Environ Eng Res > Volume 26(6); 2021 > Article
Pruthi and Bhardwaj: Modeling air quality index using optimized neuronal networks inspired by swarms

### Abstract

Air quality prediction is a significant field in environmental engineering, as air and water are essential for life on Earth. Nowadays, a common parameter used worldwide to measure air quality is termed as Air quality index. The parameter is measured based on the air pollutant concentration. The hybrid neuronal networks have been widely used for modeling air quality index. In the quest of optimizing the error in modeling air quality index, the existing adaptive neuro-fuzzy inference system is improved in this study using algorithms based on evolution and swarm movement. The model is based on the prominent air pollutants- nitrogen oxide, particulate matter of size equal to or less than 2.5microns (PM2.5), and sulphur dioxide. The proposed hybrid model using wavelet transform, particle swarm optimization, and adaptive neuro-fuzzy inference system accurately predicts the Air Quality Index and can be used in the public interest to take necessary precautions beforehand.

### 1. Introduction

In a world of industrialization and modernization, air pollution appears to be on the rise. A recent report IQAir Visual 2018 concluded that Delhi is a highly polluted capital across the world and ranked 11th. India rules the list with 22 of the worst 30 cities globally [1]. Air pollution is an insidious destroyer of the country’s health and wealth. With every inhale, microscopic particles get deep into the lungs. Air pollution is the major cause of cancers, strokes, and heart disease [2]. In recent studies, it is found that pollution is stunting children’s growth and development [3, 4]. The total number of cases is likely to rise in the coming years if pollution is not regulated. Moreover, additional deaths as well as disabilities will be introduced [5]. Air pollution has reduced the average life expectancy to 1.8 years. \$225 billion is the estimated financial cost in lost labor and a thousand times more cost in healthcare. Rising pollution and its severity have forced researchers and scientists to carry out various studies involving its health effects and future trends. Air pollution dynamics is a complex process due to randomness involved in air pollutants behavior. Adaptive Neuro-Fuzzy Inference System (ANFIS) is effective in dealing with non-linear real-time problems. ANFIS has been widely used in disaster management, rock engineering [6, 7] healthcare sector, finance, and many other real-time fields [810]. ANFIS deals with both regression and classification problems [11].
The large error existing in the air quality modeling is discussed and optimized in this study. The major drawback observed in the past studies is the dependency of the model on various parameters. The complexity involved due to the various parameters leads to a large error. The present study aims to develop a less resource-intensive and more effective model in predicting air quality. ANFIS is used as a regression tool. The learning algorithm of classic ANFIS is based on the gradient descent method which is replaced with the evolutionary algorithms in the present study. The efficiency of the proposed model is validated by applying it to the data monitored at the Shadipur area of India. Shadipur is an industrial cum residential area covering all the precursors for polluting air. Hence, appropriate study area to validate the performance of model. The prominent pollutants - PM2.5, oxides of nitrogen (NO, NO2, NOx) and sulphur dioxide are studied. The daily (24-h average) air pollutant concentrations are obtained from Central Pollution Control Board. PM2.5 (μg/m3) concentrations are observed from March 2015 to June 2019 and NO (μg/m3), NOx (ppb), SO2 (μg/m3), NO2 (μg/m3) are observed from January 2010 to June 2019. The model developed is only dependent on the past values of the respective air pollutant. The study is independent of other variables. The authors have not encountered such work to the best of their knowledge. The article is organized into four sections explaining the problem undertaken and the data collected, methodology, results, and the last section concludes the work carried out.

### 2.1. Study Area and Dataset

Central Pollution Control Board (CPCB) is India’s apex body that monitors the air quality. The various stations of the organization serve almost all cities. It monitors contaminants and the parameters of the atmosphere. Delhi is one of the most polluted cities. Hence, a residential, industrial, and commercial region of Delhi covering all the human activities resulting in the formation of pollutants is considered for the study. Moreover, the subtropical climate of Delhi makes the behavior of air pollutants chaotic and contains extreme values covering the broader aspect of the applicability of the proposed models. The daily concentration (24-h) of fine particulate matter (PM2.5), oxides of nitrogen, and sulphur dioxide from January 2010–June 2019 was collected from CPCB for the current analysis. Fig. 1 depicts the areas monitored by CPCB in Delhi, India, and the study area-Shadipur.

### 2.2. Wavelet Transform

In real-time data problems, pre-processing of data plays a significant role in any kind of analysis. The presence of extreme outliers, difficulty in feature extraction, and various fluctuations in data lead to errors in modeling real-time problems. The Pre-processing of data is to solve these issues. Pollutant sequence preliminary analysis indicates sudden shifts and spontaneous variations. Wavelet transform is employed to extract all the characteristics of the underline sequence. For further insights refer to Rashmi and Dimple [12]. In this study Daubechies (Db5) wavelet is considered.

### 2.3. Adaptive-Neuro Fuzzy Inference System

ANFIS is a fusion of neuronal networks and fuzzy systems. It is a widely used method for regression problems. It is based on on-premise and consequent parameters. In the classic ANFIS model, the parameters are tuned using a gradient descent algorithm as used by various researchers in the past [1214]. ANFIS is based on targeted data and input. The learning algorithm builds the relationship between input and output in the Fuzzy if-then rules structure. The performance of the model is based on the learning algorithm. The parameters are tuned in the present work using various techniques of optimization-swarm intelligence, genetic algorithm, ant colony, and differential evolution, as discussed below.

#### 2.3.1. Particle swarm optimization

In 1995, Eberhart and Kennedy developed the PSO technique [15]. Compared to other evolutionary algorithms the algorithm requires fewer parameters. The output vector y in RD in PSO is based on position vector q and velocity vector w of the particle. For each iteration, velocities of all variables are modulated based on inertia weight (W), cognitive (d1), and social (d2) acceleration. For (n+1)th epoch, velocity and position are updated as:
##### (1)
$wiDn+1=WwiDn+d1s1n(qiDn-yiDn)+d2s2n(qiDn-yiDn)yiDn+1=yiDn+wiDn+1}$
where, s1,s2U(0,1) and d1 + d2 ≤ 4. Consider the particle’s best position as pbest. Compare the current position of the particle with that of pbest. If the current position is better than pbest, then pbest is the current position otherwise pbest is the best global position (gbest). The optimal values for tuning ANFIS parameters in this study are taken as W = 1, d1 = 1, and d2 = 2 using the trial and error process. The maximum iteration for all the algorithms is taken as 1000.

#### 2.3.2. Genetic algorithm

John Holland developed GA in the 1970s [16], and applied henceforth to solve different types of problems. Using evolutionary biology the genetic algorithm is concerted. The algorithm is built based on descent, mutation, and crossover ideas. The important aspect of GA over the other evolutionary strategies is that it successfully works in the presence of more varied. This is a nature-influenced optimization algorithm. The algorithm operates on a chromosome population. The emphasis is not on one search space single point or one chromosome. Properties displayed by the population at all stages are dependent on the characteristics of the preceding stage. The cost function determines chromosomal output by the added fitness function. De et al. [17] will provide further insights into the genetic algorithm. Mutation percentage and mutation rate are taken as 0.4, 0.7, and 0.15, respectively, using the trial and error process crossover ratio.

#### 2.3.3. Ant colony optimization

ACO is influenced by ants. ACO was developed by Dorigo and colleagues in the early 1990s [17]. From then on, the algorithm is incorporated for various optimization problems. The principle of ACO is based on the mechanism of how ant optimizes their path for food. Ants reduce their journey towards food by leaving a (chemical) pheromone trail as they walk. The chemical helps other ants for food search. The shorter path is indicated by a strong trail of pheromone. The stronger pheromone draws the attention of other ants. The ants mostly choose shorter path until all find the shortest path. The ACO used the mechanism of ants and develop artificial ants starting from the initial node. The artificial ants move to feasible neighbor nodes. Each ant builds a path using the state transition rule;
##### (2)
$P(s,v)={argmaxv∈J(s){[η(s,v)]α[η(s,v)]β},if r≤r0R ,otherwise$
η(s,v) represents pheromone (desirability of (s,v)) on edge (s,v). r is the parameter that governs the relative value of desired, r0 is initialized with 0 ≤ r0 ≤ 1, r belongs to rand([0,1]). r0 = 0.5 for carrying out the present study. J(r) is the set of edges available at point r of decision. S is a random variable chosen according to the probability distribution given below:
##### (3)
$P(s,r)={[η(s,v)]α[η(s,v)]β∑v∈J(s)[η(s,v)]α[η(s,v)]β,if r∈J(s)0,otherwise$
Amount of pheromone modifies as η(s,v) ← (1−ρ)η(s,v)+ρη0, 0<ρ<1
where ρ is the pheromone evaporation coefficient representing. The global modified amount when all ants arrived at the destination is given by
##### (4)
$η(s,r)←(1-δ)η(s,r)+Δη(s,r)$
where,
$Δη(s,r)={1L,if (s,r)∈global best tour0, otherwise$
L denotes the global best tour length from the initial stage; the δ is the global evaporation coefficient parameter, and the last term is the increase in desirability [18].

#### 2.3.4. Firefly algorithm

This algorithm is designed on fireflies flashing characteristics [19]. FFA structure is based on (i) Firefly (assumed to be unisex) ability to captivate other; (ii) the intensity of the luminous; and (iii) amount of light emitted by the firefly.
##### (5)
$J=J0e-αd2$
##### (6)
$v(d)=v0e-αd2$
where J is the light intensity and v(d) attractiveness at distance-d to the firefly. At d = 0, J = J0 and v(0)=V0, and α is the light absorption coefficient. d is defined as [20, 21]:
##### (7)
$djk=‖yj+yk‖=∑i=1r(yj,i-yk,i)$
where yj and yk are fireflies positions j and k. Firefly is captivated by yet brightness-based firefly. The movement of the firefly is given by
##### (8)
$yj=yj+β0e-αd2(yk-yj)+ηεj$
ηɛj is the random movement in case of absence of brightness, η varies between 0 and 1 and the second term in the equation is the captivation factor with coefficient as β0. FFA is used to tune the premise parameter of ANFIS with optimal values of coefficients as α=1 and β0=2, using trial and error process.

#### 2.3.5. Differential evolution

The well-known evolutionary algorithm is based on mutation, crossover, and selection. DE is widely used for optimization problems in various fields [22]. It has been widely applied as opposed to other algorithms due to its simple structure and faster convergence rate. The algorithm is focused on biological processes that involve survival if environmental and genetic features are to be complied with. DE begins its operation by creating a random population, where each person in the population represents a problem-solving solution. The search parameter is initialized, as are the total number of generations. For the description of the algorithm refer to Wei et al. [23]. The optimal crossover probability is taken as 0.2 and scaling factor lower and upper bounds as 0.2 and 0.8.

#### 2.3.6. Proposed algorithm

1. x(t) at time t is considered where x(t) represents daily (24 h) concentration of air pollutants on day t.

2. x(t) is decomposed using the wavelet transform as mentioned in section 2.3.1 using high and low filters. x(t) is the sum of an (approximation at level n) and d1,d2,. . . .,dn (details at level n). Daubechies wavelet(db5) is considered in the present study due to its property to extract fluctuations nicely.

3. Instead of x(t), the smoothed decomposed series are used for further analysis. Let y(t) denote the approximation at level 5 i.e. y(t) = a5(t).

4. The autocorrelation function (ACF) for y(t) is computed as described by Mohammad et al. [24] to find out the dependence of y(t) on lag values. Let the optimized lag is τ. The input set is past τ values of the series and the output value is y(τ+1).

5. The series is divided into training (70%) and testing (30%) datasets.

6. The parameters as described in section 2.3 are obtained. Using the algorithm described in sections 2.3.1–5, the premise and consequent parameters are trained.

7. The parameters are trained to obtain the optimized error. The simulations are carried using Matlab R2019a software.

8. Steps (4)–(7) are carried out for d1,d2,. . . .,dn. The final output is obtained adding the trained values of approximation and details. The test dataset is simulated using the model. Further effectiveness of the method is verified using trained and tested datasets.

The parameters are trained using different algorithms and the same procedure is followed. The models based on different algorithms are denoted as are compared to obtain the best model.

### 2.4. Evaluation Criterion

The efficacy of the model is measured against the existing models. The observed-predicted pairs (yO(t) and yp(t) w.r.t time t) for training and testing datasets are considered. The determinism coefficient (R2) defines the relation between the aforementioned pairs. The parameters for determining errors are based on various values, and they primarily combine absolute and relative errors. Here are some of the error measurements:
##### (9)
$R2=1-∑t=1m(yo(t)-yP(t))2∑t=1m(yo(t)-1m∑t=1myo(t))2Mean Absolute Error,MAE=∑t=1m|yo(t)-yP(t)|mMean Absolute Percentage Error,MAPE=∑t=1m|yo(t)-yP(t)yo(t)|m×100Root Mean Square Error,RMSE=1m∑t=1m(yo(t)-yP(t))2}$
To forecast the air quality, the analysis is carried out on the air pollutants. The Air Quality Index (AQI) is the metric for transmitting air quality to the public whether it is dangerous or safe to go out or take precautions. AQI standard for India was introduced in the year 2014. The best model is evaluated based on equation 9. As per CPCB for India, AQI is evaluated using formulas mentioned in equations 1012. Using the best model the pollutant is predicted and correspondingly air quality sub-index is evaluated. The prominent sub-index gives the AQI. AQI in the present study is used to validate the proposed model. AQI value is calculated and divided into categories-Good (0–50), Satisfactory (51–100), Moderately polluted (101–200), Poor (201–300), Very poor (301–400), and Severe (401–500) as per CPCB norms.
##### (10)
$PM2.5 Air Quality Subindex={X*5030,0250$
where, X represents PM2.5 concentration in μg/m3.
##### (11)
$SO2 Air Quality Subindex={X*5040,01600$
where, X represents SO2 concentration in μg/m3.
##### (12)
$NOx Air Quality Subindex={X*5040,0400$
where, X represents NOx concentration in ppb(parts per billion).

### 3. Results and Discussions

The random behavior of air pollutants makes the task of predicting air quality complex. The study aims to build a model from which high prediction accuracy with minimal input parameters can be obtained. The complexity comes into the frame when the series is non-stationary. The extreme outliers make the problem more challenging. The studies related to model air quality has been carried out for various environmental pollutants like NO2, PM2.5, and SO2 which play a significant role in determining the air quality. Some of the important work is shown in table 1. The problem was previously dealt with using ANFIS modeling but the large error between the predicted and observed value was observed (refer to Table 1). The drawback found in classic ANFIS modeling was due to the gradient descent (GD) method. It is observed that in classic ANFIS modeling, the GD algorithm gets trapped in local minima. The tuning of premise parameters was inadequate leading to inadequate predictions. Moreover, too many parameters are also one of the reasons for erroneous prediction. The present work is an attempt to minimize the parameters at the same time improving the air quality prediction. In the current scenario, oxides of nitrogen, particulate matter, and sulphur dioxide are prominent pollutants. Though the air quality index is dependent on NOX, PM2.5, and SO2, NO and NO2 are also predicted in the present study as both have a significant correlation with NOX. The air quality index is dependent on the prominent air quality sub-index corresponding to the pollutant. The proposed hybrid models were validated for the Shadipur area of India. The hybrid model combines the decomposition filter, fuzzy inference system, algorithm for optimizing parameter, and neuronal networks.
The correlation analysis of the pollutants and meteorological parameters was studied to optimize the choice of parameters. It was found that no significant correlation existed between the weather series available (relative humidity, wind speed, and temperature) and the pollutant considered for the available data. The other attempt to find the dependent parameters of the series was to carry out a partial autocorrelation function (PACF). It is observed that in comparison to the past concentration of the pollutant no significant correlation was observed with meteorological and other pollutants. Based on the partial correlation function of pollutant, the optimized lag considered is six. Hence, the concentration of past six days is considered for predicting concentration of the seventh day. For decomposition analysis Daubechies wavelet (Db5) is used. The membership function used in the fuzzy inference system is a Gaussian function. The premise parameters are tuned using the gradient descent method and evolutionary algorithms and consequent parameters using an algorithm mentioned described in classic learning. The model performance is summarized using various statistical tools as described in section 2.4.
The performance analysis of various models in Tables 26 depicts the role of wavelet decomposition in analyzing the non-stationary series. Without extracting the features i.e. without using low and high filters, a large difference is observed between predicted and observed data. ANFIS and WANFIS models are also compared for each air pollutant to signify the importance of wavelet transform. Further, the evolutionary algorithm implemented for tuning premise parameters has reduced the error between predicted and observed air pollutant concentrations to a larger extent. The bold glyphs in the tables signify the errors corresponding to the best model. It is observed that for NO, NO2, NOx, and PM2.5 proposed Wavelet Transform-Adaptive Neuro-Fuzzy Inference System-Particle Swarm Optimization (WANFIS-PSO) gives better results compared to other models. The genetic algorithm is very much close to PSO. The next step for the best model was to check the computation time.
While tuning the parameters it is observed that differential evolution converges at a very fast rate. Particle Swarm Optimization and Genetic Algorithm take approximately 80 seconds to converge while FFA has a slow convergence rate compared to others. FFA gives better results than ACOR and DE. ACOR is most often used for continuous problems. It is observed that ACOR possesses random behavior in case of outliers hence very large relative error. The comparison of algorithms in the study covers almost all aspects in the present scenario to develop a good model for AQI prediction. The daily (24-h) AQI value is evaluated based on the prominent pollutant. The observed and predicted concentrations of pollutants and AQI values corresponding to the best model are very close for the tested data as depicted in Fig. 2(a)–(e) and Fig. 2(f), respectively. AQI prediction met 88.63% accuracy and remaining AQI values lie very close to the breakpoints of the categories as defined in section 2.4. The accuracy level in predicting the air quality index validates the study to be used for making policies and beforehand precautions to be marked safe from air pollution.

### 4. Conclusion

The atmospheric dynamics is complicated due to the extreme outliers and data unavailability making the study highly expensive. The air quality index model developed in the present study is effective and less complex in forecasting the one-step-ahead quality of the air we breathe in. The proposed model is only dependent on the lagged values of the prominent air pollutant reducing the complexity of the model as compared to the existing ones. Though the pollutant series have extreme outliers the proposed hybrid model using wavelet transform, adaptive neuro-fuzzy inference system, and particle swarm optimization has significantly optimized the error. Thus, an effective model for predicting air quality index is obtained which can be adopted by air pollution agencies and the Government for policymaking. The model developed in the present work can be efficiently used and applied to any real-time series to observe future behavior.

### Acknowledgment

The authors are thankful to Guru Gobind Singh Indraprastha University, Delhi, India for providing research facilities and financial support.

### Notes

Author Contributions

D.P. (Ph.D. student) conducted all the experiments and wrote the manuscript. R.B. (Professor) revised the manuscript.

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##### Fig. 1
Study Area- Industrial cum residential area, Shadipur, Delhi, INDIA (permission from the International Journal of Environmental Science and Technology Springer Nature).
##### Fig. 2
Predicted and Observed concentration for the tested dataset of pollutant (a) NO, (b) NO2, (c) NOX, (d) PM2.5, (e) SO2 and (f) AQI values.
##### Table 1
Comparison of the Past Relevant Studies and the Present Work
Author Input Study Region Methods Output : Correlation Coefficient
Rashmi and Dimple [12] Embedded NO2 Time series Shadipur, Delhi (Commercial, Industrial and residential area Wavelet- Artifical Neural Network Fuzzy Inference System NO2: R = 0.9762
Fabio et al. [25] Meteorological data, PM10, CO Pescara valley (industrial area and Busiest Port) MLR (multiple linear regression model), neural network model PM2.5 :0.86 ≤ R ≤ 0.91
Ulderico et al. [26] SO2, NO2 past values Palermo (Italy) Recurrent Neural Network (Elman model) SO2: 0.89 ≤ R ≤ 0.0.96
NO2: 0.90 ≤ R ≤ 0.98
Ian [27] NO, NO2, CO, O3, temperature, wind speed and direction Chilliwack (eastern LFV) Artificial neural network (ANN) multiple regression models (MLR) PM2.5 :0.69 ≤ R ≤ 0.75
Polaiah et al. [28] Wind Speed and direction, Temperature, Humidity, Atmospheric Pressure etc. Visakhapatnam, Andhra Pradesh ANN NO2: R = 0.955
Joaquin et al. [29] Daily average PM2.5, wind parameters, PM2.5 (maximum), humidity and temperature Ciudad Juárez and El Paso Multilayer Perceptron Neural Network (MLP), a Square Multilayer Perceptron (SMLP) and Radial Basis Function network (RBF) PM2.5: 0.284 ≤ R ≤ 0.679
Marijia et al. [13] Wind speed, wind direction, temperature, humidity, pyrometallurgical process sulfur emission Bor, Serbia(urban area in vicinity of copper smelter) ANFIS SO2: R = 0.725
Sait et al. [30] Wind Speed, Temperature, particulate matter concentrations Izmir, Turkey ANN SO2: R = 0.97
Wei and Jingyi [31] Average PM2.5, PM10, SO2, CO, NO2, O3, minimum and maximum day temperature. Baoding City, China (industrial and energy structure) Principal Component Analysis and improved Least Square Support Vector Machine with Cuckoo Search Algorithm PM2.5 14.47 ≤ RMSE ≤ 22.89
Ignacio et al. [32] Wind Speed, Wind Direction, Temperature, Pollutant Past Values Campo de Gibraltar (industrial area), Spain Multiplayer perceptron model (MLR), Autoregressive Integrated Moving Average, Persistence (PER) SO2 :0.26 ≤ R ≤ 0.73
Present Work Embedded Pollutant Series Shadipur, Delhi Wavelet- Artifical Neural Network Fuzzy Inference System- Particle Swarm Optimization/Genetic Algorithm PM2.5: R = 0.994
SO2: R = 0.991
NO2: R = 0.994
NO: R = 0.991
NOx: R = 0.993
##### Table 2
Performance Analysis of the Models for Predicting Nitrogen Oxide (NO)
MODEL WANFIS-PSO ANFIS-PSO WANFIS-GA ANFIS-GA WANFIS-FFA ANFIS-FFA WANFIS-DE ANFIS-DE WANFIS-ACO ANFIS-ACO
R2 Training 0.9827 0.6161 0.9802 0.5899 0.9491 0.5775 0.6631 0.5484 0.0101 0.5447
Testing 0.9713 0.5075 0.978 0.5233 0.9508 0.5775 0.6316 0.5362 0.0096 0.541

RMSE Training 5.2941 24.9204 5.6537 25.8316 9.1226 28.4114 24.9419 27.0214 191.1694 27.1222
Testing 7.9566 33.1202 6.9655 32.4669 10.4381 28.4114 30.487 32.0249 215.7535 31.9014

MAE Training 3.1405 14.7228 3.4886 15.2701 6.5133 20.8815 16.2929 15.7738 118.0759 15.6743
Testing 4.4595 19.754 4.506 19.8969 7.1135 20.8815 20.8836 19.5628 138.4949 19.3828

MARE Training 22.745 112.2138 24.9821 124.5905 61.6391 230.6897 138.5161 127.6262 1.01E+03 123.3864
Testing 16.6506 70.8322 17.3578 74.5642 33.6449 230.6897 95.4234 73.9303 560.8402 72.0253
##### Table 3
Performance Analysis of the Models for Predicting Nitrogen Dioxide (NO2)
MODEL WANFIS-PSO ANFIS-PSO WANFIS-GA ANFIS-GA WANFIS-FFA ANFIS-FFA WANFIS-DE ANFI-SDE WANFIS-ACO ANFIS-ACO
R2 Training 0.9877 0.7149 0.9872 0.7042 0.9183 0.7165 0.7812 0.6893 0.0955 0.6935
Testing 0.9906 0.757 0.9902 0.7533 0.928 0.6905 0.8094 0.7592 0.0984 0.6935

RMSE Training 4.153 20.0262 4.2437 20.4163 10.942 21.7503 20.2163 21.0403 154.115 20.7621
Testing 2.8926 14.7287 2.9582 14.8509 8.2206 18.563 14.2791 14.692 111.8062 20.7621

MAE Training 2.6672 12.9012 2.8512 13.2187 7.7783 16.9302 13.8941 13.4367 89.3785 13.3784
Testing 1.9186 9.7879 1.9513 9.9526 5.6154 14.5151 10.034 9.5305 61.8355 13.3784

MARE Training 19.7852 113.1708 22.175 111.4631 62.9307 191.4781 117.6548 109.4562 579.1208 118.1893
Testing 4.5629 26.7375 4.6033 27.749 13.9168 57.1857 27.6157 25.043 158.6515 118.1893
##### Table 4
Performance Analysis of the Models for Predicting Nitrogen Oxides (NOx)
MODEL WANFIS-PSO ANFIS-PSO WANFIS-GA ANFIS-GA WANFIS-FFA ANFIS-FFA WANFIS-DE ANFI-SDE WANFIS-ACO ANFIS-ACO
R2 Training 0.9867 0.661 0.985 0.6393 0.9291 0.6282 0.6648 0.6308 0.054 0.6276
Testing 0.9595 0.5444 0.9688 0.5572 0.856 0.5311 0.632 0.5558 0.0187 0.557

RMSE Training 5.7852 29.1889 6.1414 30.1249 13.458 34.4203 31.6257 30.481 184.2189 30.5948
Testing 10.2779 34.5928 9.0363 34.0663 20.3379 37.5671 35.2764 34.1605 238.4032 34.0544

MAE Training 3.762 18.0986 3.9744 18.8794 10.3557 27.5149 21.3677 18.8559 129.6917 18.8685
Testing 5.2406 21.019 5.1722 21.0462 10.5809 28.4276 23.995 20.8502 145.7377 20.8199

MARE Training 18.2935 101.813 18.5618 108.919 63.9923 303.8288 80.1258 106.3378 1.20E+03 106.3477
Testing 11.2621 39.4309 11.5561 41.5537 25.7137 73.0377 54.9069 39.3024 367.5926 40.0871
##### Table 5
Performance Analysis of the Models for Predicting Particulate Matter PM2.5
MODEL WANFIS-PSO ANFIS-PSO WANFIS-GA ANFIS-GA WANFIS-FFA ANFIS-FFA WANFIS-DE ANFI-SDE WANFIS-ACO ANFIS-ACO
R2 Training 0.9877 0.6912 0.9853 0.6759 0.9514 0.6914 0.7355 0.6543 0.0132 0.6535
Testing 0.9853 0.6218 0.9854 0.6416 0.9043 0.6091 0.7889 0.6402 9.76E-05 0.6396

RMSE Training 10.1658 42.5825 21.4381 52.1522 20.6936 55.1953 50.3766 45.2659 345.9455 45.107
Testing 9.0462 46.809 17.2591 44.6346 23.9442 63.7773 36.3864 44.9461 360.0478 44.6953

MAE Training 6.4536 19.5684 12.914 28.8247 15.0175 38.0123 34.959 21.8757 242.7545 20.7134
Testing 6.1653 30.7722 11.958 30.4063 16.6529 54.6023 27.1786 31.6624 275.1605 30.5494

MARE Training 6.5777 19.8071 5.6767 30.8871 17.0188 56.04 41.724 25.1531 284.729 21.9384
Testing 5.9886 30.5088 5.4756 31.1767 16.1643 74.5 27.9868 34.742 293.0874 31.1902
##### Table 6
Performance Analysis of the Models for Predicting Sulphur Dioxide SO2
MODEL WANFIS-PSO ANFIS-PSO WANFIS-GA ANFIS-GA WANFIS-FFA ANFIS-FFA WANFIS-DE ANFI-SDE WANFIS-ACO ANFIS-ACO
R2 Training 0.9815 0.6169 0.9823 0.6031 0.9534 0.4992 0.5435 0.5688 4.51E-04 0.5531
Testing 0.9792 0.5076 0.9817 0.5074 0.7894 0.4383 0.4606 0.4999 9.41E-05 0.4967

RMSE Training 1.3731 6.2461 1.3419 6.3677 2.2258 8.8814 8.601 6.6253 65.4892 6.7444
Testing 0.9536 4.6432 0.8909 4.6311 3.2581 7.3658 6.1823 4.6738 56.0997 4.6791

MAE Training 0.7505 3.4773 0.7672 3.516 1.4525 7.2184 5.5394 3.6001 45.1907 3.6418
Testing 0.6069 2.9789 0.583 2.9574 1.3042 6.2474 4.5481 2.9866 38.7643 2.98

MARE Training 11.4649 51.7641 11.6339 51.372 22.2842 140.8222 82.0887 53.3888 666.2866 55.1915
Testing 6.3206 33.1995 6.0066 32.8453 14.7799 89.5434 49.3311 33.1355 411.338 34.0932
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