]	London, UK	Ensemble neural networks	O3 and PM10
2019	[149]	São Carlos-SP, Brazil	MLP-NN and NARX-NN	PM10	2019	[150]	London, UK	Ensemble learning technique	SO2
2019	[151]	Rio de Janeiro, Brazil	ANN	PM2.5	2019	[152]	London, UK	Ensemble data mining	NO2
2019	[153]	Shiraz, Iran	NARX-NN	CO	2019	[154]	Tamil Nadu, India	Bagging ensemble	O3
2019	[155]	Bangi, Malaysia	ANN	O3	2019	[156]	Northern China	Stacking ensemble	PM2.5
2020	[157]	Kanpur, India	MLP-NN	O3	2019	[158]	Southern China	BP-NN ensembles	PM2.5
2020	[159]	USA, UK, and Italy	ANN	O3	2020	[160]	Tehran, Iran	Nonlinear ensemble model	AQI
2020	[161]	Five regions, Taiwan	BP-NN	PM2.5	2020	[162]	Beijing, Tianjin, and Hebei of China	Stacking-driven ensemble model	PM2.5
2020	[163]	Nan, Thailand	MLP-NN	PM10	Hybrid and Other Models
Deep Learning Models					2002	[67]	Downtown, Hong Kong	Hybrid (PCA-RBF-NN)	PM10
2015	[88]	Central Italy	R-NN	O3	2007	[42]	Oporto, Portugal	Hybrid (PCA-FFNN)	O3
2016	[132]	Beijing City, China	Deep learning	PM2.5	2008	[43]	Szeged, Hungary	PCA-SVM and PCA-ANN	NOx
2017	[38]	Aarhus city, Denmark	Deep learning	O3	2008	[164]	Kuwait	Hybrid (PCR, ANN, and PCA assisted ANN)	O3
2017	[23]	Pescara, Italy	R-NN	PM10 and PM2.5	2011	[41]	Greece and Finland	Hybrid (PCA-ANN)	PM10 and PM2.5
2018	[165]	China	Deep learning	PM10	2011	[82]	Nantou, Taiwan	Hybrid	PM10 and NOx
2018	[166]	Kuwait	Deep learning	O3	2011	[45]	Dilovasi, Turkey	Hybrid (PCA-MLP-NN)	O3
2019	[39]	Taipei City, Taiwan.	LSTM	PM2.5, PM10, and NOx	2012	[47]	California and Texas, USA	HMM technique with Gamma distribution	O3
2019	[167]	Beijing, China.	Deep learning	PM2.5	2012	[46]	Rub’ Al Khali, Saudi Arabia	GMDH technique	O3
2019	[168]	Guangdong, China	Deep learning	PM2.5	2012	[169]	Tehran, Iran	Type-2 fuzzy	CO
2019	[170]	Tehran, Iran	Deep learning	PM2.5	2013	[171]	Delhi, India	PCA-ANN	AQI
2019	[73]	Beijing, China	Deep neural network	PM2.5, NO2, and SO2	2013	[172]	Gansu, China	Hybrid	O3
2020	[161]	Five regions, Taiwan	CNN and LSTM	PM2.5	2015	[173]	Düzce Province, Turkey	Hybrid (PCA-ANN)	PM10
SVM Models					2015	[85]	Guangzhou, China	Hybrid	PM2.5
2002	[174]	Hong Kong	SVM	RSP	2015	[81]	Salamanca, Mexico	Hybrid	PM10
2003	[175]	Mong Kok, Hong Kong	SVM and PCA-RBF-NN	RSP	2015	[176]	China	Hybrid (wavelet-based MLP-NN)	PM2.5
2005	[177]	Hong Kong	SVM and RBF-NN	NOx and RSP	2015	[178]	Delhi, India	PSO-ANFIS	SO2 and O3
2014	[29]	Rio de Janeiro, Brazil	SVM and ANN	O3	2015	[179]	Taiyuan, China	Hybrid ANN and hybrid SVM	PM10 and SO2
2014	[180]	Tehran, Iran	RBF-SVM	O3	2015	[181]	Agra, India	PCA-ANN	NO2
2014	[182]	India	SVM	O3	2016	[183]	Nan’an, China	Hybrid (wavelet-based BP-NN)	PM10, SO2, and NO2
2016	[132]	Beijing City, China	SVM	PM2.5	2016	[184]	London, UK	Hybrid (PCA-ANN)	PM10 and PM2.5
2017	[185]	Beijing, Tianjin, and Shijiazhuang of China	Multi-dimensional collaborative SVR	AQI	2017	[83]	Tunisia	Hybrid (RF and SVM)	PM10
2018	[28]	Spain	SVM	PM10	2017	[44]	Central London, UK	PCA-MLP-NN	NO2
2018	[30]	Singapore	SVM and BP-NN	CO2 and TVOC	2017	[68]	Taicang, China	Hybrid (PCA-GA-ANN)	AQI
2018	[186]	Beijing, China	Space-time SVM and global SVM.	PM2.5	2017	[187]	Kunming and Yuxi, China	Hybrid (CI-FPA-SVM)	PM2.5 and PM10
2019	[188]	Beijing, China	SVR	AQI and NOx	2017	[189]	Hebei Province, China	Hybrid method (PCA-CS-SVM)	PM2.5
2020	[163]	Nan, Thailand	SVR	PM10	2017	[190]	Shangdianzi, China	Hybrid	PM2.5
Evolutionary NN and SVM Models					2018	[191]	Kolkata, India	Type-2 fuzzy	AQI
2003	[192]	Downtown, Hong Kong	PSO-ANN	CO, NOx, RSP	2018	[193]	Datong, Taiwan	ANFIS-WELM, ANFIS, WELM, GA-BPNN	CO, NO, PM2.5, and PM10
2004	[194]	Northern Greece	GA-FF-NN	PM10	2018	[195]	Egypt	Hybrid	PM10
2004	[196]	Helsinki, Finland	GA-MLP-NN	NO2	2018	[197]	CZT, China	Hybrid Grey–Markov	PM10
2006	[31]	Athens, Greece	GA-ANN	PM10	2019	[198]	Taipei, Taiwan	Hybrid (multi-output and multi-tasking SVM)	PM2.5
2013	[199]	European countries	GA-GR-NN	PM10	2019	[200]	Varanasi, India	Hybrid (PCA and ANN)	PM10
2014	[201]	New Zealand	GA-ANN	NO2	2019	[71]	Yancheng, China	Hybrid	PM2.5
2015	[202]	Helsinki, Finland	GA-NN	PM10 and PM2.5	2019	[72]	Hangzhou, China	Hybrid (RF and R-NN)	SO2, NO2, CO, PM2.5, PM10, and O3
2016	[203]	Aghdasiyeh, Iran	GA-BP-NN	PM10	2019	[204]	Jing-Jin-Ji, China	Hybrid model	PM2.5
2017	[205]	India	GWO-SVM	AQI	2019	[76]	China	Hybrid	Indoor AQ
2018	[206]	China	GA-BP-NN	PM2.5	2019	[48]	Wrocław, Poland	RFP technique	NO2
2019	[84]	Beijing, China	PSO-SVM	PM2.5	2019	[80]	Beijing and Yibin, China	Hybrid	PM2.5
2019	[207]	Beijing, China	PSO-SVM and GA-SVM	AQI	2019	[208]	China	Hybrid (wavelet-based ARIMA, ANN, and SVM)	PM2.5
2019	[209]	Coc Sau, Vietnam	PSO-SVM	PM10	2019	[210]	China	CEEMD-CSA-GWO-SVR	NO2 and SO2
2019	[211]	Beijing, China	QPSO, PSO, GA, and GS-based SVM	NO2 and PM2.5	2020	[212]	China	SCA-ELM	AQI
2020	[163]	Nan province, Thailand	GA-MLP-NN and GA-SVM	PM10	2020	[124]	Delhi, India	Wavelet-ANFIS-PSO and wavelet-ANFIS-GA	PM2.5

. This section reviews and analyses such modeling approaches thoroughly.

3.1. Artificial Neural Networks Models

ANNs are very popular in modeling complex and non-linear engineering problems as they are capable of parallel computing abilities and adaptive to external disturbances. In general, they consist of input, hidden, and output layers. The hidden layers process the input variables employing different squashing functions and send them to the output layer. They are also flexible, less assumption dependent, and adaptive in modeling environmental issues, making them popular in AQM [86]. Naturally, they have salient advantages over traditional statistical models in air quality forecasting [87]. The tested ANN structures for air pollutants prediction include multilayer perceptron neural networks (MLP-NN), radial basis function neural networks (RBF-NN), square multilayer perceptron neural networks (SMLP-NN), ward neural networks (W-NN), pruned neural networks (P-NN), recursive neural networks (R-NN), general regression neural networks (GR-NN), graph convolutional neural network (GC-NN), and backpropagation neural networks (BP-NN) (Table 2). This subsection provides critical reviews of neural network-based approaches in air quality modeling throughout the world.

Hrust et al. [20] have employed ANN to forecast four air pollutants (NO₂, O₃, CO, and PM₁₀) in Zagreb, Croatia as a function of meteorological variables and concentrations of the respective pollutants. Biancofiore et al. [23] predicted daily average PM₁₀ and PM_2.5 concentrations 1-day to 3-days ahead in Pescara, Italy employing R-NN using meteorological data and air pollutant (i.e., PM₁₀ and CO) concentrations. Radojević et al. [21] employed ward and general regression neural networks (W-NN and GR-NN) to estimate the daily average concentrations of SO₂ and NO_x in Belgrade, Serbia using meteorological variables and periodic parameters (hour of the day, day of the week, and month of the year) as inputs. Pawlak et al. [22] developed an ANN model to predict the maximum hourly mean of surface O₃ concentrations for the next day in rural and urban areas in central Poland. The model used six input variables, including four forecasted meteorological parameters, recorded the O₃ concentration of the previous day, and the month. Corani [57] compared the performance of the FF-NN model with the pruned neural network (P-NN) and lazy learning for predicting O₃ and PM₁₀ concentrations in Milan, Italy. The author used air pollutant data (O₃, NO, and NO₂) and meteorological data (pressure, temperature, wind speed, solar radiation, rain, and humidity) as the inputs for the prediction of O₃ concentrations. For PM10 concentration, the predictions used only two air pollutant data (PM₁₀ and SO₂) and two meteorological data (temperature and pressure). The lazy learning model outperformed other models in terms of correlation and mean absolute error.

Anderetta et al. [87] proposed an MLP-NN model with a Bayesian learning scheme to forecast hourly SO₂ concentration levels in the industrial area of Ravenna, Italy, emphasizing the high levels of SO₂ occurring during relatively rare episodes. The authors employed historical meteorological data and SO₂ concentrations of current and previous hours as inputs. Biancofiore et al. [88] modeled hourly O₃ concentration 1-h, 3-h, 6-h, 12-h, 24-h, and 48-h ahead using meteorological data, a photochemical parameter (measured UVA radiation), and air pollutant concentrations (O₃ and NO₂ concentration). The authors used R-NN architecture and measured data from central Italy. Some of the modeling exercises have placed emphasis on emission sources. Gualtieri et al. [89] have demonstrated the capability of ANN in predicting short-term hourly PM₁₀ concentrations in Brescia, Italy. The authors used hourly atmospheric pollutant (NO_x, SO₂, PM_2.5, and PM₁₀) concentrations, meteorological parameters, and road traffic counts (municipality boundary and city center traffic volumes) as the inputs.

Mlakar et al. [90] have illustrated how MLP-NN forecasted SO₂ concentrations for the next interval of 30 min in Šoštanj, Slovenia using wind data, air temperature, actual and historical SO₂ concentrations, emissions from the thermal power plant, and the time of day. Gómez-Sanchis et al. [108] have developed MLP-NN models to estimate ambient O₃ concentrations for an agriculture training center; the concentrations of the next three days were predicted independently using the same training center in Carcaixent, Spain using surface meteorological variables and vehicle emission variables as predictors. Spellman [93] and Moustris et al. [125] developed models using relevant data from multiple locations. Spellman [93] proposed an MLP-NN for estimating summer surface O₃ concentrations at five locations (London, Harwell, Birmingham, Leeds, and Strath Vaich) in the United Kingdom using surface meteorological variables as predictors. The authors found better generalization performance of the MLP-NN over conventional regression model. Moustris et al. The authors of [125] predicted maximum daily surface O₃ concentration in several locations in the greater Athens area, Greece using FF-NN. The authors used hourly meteorological data (wind speed and direction, air temperature, solar irradiance, barometric pressure, and relative humidity) and air pollution data (8-h average values of surface O₃ concentration and hourly NO₂ concentrations) as inputs for their developed model. De Gennaro et al. [120] predicted 24-h average PM₁₀ concentrations at two sites (Montseny and Barcelona) in Spain employing MLP-NN. The authors used hourly particulate matters concentrations of the previous day, meteorological data, and air masses origin as inputs.

Kurt et al. [114] developed an air pollution prediction system for one region of the Greater Istanbul Area, Turkey. The authors attempted three different ways to predict the concentrations of three air pollutants (SO₂, PM₁₀, and CO) for the next three days using FF-NN, where the meteorological data (general condition, day and night temperatures, wind speed and direction, pressure, and humidity) were used as inputs in the first experiment data. In the second experiment, the concentrations of the second and third days were predicted cumulatively using the previous days’ model outputs. The performance of the proposed models improved in the third experiment due to the use of the effect of the day of the week as the input parameter. Kurt and Oktay [117] updated the prediction model used in their previous research [114] by considering spatial features along with the air pollutant data from ten different air quality monitoring stations in Istanbul to forecast the same air pollutants levels three days in advance. The authors concluded that the distance-based geographic model ensured better performance when compared to the non-geographic model. Therefore, the employed input variables were the meteorological data (general condition, day and night temperatures, humidity, pressure, wind speed, and direction), periodic data (day of the week and date), and air pollutant concentrations (SO₂, PM₁₀, and CO). Ozdemir and Taner [123] modeled PM₁₀ concentrations in Kocaeli, Turkey using ANN and multiple linear regression (MLR) techniques, and achieved better prediction accuracy with the ANN technique than the MLR. They used hourly meteorological data (air temperatures, wind speed and direction, relative humidity, and air pressure) and pollutant levels (monthly average, minimum, maximum, and standard deviation of monthly PM₁₀ concentrations).

Perez and Reyes [110] forecasted hourly maximum PM₁₀ concentrations for the next day using MLP-NN in Santiago, Chile as a function of measured concentrations of PM₁₀ until 7 p.m., and measured and forecasted the meteorological variables. The meteorological variables were the difference between the maximum and minimum temperature on the present day, the difference between the maximum and minimum forecasted temperature of the next day, and the forecasted meteorological potential of atmospheric pollution. Schornobay-Lui et al. [149] employed MLP-NN and non-linear autoregressive exogenous (NARX) neural networks (NARX-NN) to model short-term (daily) and medium-term (monthly) PM₁₀ concentrations in São Carlos, Brazil. They used only monthly average meteorological data (temperature, relative humidity, wind speed, and accumulated rainfall) for monthly PM₁₀ concentration prediction, whereas for predicting daily PM₁₀ concentration (for the next day) they used PM₁₀ concentrations along with meteorological data as inputs. Ha et al. [128] employed RBF-NN to predict the 8-h maximum average O₃ concentrations in the Sydney basin in New South Wales, Australia using NO_x and VOC emissions, ambient temperature, location coordinates, and topography as inputs. Wahid et al. [118] estimated the 8-h maximum average of O₃ concentration in the Sydney basin employing RBF-NN. They modeled O₃ concentration as a function of NO_x emission, ambient temperature, location coordinates, and topography.

ANN models are widely explored in AQM due to their satisfactory performances. However, the models can be unstable in a few cases as they are highly dependent on data and can easily fall into local optima instead of finding the global optima [213]. In addition, network training, the amount and quality of training data, and the network parameters (number of hidden layers, transfer function type, number of epochs, number of neurons, and initial weights and biases) significantly influence their performance. A conventional ANN works efficiently when the approximated function is relatively monotonic with only a few dimensions of the input features, but may not be efficient in other cases [214]. A monotonic function is either entirely non-increasing or non-decreasing and its first derivative (which need not be continuous) does not change significantly. They experience the greatest difficulty in approximating functions when the input features are not linearly separable [215]. In typical ANN models, all input variables are connected to neurons of the hidden layer that may affect the generalization ability [216].

3.2. Support Vector Machine Models

Boser et al. [217] introduced the SVM technique, which was primarily limited to solving classification problems, to efficient data analysis. With the passage of time, the researchers extended the technique to regression problems. In regression problems, the SVM technique constructs an optimal geometric hyperplane to distinguish the available data and to map them into the higher dimensional feature space by forming a separation surface through the employment of various functions, including sigmoidal, polynomial, and radial basis functions [218,219]. While they are dealing with regression problems, the SVM is known as support vector regression. However, in this paper, the term SVM is used for both the support vector machine and regression. The structural risk minimization principle adopted in SVM seeks to minimize an upper bound of the generalization error that results in better generalization performance when compared to the conventional techniques.

Like other engineering problems, the SVM has also been employed in the AQM field. Ortiz-García et al. [27] applied SVM and MLP-NN for predicting hourly O₃ concentrations at five stations in the urban area of Madrid, Spain. They explored the influence of four previous O₃ measurements (at a given station and at the neighboring stations) and the influence of meteorological variables on O₃ predictions. Luna et al. [29] employed ANN and SVM to predict O₃ concentrations in Rio de Janeiro, Brazil using available primary pollutants (CO, NO_x, and O₃) and meteorological data (wind speed, solar irradiation, temperature, and moisture content). The authors found solar irradiation and temperature as the most dominant inputs and observed better predictability with SVM than ANN. Yang et al. [186] illustrated space-time SVM to predict hourly PM_2.5 concentrations in Beijing, China and compared the results with space-time ANN, ARIMA, and global SVM. The presented results confirmed the superiority of the space-time SVM over other techniques. The study employed historical PM_2.5 concentration data and meteorological data as inputs for the tested models. Wang et al. [175] illustrated an adaptive RBF-NN and an improved SVM for predicting RSP concentration in Mong Kok Roadside Gaseous Monitory Station, Hong Kong. The authors used six pollutant (SO₂, NO_X, NO, NO₂, CO, and RSP) concentrations and five meteorological variables (wind speed and direction, indoor and outdoor temperatures, and solar radiation) as inputs. The authors found better generalization performance in the SVM technique than the adaptive RBF-NN technique. However, the SVM technique was very slow compared to the RBF-NN technique. Mehdipour and Memarianfard [180] predicted tropospheric O₃ concentration in Tehran, Iran using SVM as a function of daily maximum pollutant concentrations (SO₂, NO₂, CO, PM_2.5, and PM₁₀) and daily average meteorological data (ambient air temperature, wind speed, and relative humidity). The authors found the RBF-kernel-function-based SVM as the best performing technique.

It is generally perceived that the SVM has higher generalization capability compared to the classical NN model, but the design of the SVM model heavily depends on the proper selection of kernel functions and their parameters. It is also reported that they can be very slow in the training phase [220].

3.3. Evolutionary Neural Network and Support Vector Machine Models

Evolutionary computation can be used to tune the weights and biases, to choose the number of hidden layers and neurons, to select the squashing functions, and to generate appropriate architectures for artificial neural networks [221,222,223,224]. They can also be employed to tune the key parameters of the SVM while solving classification or regression problems [25,209,225]. Among many evolutionary computational techniques, the genetic algorithm (GA), bat algorithm (BA), differential evolution (DE), particle swarm optimization (PSO), gravitational search algorithm (GSA), cuckoo search algorithm (CSA), sine cosine algorithm (SCA), grey wolf optimizer (GWO), and backtracking search algorithm (BSA) are well known for the aforementioned purposes.

Kapageridis and Triantafyllou [194] used GA to optimize the topology and learning parameters of time-lagged FF-NN. The model predicted a maximum 24-h moving average of PM₁₀ concentration for the next day at two monitoring stations in northern Greece. The authors used meteorological data (minimum humidity, maximum temperature, the difference between the maximum and minimum temperature, and average wind speed) and the maximum PM₁₀ concentration of the previous day as inputs. Niska et al. [196] introduced GA for selecting the inputs and designing the topology of an MLP-NN model for forecasting hourly NO₂ concentrations at a busy urban traffic station in Helsinki, Finland. Among the many available input variables, the authors selected NO₂ and O₃ concentrations, sine and cosine of the hour, sine of the weekday, temperature, wind speed and direction, solar elevation, and friction velocity as inputs for the GA-tuned MLP-NN-based on experience. Grivas and Chaloulakou [31] modeled hourly PM₁₀ concentrations employing GA-ANN in Athens, Greece using the combination of meteorological data, air pollutant data (PM₁₀ concentrations), and temporal data (hour of the day, day of the week, and seasonal index). Lu et al. [192] developed a PSO-tuned ANN approach for modeling air pollutant parameters (CO, NO_x, NO₂, and RSP) for the downtown area of Hong Kong using original pollutant data. Liu et al. [84] illustrated the PSO-SVM technique for daily PM_2.5 grade predictions in Beijing, China as a function of meteorological data (average atmospheric pressure, relative humidity, and air temperature, maximum wind speed and direction, and cumulative precipitation) and hourly average air pollutant data (PM_2.5 and PM₁₀). The PSO-SVM displayed better accuracy compared to the GA-SVM, AdaBoost, and ANN models for PM_2.5 grade prediction. Chen et al. [207] employed a PSO-driven SVM technique to predict short-term atmospheric pollutant concentration in Temple of Heaven, Beijing, China and found a faster response for PSO-SVM over GA-SVM. Li et al. [211] employed quantum-behaved particle-swarm-optimization-assisted (QPSO) SVM to predict NO₂ and PM_2.5 concentrations for the next four hours in the Haidian District of Beijing, China. The authors used hourly measurements for five air pollutants (PM_2.5, NO₂, CO, O₃, and SO₂), and six meteorological parameters (weather condition, wind speed and direction, temperature, pressure, and relative humidity) as inputs for their developed model. The authors also found that their QPSO-SVM outperformed PSO-SVM, GA-SVM, and GS-SVM. The evolutionary algorithms can tackle the practical problems and obtain better generalization performance, but the process is computationally expensive.

3.4. Fuzzy Logic and Neuro-Fuzzy Models

The fuzzy logic model deals with the imprecisions and uncertainties of real-world applications using a set of manually extracted “if-then” rules [226,227,228]. It creates rules controlling conceivable relationships between input and output features through a fuzzification process that transforms the inferable features into the membership values. Then, it follows a defuzzification process to infer the quantifiable output according to the rules and the input data [122]. It is simple, flexible, customizable, and can handle problems with imprecise and incomplete data. However, it is tiresome to develop rules and membership functions. Besides, it makes the analysis difficult as the outputs can be interpreted in a number of ways [229]. In response, fuzzy logic model and artificial neural networks (neuro-fuzzy systems) can be combined together, where the fuzzy logic performs as an inference mechanism under cognitive uncertainty and the neural network possesses the learning, adaptation, fault-tolerance, parallelism, and generalization capabilities [97]. Similar to many engineering problems, the neuro-fuzzy systems have also been employed to model air pollutant concentrations.

Carnevale et al. [36] have suggested a neuro-fuzzy approach to identify source-receptor models for O₃ and PM₁₀ concentrations prediction in northern Italy by processing the simulations of a deterministic multi-phase modeling system. The authors used daily NO_x and VOC emissions for O₃ modeling, whereas NH₃, NO_x, primary PM₁₀, SO_x, and VOC for PM₁₀ modeling as input variables. Morabito and Versaci [37] demonstrated a fuzzy neural identification technique to forecast short-term hydrocarbon concentrations in local air at Villa San Giovanni, Italy. The authors used measured air pollutants (CO, NO, NO₂, O₃, PM₁₀, and SO₂) data, meteorological data, and vehicle movements as input variables. Hájek and Ole [104] predicted hourly average O₃ concentrations for the next hour at the Pardubice Dukla station, Czech Republic using air pollutant data (NO_x, NO, NO₂, and O₃), temporal data (month of the year), and meteorological data of the present hour. They employed several soft computing techniques, including ANN, SVM, and the fuzzy logic model. The presented results confirmed the superiority of the fuzzy logic model over other models. Yildirim and Bayramoglu [97] developed an adaptive neuro-fuzzy inference system (ANFIS) for the estimation of SO₂ and total suspended particulate matter (TSP) in Zonguldak, Turkey. The authors used meteorological data (wind speed, pressure, precipitation, temperature, solar radiation, and relative humidity) and air pollutant concentrations (SO₂ or TSP) of the previous day as inputs. They found temperature and air pollutant concentration as the most dominant input variables. Yeganeh et al. [119] estimated ground-level PM_2.5 concentration using ANFIS, SVM, and BP-NN techniques in Southeast Queensland, Australia. They used satellite-based, meteorological, and geographical data as inputs. The presented results confirmed the superiority of the ANFIS model over other models. Yeganeh et al. [121] predicted the monthly mean NO₂ concentration by employing ANFIS in Queensland, Australia. The authors improved the prediction accuracy of their developed model using satellite-based and traffic data in conjunction with comprehensive meteorological and geographical data as inputs.

Tanaka et al. [91] adopted a self-organizing fuzzy identification algorithm for modeling CO concentrations for the next hour in a large city in Japan. The authors used CO concentration data, meteorological data (wind speed, temperature, and sunshine), and traffic volume for the previous four hours as inputs. Chung et al. [122] employed a fuzzy inference system (FIS) to predict PM_2.5 and Pb concentrations in mid–southern Taiwan using geographic coordinates and time as inputs. Heo and Kim [95] employed fuzzy logic and neural network models (neuro-fuzzy system) consecutively to forecast the hourly maximum O₃ concentrations for the next day at four monitoring sites in Seoul, Korea. The authors used air pollutants data (CO, NO₂, O₃, and SO₂) and meteorological data (wind speed and direction, temperature, relative humidity, and solar radiation) as input variables. The prediction accuracy of their developed model was continually verified and augmented through corrective measures. Mishra et al. [113] analyzed the haze episodes and developed a neuro-fuzzy system to forecast PM_2.5 concentrations during haze episodes in the urban area of Delhi, India. The air pollutants (CO, O₃, NO₂, SO₂, and PM_2.5) and meteorological parameters (pressure, temperature, wind speed and direction, relative humidity, visibility, and dew point temperature) were used as inputs. The presented results confirmed the superiority of the neuro-fuzzy model over ANN and MLR models. Jain and Khare [102] developed a neuro-fuzzy model for predicting hourly ambient CO concentrations at urban intersections and roadways in Delhi, India. The authors used measured hourly CO data, meteorological data (sunshine hours, wind speed and direction, humidity, temperature, pressure, cloud cover, visibility, stability class, and mixing height), and traffic data (two-wheelers, three-wheelers, diesel-powered, and gasoline-powered vehicles) as inputs. The authors adopted the correlation matrix technique, PCA, and fuzzy Delphi method to identify the most dominant input variables.

3.5. Deep Learning Models

Deep learning is a subset of machine learning techniques that are built using artificial neural networks. It deals with a sufficiently large amount of data without pre-processing. In deep learning, the ANN takes inputs and processes those using weights and biases in many hidden layers to spit out a prediction. Weights and biases are adjusted during the training processes to make a better prediction. This process can easily overcome the bottlenecks and overfitting issues related to the shallow multi-output long short-term memory model. It is employed to model both regression and classification problems [230]. The application of deep learning models for air quality modeling has been following an increasing trend.

Zhou et al. [39] proposed a multi-step-ahead air quality forecasting technique, employing a deep multi-output long short-term memory neural network model incorporating three deep learning algorithms (i.e., mini-batch gradient descent, dropout neuron, and L2 regularization) using meteorological and air quality data as inputs. The model predicted PM_2.5, PM₁₀, and NO_x concentrations simultaneously in Taipei City, Taiwan. Besides, the model overcame the bottlenecks and overfitting issues related to the shallow multi-output long short-term memory model. Athira et al. [165] predicted PM₁₀ concentrations using deep learning technique (R-NN, long short-term memory, and gated recurrent unit) in China and found gated recurrent unit as the best performer amongst the employed techniques. The authors used meteorological data as inputs to the deep learning technique. Peng et al. [132] illustrated a spatiotemporal deep learning method for hourly average PM_2.5 concentration prediction in Beijing City, China and compared the prediction results with spatiotemporal ANN, ARIMA, and SVM. According to the presented results, the deep learning technique outperformed the other techniques. The authors used the air quality data for previous intervals as inputs. Tao et al. [167] proposed a deep learning-based short-term forecasting model to predict PM_2.5 concentrations at the US Embassy in Beijing, China.

3.6. Ensemble Models

Ensemble models combine a set of individual methods by means of aggregation rules to solve a given problem and produce a better-aggregated solution. Every single method is trained individually and produces a different and/or closer solution [231,232,233,234]. In general, these models use generated solutions of the individual techniques as inputs and produce ultimate solutions using a wide range of processing methods, including averaging, voting, boosting, bagging, and stacking [235]. Averaging (for regression problems) and voting (for classification problems) are the most popular due to their simplicity and better interpretability. These models are also known as committees of learning machines.

Valput et al. [40] modeled hourly NO₂ concentration in Madrid, Spain using ensemble neural networks as a function of meteorological data, pollutant data (hourly average NO₂, NO, CO, and SO₂), and traffic data (intensity and road occupation). Maciag et al. [148] proposed a clustering-based ensemble of evolving spiking neural networks to forecast air pollutants (O₃ and PM₁₀) concentrations up to six hours in the Greater London Area. The presented results demonstrated the superiority of the proposed ensemble technique over ARIMA, MLP-NN, and singleton spiking neural network models. Bing et al. [131] modeled daily maximum O₃ concentration in the metropolitan area of Mexico City, Mexico using four individual soft computing techniques (ANN, SVM, RF, and MLR) and two ensemble techniques (linear and greedy). Among the employed soft computing techniques, the linear ensemble model outperformed other techniques. Feng et al. [158] developed a BP-NN ensemble to forecast the daily PM_2.5 concentration in Southern China using daily assimilated surface meteorological data (including air temperature, relative humidity, pressure, and winds) and daily fire pixel observation as inputs. The authors observed significant improvement in the air pollutant prediction capability of the employed ensembles technique. Wang and Song [139] designed a deep spatial-temporal ensemble model to improve air quality pollutant (PM_2.5) prediction in 35 stations in Beijing, China using historical air pollutant data (CO, NO₂, SO₂, O₃, PM_10, and PM_2.5) and meteorological data as inputs. The authors found their proposed model outperformed other models including linear regression and a deep neural network.

3.7. Hybrid and Other Models

A combination of multiple techniques is known as a hybrid modeling technique and these are very popular in modeling air pollutant concentrations throughout the world. The authors of [41] employed MLP-NN to forecast the daily mean PM₁₀ and PM_2.5 concentrations for the next day in Greece and Finland where the input features were selected through the PCA method.

Sousa et al. [42] compared the effectiveness of PCA-based FF-NN with MLR and original data-based FF-NN to predict hourly O₃ concentration for the next day in Oporto, Portugal. The authors considered hourly O₃, NO, and NO₂ concentrations and hourly mean temperature, wind velocity, and relative humidity as the inputs to the predictive models. Cortina-Januchs et al. [81] modeled hourly average PM₁₀ concentration for the next day in Salamanca, Mexico using clustering-based ANN as a function of historical pollutant data (PM10 concentration) and meteorological data of the current day. They used FCM and FKM clustering approaches to process the input data. Lin et al. [82] predicted three air pollutants (PM₁₀, NO_x, and NO₂) using immune-algorithm-tuned SVM (IA-SVM) in Nantou station, Taiwan from their historical measured values. The authors preprocessed the raw data employing logarithmic, scaling, and normalization techniques. They found logarithmic IA-SVM was the most effective prediction technique in terms of overall MAPE values. The combination of ANFIS and a weighted extreme learning machine (WELM) model outperformed neuro-genetic, ANFIS and other models in predicting air pollutant (CO, No, PM_2.5, and PM₁₀) concentration in Datong, Taiwan using measured time series air pollutant data [193]. Cheng et al. [208] employed wavelet decomposition to mine useful information from the measured weather data and used ARIMA, ANN, and SVM to predict PM_2.5 in five Chinese cities. The authors confirmed the superiority of the hybrid approaches over non-hybrid approaches through exhaustive simulations. Bai et al. [183] demonstrated wavelet-decomposition-based BP-NN technique to estimate daily air pollutant (PM₁₀, SO₂, and NO₂) concentration in Nan’an District of Chongqing, China. The authors used the wavelet coefficients of the previously measured air pollutant concentrations and local meteorological data as inputs. Apart from the reviewed single and hybrid AQM techniques, other modeling approaches including GMDH, HMM, and RFP techniques, have also been explored to model air pollutant concentration. For instance, the authors of [46] employed a GMDH approach to model O₃ concentration in Rub’ Al Khali, Saudi Arabia using meteorological data (wind speed, temperature, pressure, relative humidity) and air pollutant data (NO and NO₂). Conversely, Zhang et al. [47] illustrated an HMM with Gamma distribution to predict O₃ level in California and Texas, USA as a function of measured air pollutant data (O₃, NO, and NO₂) and measured and predicted meteorological data (temperature, wind speed, relative humidity, and solar radiation). The authors used the wavelet decomposition technique to reduce the input data size by extracting useful features. The authors of [48] proposed an RFP technique to model NO₂ concentration in Wrocław, Poland by using hourly meteorological data (air temperature, wind speed and direction, relative humidity, and atmospheric pressure), hourly traffic counts, and temporal data (month of the year and day of the week).

3.8. Generalized Overview

The authors of [236] and [237] proved that the single-hidden-layer feed forward neural networks are the universal approximators of continuous target functions. Similarly, Hammer and Gersmann [238] illustrated the universal function approximation capabilities of the support vector machine. Researchers investigated different variations of the fuzzy logic systems and demonstrated their capabilities as universal function approximators. Ying [239], proved that Takagi–Sugeno (TS) fuzzy systems are the universal approximators for a multi-input and single-output problem. Therefore, the mentioned soft computing models have become theoretically valid candidates for modeling air pollutants. The models attempt to build relations between pollutant levels with the information related to other relevant pollutants, pollutant characteristics, meteorological conditions and pattern, and terrain types and characteristics. If multiple models are used for same air quality modeling problems, it is expected that the model performance will mainly depend on the selection of appropriate inputs, the size of datasets, the run-time, the hyper-parameters of the models, and the inherent model suitability for the specific problem in multi-dimensional space.

Therefore, researchers have started to model air pollutants using ANN, SVM, and fuzzy logic approaches from the beginning. With the passage of time, it has been observed that evolutionary optimization techniques are playing vital roles in achieving better generalization performance by tuning the key parameters of the primarily employed soft computing approaches in AQM. Likewise, researchers moved from fuzzy logic models to neuro-fuzzy and ANFIS models that enhance overall performance. The ensemble models exploit the advantages of the individual models and cutoff the drawbacks (if there are any). Besides, the deep learning methods are better candidates than the shallow machine learning techniques for handling massive and verities of information received from the advanced measurement infrastructures and sensors. Hence, the ensemble models perform better than the individual models and the deep learning models have been exhibiting superiority, especially for large datasets.

In general, environmental data are complex to model as they are functions of several variables that share a complicated and non-linear relationship with each other [240]. The soft computing models that address the limitations of other models and ensure higher prediction accuracies and reliability for a specific pollutant in specific air quality episode should not be considered as effective, accurate, and reliable in all cases. The discussed notion motivates the research for the exploration and exploitation of more techniques in the field of AQM that can vary based on area, pollutant type, and data availability.

4. Potential Soft Computing Models and Approaches

Among many potential techniques, different variations of artificial neural networks, evolutionary fuzzy and neuro-fuzzy models, ensemble and hybrid models, and knowledge-based models should be further explored. Besides, there is a continuous need for the development of a universal model, as most of the explored models are either site-dependent or pollutant dependent. This section discusses future research directions and potential soft computing models that can be investigated in air quality modeling throughout the world.

4.1. Variations of ANN Models

As can be observed from Section 3, ANN approaches were widely explored in AQM and in most cases MLP-NN, BP-NN, RBF-NN, or R-NN were employed. Other available variations of ANN (GR-NN, GC-NN, P-NN, W-NN, and others) models that successfully demonstrated their capabilities in modeling complex and non-linear problems in other engineering fields have not been explored significantly [11]. Many of them (extreme learning machine, multitasking, probabilistic, time delay, modular, and other hybrid neural networks) are rarely explored. Besides, deep neural network models received great attention in modeling PM_2.5 concentrations, but other air pollutants have not been modeled significantly. Therefore, such unexplored and rarely explored variations of the neural networks can be investigated in future works for modeling all types of air pollutant concentrations.

4.2. Evolutionary Fuzzy and Neuro-Fuzzy Models

Fuzzy systems are the proven tools for many applications for modeling complex and non-linear problems. However, the lack of learning capabilities in the fuzzy systems has encouraged researchers to augment their capabilities by hybridizing them with the EO techniques [241,242,243,244]. Among the many EO techniques, GA, GWO, CSA, SCA, and PSO are widely used and well-known global search optimization approaches with the ability to explore a large search space for suitable solutions [245,246,247]. Besides, the type-2 fuzzy set is capable of handling more uncertainties than the type-1 fuzzy set that has been successfully applied in a wide range of areas [248,249,250]. Therefore, considering the potentiality of the fuzzy logic approaches, these can be explored in the field of AQM.

4.3. Group Method Data Handling Models and Functional Network Models

Long-term research in the field of neural networks and advanced statistical methods has contributed to the evolution of an abductory induction mechanism that is known as GMDH [251]. It automatically synthesizes abductive networks from a database of inputs and outputs with complex and nonlinear relationships. Other extensions of the neural network models include the functional network models (FNM) [252]. This determines the structure of a network and data using domain knowledge and estimates unknown neuron functions. Both GMDH and FNM were explored in many relevant applications [253,254,255]. These rarely explored extensions of the neural networks can be further investigated in AQM.

4.4. Case-Based Reasoning and Knowledge-Based Models

Case-based reasoning solves new problems by recalling the experiences and solutions of similar past problems [256]. It deals with the given problems following four steps, namely retrieve, reuse, revise, and retain [257]. Another soft computing technique, the knowledge-based system, attempts to solve problems by giving advice in a domain and utilizing the knowledge provided by a human expert [258]. Researchers have employed both techniques to solve many complex problems [259,260,261]. These techniques can be investigated in AQM, as none of them have yet been explored.

4.5. Ensemble and Hybrid Models

As discussed earlier, ensemble models employ multiple learning techniques in parallel and combine their outputs to produce a better generalization performance. In a real-world situation, they aim to manage the strengths and weaknesses of each model and end up with the best possible solutions [262]. Recently, such models received huge momentum in modeling AQM, but this was limited to a few specific pollutants (mainly PM_2.5). Researchers should invest more time into these attractive tools as they will become some of the most prominent tools for AQM in the future.

4.6. Development of Universal Models

Most of the discussed models are either site dependent or pollutant dependent. There is no guarantee that a specific model developed for a specific site will be stable and reliable for another location with different meteorological conditions. Therefore, there is always a need for the development of a universal model for AQM. Besides, the comparison between the site-specific models could be an attractive option for future research as it aids in developing site characterizations. Such research may enable the creation of guidelines for site-specific model development.

4.7. Appropriate Input Selection Methods

As discussed in Section 2, several approaches have been reported to reduce the input space by selecting the most dominant input variables. In addition, most of the approaches selected air pollutant and meteorological data as inputs. A few of the considered other types of data, including temporal, traffic, geographical, and sustainable data. Therefore, the present authors believe that the comparison of such input selection methods considering all available input data types could be an attractive field of research in AQM. Besides, the selection of proper decomposition components for the reduction of data dimensionality could be considered as another potential research direction, as the inclusion of many components in input space may result in model complexity and the accumulation of errors. Moreover, other available data pre-processing and feature extraction techniques employed for relevant fields could also be explored.

5. Conclusions

Soft computing models have become very popular in air quality modeling as they can efficiently model the complexity and non-linearity associated with air quality data. This article critically reviewed and discussed existing soft computing modeling approaches. Among the many available soft computing techniques, the artificial neural networks with variations of structures and the hybrid modeling approaches combining several techniques were widely explored in predicting air pollutant concentrations throughout the world. Other approaches, including support vector machines, evolutionary artificial neural networks and support vector machines, fuzzy logic, and neuro-fuzzy systems, have also been used in air quality modeling for several years. Recently, deep learning and ensemble models have received huge momentum in modeling air pollutant concentrations due to their wide range of advantages over other available techniques. Additionally, this research reviewed and listed all possible input variables for air quality modeling. It also discussed several input selection processes, including cross-correlation analysis, principal component analysis, random forest, learning vector quantization, rough set theory, and wavelet decomposition techniques. Besides, this article sheds light on several data recovery approaches for missing data, including linear interpolation, multivariate imputation by chained equations, and expectation-maximization imputation methods.

Finally, it proposed many advanced, reliable, and self-organizing soft computing models that are rarely explored and/or not explored in the field of air quality modeling. For instance, functional neural network models, variations of neural network models, evolutionary fuzzy and neuro-fuzzy systems, type-2 fuzzy logic models, group method data handling, case-based reasoning, ensemble, and hybrid models, and knowledge-based systems have the immense potential for modeling air pollutant concentrations. Moreover, the modelers can compare the effectiveness of several input selection processes to find the most suitable one for air quality modeling. Furthermore, they can attempt to build universal models instead of developing site-specific and pollutant-specific models. The authors believe that the findings of this review article will help researchers and decision-makers in determining the suitability and appropriateness of a particular model for a specific modeling context.