Prediction of Hourly PM 2.5 and PM 10 Concentrations in Chongqing City in China Based on Artificial Neural Network

Accurate prediction of air pollution is a difficult problem to be solved in atmospheric environment research. An Artificial Neural Network (ANN) is exploited to predict hourly PM 2.5 and PM 10 concentrations in Chongqing City. We take PM 2.5 (PM 10 ), time and meteorological elements as the input of the ANN, and the PM 2.5 (PM 10 ) of the next hour as the output to build an ANN model. Thirteen kinds of training functions are compared to obtain the optimal function. The research results display that the ANN model exhibits good performance in predicting hourly PM 2.5 and PM 10 concentrations. Trainbr is the best function for predicting PM 2.5 concentrations compared to other training functions with R value (0.9783), RMSE (1.2271), and MAE (0.9050). Trainlm is the second best with R value (0.9495), RMSE (1.8845), and MAE (1.3902). Similarly, trainbr is also the best in forecasting PM 10 concentrations with R value (0.9773), RMSE value (1.8270), and MAE value (1.4341). Trainlm is the second best with R value (0.9522), RMSE (2.6708), and MAE (1.8554). These two training functions have good generalization ability and can meet the needs of hourly PM 2.5 and PM 10 prediction. The forecast results can support fine management and help improve the ability to prevent and control air pollution in advance, accurately and scientifically.


INTRODUCTION
In the past 40 years, the rapid urbanization and economic growth in China have been accompanied by dramatic changes in land use and rapid growth in pollution emissions.Air pollution has become a major environmental problem of widespread concern to the government, the public and the international community (Huang et al., 2014;Geng et al., 2021;Li et al., 2022b;Liu et al., 2022).Air pollution affects climate change, ecosystems, virus transmission, human health and sustainable socio-economic development (Crippa et al., 2022;Guo et al., 2023b).The change in air pollution time series is nonlinear, and it is affected by meteorological conditions (Guo et al., 2021(Guo et al., , 2023a;;Islam et al., 2023).Ambient PM2.5 and PM10 are the main air pollutants.In 2019, PM2.5 pollution caused about 7 million premature deaths worldwide (Fowler et al., 2020).China is one of the regions that suffer the most serious health hazards from PM2.5 pollution.PM2.5 pollution in China led to the premature deaths of about 2.1 million people in 2017 (Geng et al., 2021).Therefore,

Artificial Neural Network
ANN consists of one or more median layers (for facilitating the convergence of the ANN), an output layer (to obtain the collected values), and an input layer (where input variable data will be collected).Artificial neural network is a branch of AI, which copies the biological training system (Goudarzi et al., 2021).The ANN for predicting hourly PM2.5 and PM10 concentrations has 3 layers (Fig. 1).The input layer includes hour (H) (n), PM2.5 (PM10) (n), air pressure (AP) (n), sea level pressure (SLP) (n), maximum air pressure (MAP) (n), minimum air pressure (MAP) (n), maximum wind speed (MWS) (n), extreme wind speed (EWS) (n), wind direction of extreme wind speed (WDEWS) (n),

Model Fitting and Evaluation
In order to evaluate the accuracy and prediction ability of the proposed ANN forecasting model, this study calculated three indicators, namely, correlation coefficient (R), root mean square error (RMSE) and mean absolute error (MAE).RMSE, MAE, and R are defined in Eqs. ( 1), ( 2) and (3), respectively. ) where F is the number of the original (raw) PM2.5 (PM10) data, Cl is the measured PM2.5 (PM10), C� is the average of the original (raw) PM2.5 (PM10), Bl is the simulated PM2.5 (PM10), and B� is the average of the PM2.5 (PM10) simulated by the ANN model.

The Change Characteristics of Air Pollution in Chongqing
The changes of PM2.5 and PM10 concentrations in Chongqing show a downward trend (Fig. 2).The annual average concentrations of PM2.5 and PM10 in 2014 are respectively 62.9 and 94.7 µg m -3 .However, those are 31.3and 48.3 µg m -3 .These results show that the annual average concentrations of PM2.5 and PM10 from 2014 to 2022 fell by 50.2% and 48.9%, respectively.The clean air policy plays a key role in improving air quality in Chongqing.Nevertheless, the annual average concentrations of PM2.5 and PM10 in Chongqing are still higher than the new guidance values of the World Health Organization (WHO).

Design of Network Structures and Training Algorithms
We use error analysis to determine the network structures, training functions and transfer functions.Table 1 shows the influence of different neurons in the hidden layer on the PM2.5 prediction results.The best network structure for predicting PM2.5 concentrations (n + 1) is discriminated as 18-11-1.Table 2 displays the performances of the thirteen kinds of training functions for predicting PM2.5 concentrations (n + 1) in Chongqing City, demonstrating that the trainbr training functions   .3902).Table 3 shows the impact of different transfer functions on PM2.5 prediction results.Transfer function (logsig -purelin) for predicting PM2.5 concentrations in Chongqing City is better than others during training and predicting epochs.Similarly, Table 4 shows also the influence of different neurons in the hidden layer on the PM10 prediction results.The best network structure for predicting PM10 concentrations (n + 1) is distinguished as 18-17-1.

Comparative Analysis of Training Algorithms
We also compared and analyzed the trained and predicted PM2.5 concentrations and PM10 concentrations.Fig. 3 exhibits the measured PM2.5 concentrations (n + 1), simulated PM2.5 concentrations (n + 1), and the predicted PM2.5 concentrations (n + 1) in Chognqing City.The both training functions (trainbr and trainlm) not only simulate PM2.5 concentrations (n + 1) very well during the training epoch, but also predict PM2.5 concentrations (n + 1) very well during the predicting epoch.Further analysis demonstrates that trainbr is better than trainlm in both training and  minimum or maximum PM10 concentrations.The trainbr and trainlm predicted PM10 concentrations (n + 1) in an acceptable accuracy level in Chongqing City.The agreement between the measured PM10 concentrations (n + 1) and predicted PM10 concentrations (n + 1) is also very good by utilizing trainbr and trainlm.The prediction data of traibr and trainlm is relatively close to the real data.

Comparison with Other Literatures
There are many prediction models based on time series analysis for predicting the concentrations of PM2.5 and PM10.The staging evolving spiking neural network (Staging-eSNN) model is established for predicting PM2.5 concentrations in the next 1-24 hours.RMSE of the model is about 9.1, 10.5, 10.9, 13 µg m -3 in the next 1, 3, 6, 12 hours in Shanghai (Liu et al., 2021).MLR, SVR and ANNs are used to forecast hourly PM2.5 and O3 concentrations in Manizales, Colombia.The ANN model for forecasting O3 exhibits the highest R (0.94), and the lowest RMSE (4.63).However, the developed ANN model is mediocre for PM2.5 with R (0.43), RMSE (5.45), MAE (4.19) (Cifuentes et al., 2021).A spatial pyramid pool (SPP) network is added between LSTM and CNN to build a CNN-SPP-LSTM network for hourly PM2.5 prediction in Qingdao.Compared to the LSTM-dense, the CNN-SPP-LSTM structure algorithm caused better hourly PM2.5 prediction performance with RMSE (29.244),MAE (16.146),R (0.828) (Li et al., 2022a).The extreme gradient boosting (XGBoost) model has better hourly PM2.5 prediction ability with R 2 (0.762) in Changsha than the fully connected neural network (FCNN) deep learning model with R (0.6337) (Peng et al., 2022).The novel hybrid CEEMDAN-CNN-LSTM model for daily PM2.5 prediction has the smallest RMSE (12.68) and MAE (9.6) and the highest R 2 (0.86) in Binzhou City (Xu et al., 2022).The ICNN with a 1-h time step is used for forecasting hourly PM10 and PM2.5 in South Korea.The ICNN model exhibits high prediction performance, hinted by the R 2 values of 0.976 and 0.975 for hourly PM2.5 and PM10, respectively, and the low RMSE values of 1.64 and 2.745 (Chae et al., 2021).The ensemble EEMD-LSTM model is proposed to predict hourly PM2.5 concentration at Batu Muda in an urban area.The EEMDLSTM model yields the lowest forecasting errors (RMSE of 4.8949, MAE of 2.7724) and highest R 2 (0.9673) compared to the other deep learning models (Zaini et al., 2022).The novel hybrid WPD-SE-VMD-Q-GRU method is proposed in hourly PM2.5 forecasting in Haerbin City. the WPD-SE-VMD-Q-GRU has the best effect with MAE (2.2342), MAPE (4.4552%), RMSE (2.9437) (Zheng et al., 2022).The new hybrid CEEMDAN-COOT-VMD-JAYA-LSSVM for daily PM2.5 concentration in Xi'an and Shenyang is proposed.The prediction result of CEEMDAN-COOT-VMD-JAYA-LSSVM has good prediction effect with RMSE (2.843), MAE (1.8344), MAPE (2.94%), R 2 (0.99525) (Yang et al., 2022).The Linear Mixed Effects (LME) model is used to predict the monthly-average PM2.5 concentrations to study the spatial and temporal patterns in PM2.5 concentrations in two megacities in peninsular India between 2016 and 2019.The RMSE, Mean Prediction Error (MPE) and Relative Prediction Error (RPE) of the Linear Mixed Effects (LME) model for Bengaluru are about 8.4 µg m -3 , 6.4 µg m -3 , and 21.4%, respectively.The corresponding values in the case of Hyderabad are about 11.3 µg m -3 , 8.2 µg m -3 , and 25%, respectively (Lavanyaa et al., 2022).Machine learning (ML) approaches are used to predict PM2.5 in Bishkek.The MAE, Mean Squared Error (MSE), and RMSE of the ANN are about 20, 1953, and 44 µg m -3 , respectively.The corresponding values for Random Forest Regressor (RFR) with Hyperparameter Tuning (HPT) are about 13, 800, and 28 µg m -3 , respectively.The corresponding values for Xgboost Regressor (XgbR) with HPT are about 13, 742, and 27 µg m -3 , respectively.The calculated evaluation metrics show that the best results are obtained for XgbR with HPT and RFR with HPT (Isaev et al., 2022).The Weather Research and Forecasting (WRF) model is used for simulating the meteorological prediction data in Ho Chi Minh City.The input data of the PM2.5 predictive machine learning model includes meteorological data (humidity, wind direction, temperature, and wind speed) and PM2.5 concentration data.The R 2 , RMSE, MAE, and Mean Absolute Percentage Error (MAPE) of the Neural Network Regression are about 0.66, 7.97, 5.56 and 32.26 µg m -3 , respectively.The corresponding values for the Extra Trees Regression 0.68, 7.68, 5.38, and 32.27 µg m -3 , respectively (Minh et al., 2021).The ML models are used to forecasting PM10 and PM2.5 concentrations in selected Polish agglomerations.Employing analysis and cross-validation, XGBoost performs the best, followed by random forests and neural networks, and stepwise regression performs the worst.The four regression models obtain R values of 0.97-0.99 and RMSE values of 4.0-13.5 and 2.2-9.6 for the PM10 and PM2.5, respectively (Czernecki et al., 2021).Feedforward-Backpropagation Neural Network is used to forecast the PM2.5 concentration in Malaysia.Trainlm is the most reliable prediction model with R 2 of 0.9834, RMSE of 2.398, MAE of 1.784 and MAPE of 0.106 (Chinatamby and Jewaratnam, 2023).The hybrid forecasting system based on convolutional neural network integrated with spatial-temporal attention and residual learning (STA-ResCNN) is used to forecast PM2.5 and PM10 concentrations in the Yangtze River Delta urban agglomeration.The STA-ResCNN model produces the PM2.5 prediction performance with the RMSE of 6.986, MAE of 3.918, MAPE of 12.623% in Shanghai.The STA-ResCNN model again exhibits the PM10 prediction performance with the lowest RMSE of 11.971, MAE of 6.938, MAPE of 15.048% in Shanghai (Zhang et al., 2023).The LSTM+LSTM model has a good generalization ability with an R 2 accuracy rate of 0.90 in predict next hour PM2.5 in the Istanbul Metropolitan City (Eren et al., 2023).The wavelet-packet transform (WPT) driven deep learning model is used to predict the hourly PM2.5 concentration in Qingdao.The method performs the best and achieves the lowest RMSE (3.2998) and the highest R 2 (0.9978) and Nash-Sutcliffe efficiency coefficient (NSE) (0.9955) (Zheng et al., 2023).Compared with other models, our ANN model has good accuracy.This situation demonstrates that this architecture is suitable for solving the prediction problem of serial data.

CONCLUSIONS
In this paper, an ANN model is proposed to predict 1-h ahead PM2.5 and PM10 concentrations in Chongqing City in China.Considering the nonlinear and complex relationship between PM2.5 (n + 1), PM10 (n + 1) and meteorology (n), we use multiple meteorological elements.Then, 13 training functions are applied to map weather (n), time (n), PM2.5 (PM10) (n) and PM2.5 (PM10) (n + 1) to establish an ANN model for continuous prediction.Finally, the established ANN is used for prediction to verify its effectiveness under various air pollution levels.It is found that the performance of the ANN produces excellent performance.In addition, the model based on Bayesian Regularization (BR) method greatly improves the performance of the model.
However, our research has a limitation.This research did not consider other regional factors that affect Chongqing.For example, air pollution caused by northern regions is transmitted to Chongqing through wind, but this research did not calculate its impact on air quality in Chongqing.
In the future, the proposed ANN will be exploited to investigate multistep ahead predicting for other cities.We will extend the time scale of the predictions to at least 24 hours.How to make a more accurate long term prediction of PM2.5 and PM10 concentrations is what we will continue to research.Besides that, by considering the influence of meteorological parameters and other predictor variables, the study can be extended to predict other air pollutants such as, O3, and NO2.The deep learning model will be also considered to develop multiple hybrid prediction models for future research and improvement, such as, RNN, LSTM, CNN, GRU, Interpolated convolutional neural network (ICNN), EEMD, PSO, Inverse distance weighting (IDW), Ordinary least squares (OLS), wavelet transform (WT), EMD-LSTM, ICNN, EMD-GRU, CNN-LSTM, and CEEMDAN-CNN-LSTM.We will consider the impact of geographic characteristics, other regional transmissions and air pollutant emissions, such as VOCs, SO2 and NOx.The feature importance ranking of the input parameters will been evaluated.

Table 1 .
Comparison between different neurons in hidden layer for hourly PM2.5 prediction.

Table 2 .
Comparison between various training algorithms for hourly PM2.5 prediction.
Table 5 exhibits also the performances of the thirteen kinds of training functions for predicting PM10 concentrations (n + 1) in Chongqing City, revealing that the trainbr training function has

Table 3 .
Comparison between various transfer functions for hourly PM2.5 prediction.Table6shows also the impact of different transfer functions on PM10 prediction results.Transfer function (logsig -purelin) for predicting PM10 concentrations in Chongqing City is also better than others during training, and predicting epochs.Nevertheless, the performances of trainbr are obviously superior to those of training functions.Because of the high complexity of PM10 concentrations, the prediction accuracy of the traingda algorithm is not high, but the prediction effect of the traibr algorithm is better than the other twelve prediction training functions.

Table 4 .
Comparison between different neurons in hidden layer for hourly PM10 prediction.

Table 5 .
Comparison between various training algorithms for hourly PM10 prediction. ) in Chognqing City.Similarly, the both training functions (trainbr and trainlm) not only simulate PM10 concentrations (n + 1) very well during the training epoch, but also predict PM10 concentrations (n + 1) very well during the predicting epoch.Further analysis indicates that trainbr is better than trainlm in both training and prediction epochs.Both training functions can not only copy the average PM10 concentrations, but also capture the

Table 6 .
Comparison between various transfer functions for hourly PM10 prediction.