The study and application of a novel hybrid system for air quality early-warning

Accepted Manuscript The study and application of a novel hybrid system for air quality early-warning Yan Hao, Chengshi Tian

PII: DOI: Reference:

S1568-4946(18)30520-9 https://doi.org/10.1016/j.asoc.2018.09.005 ASOC 5083

To appear in:

Applied Soft Computing Journal

Received date : 21 April 2018 Revised date : 23 August 2018 Accepted date : 4 September 2018 Please cite this article as: Y. Hao, C. Tian, The study and application of a novel hybrid system for air quality early-warning, Applied Soft Computing Journal (2018), https://doi.org/10.1016/j.asoc.2018.09.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Highlights (for review)



A modified data preprocessing technique is successfully developed.

Multi-step ahead air quality early-warning system is developed for cities in China.

Accuracy and stability of the early-warning system are improved simultaneously.

The results of the hybrid system are well-validated in three cities of China.

*Manuscript Click here to view linked References

T he study and application of a novel hybrid system for air quality early-warning







Yan Hao, Chengshi Tian*





School of Statistics, Dongbei University of F inance and Economics, Dalian, China








* Corresponding author. Address: School of Statistics, Dongbei University of F inance and Economics, Dalian 116025, China




Tel.: +86 138 8962 5565




E-mail address: [email protected].




































A bstract Air quality early-warning plays a vital role in improving air quality and human health, especially multi-step ahead air quality early-warning, which is significant for both citizens and environmental protection departments. However, most previous studies have only employed simple data decomposition to perform one-step forecasting and were aimed at enhancing forecasting accuracy or stability. Little research has improved these two standards simultaneously, leading to poor forecasting performance. Because of its significance, relevant research focused on multi-step ahead air quality early-warning is especially needed. Therefore, in this paper, a novel hybrid air quality early-warning system, which consists of four modules: data preprocessing module, optimization module, forecasting module and evaluation module, is proposed to perform multi-step ahead air quality early-warning. In this system, an effective data decomposition method called the modified complete ensemble empirical mode decomposition with adaptive noise is developed to effectively extract the characteristics of air quality data and to further improve the forecasting performance. Moreover, the hybrid Elman neural network model, optimized by the multi-objective salp swarm algorithm, is successfully developed in the forecasting module and simultaneously achieves high forecasting accuracy and stability. In addition, the evaluation module is designed to conduct a reasonable and scientific evaluation for this system. Three cities in China are employed to test the effectiveness of the proposed early-warning system, and the results reveal that the proposed early-warning system has superior ability in both accuracy and stability than other benchmark models and can be used as a reliable tool for multi-step ahead air quality early-warning.

Keywords: Air quality forecasting; Early-warning system ; Hybrid forecasting; Optimization algorithm











1 Introduction

















































 

 
   

 


  




of polluting gases has greatly damaged the environment and deteriorated the ecosystem. In recent years, air pollution has become the most serious environmental problem [1] and has led to increasing haze events in China. For example, during 27th November to 1st December 2015, China suffered from eleven severe hazes which caused serious adverse effects in North China, especially in Beijing, Henan Province and Shandong Province [2]. Furthermore, the 2016 Environmental Performance Index (EPI) illustrates that China is the second worst country among 180 countries for air quality [3]. In addition, air pollution not only directly affects the sustainable development of society but also affects people's health. Thus, the development of an accurate, simple and robust air quality early-warning system plays an important role


   
 
 

 

  

  
 
  Over the past few years, air quality forecasting has aroused great public attention, and several methods have been developed to decrease air quality forecasting error. These methods can be broadly categorized into three groups, namely: deterministic, statistical and hybrid methods. The deterministic methods can use meteorological, emission and chemistry methods to forecast air pollution concentrations [4] and do not depend on a great number of historical data [5]. However, the accuracy of deterministic methods always relies on the quality and the scale of the emission data [6]. Single statistical methods are widely used in the forecasting of concentrations of air pollutants, because they are simple to apply and more accurate than deterministic methods. For instance, Vlachogianni et al. [7] used a multiple linear regression model to forecast NOx and PM10 concentrations. Baker and Foley [8] employed a nonlinear regression model to forecast the pollutant PM2.5. However, these statistical methods cannot deal with the nonlinear features of time series [9]. Fortunately, the artificial neural network (ANN) models are capable of modeling nonlinear series [10] and are therefore regarded as powerful tools for air pollutant concentration forecasting. To the best of our knowledge, no single forecasting model can achieve high precision on all occasions, because each model has its own disadvantages [11]. For instance, the poor initial parameters of ANN will lead to unsatisfactory forecasting performance [12]. For addressing this issue, subsequent studies could employ hybrid models to obtain better forecasting accuracy [13]. Generally, the hybrid models combine different single methods to improve the effectiveness of forecasting and mainly include forecasting models (radial basis function (RBF) [14],
extreme learning machine (ELM) [15], support vector machine (SVM) [16], Elman neural network (ENN) [17], etc.), optimization algorithms (grey wolf optimizer (GWO) [18], particle swarm optimization (PSO) [19], bat algorithm (BA) [20], cuckoo search (CS) [21], whale optimization algorithm (WOA) [22], etc.) and data decomposition techniques (empirical mode decomposition (EMD) [23], ensemble empirical mode decomposition (EEMD) [24], variational mode decomposition (VMD) [25], and singular spectrum analysis (SSA) [26], etc.). For instance, Zhou et al. [27] proposed a hybrid general regression neural network (GRNN) model based on EEMD to forecast 


































































PM2.5 concentration. Qin et al. [28] developed a hybrid model that integrated EEMD, CS and back propagation neural network (BPNN) for predicting PM concentrations. Niu et al. [29] proposed a hybrid model for short-term PM2.5 concentration forecasting based on complementary ensemble empirical mode decomposition (CEEMD), support vector regression (SVR) and the GWO algorithm. Furthermore, Li and Zhu [30] used a hybrid ICEEMDAN-ICA-ELM model based on ELM, the imperialist competitive algorithm (ICA) and improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) for air quality early-warning. Moreover, from the above results in the literature, it can be concluded that hybrid models exhibit preferable predictive performance compared to single models. However, according to the above analysis, there are still many defects in most prior studies. More specifically, the drawbacks can be generalized: (1) Most of the existing studies only use simple data decomposition to extract and identify the main features of the data series, while the simple data decomposition often cannot completely capture uncertain characteristics of nonlinear and irregular data series, which leads to poor forecasting results; (2) Most previous studies have only focused on one-step forecasting, while ignoring the significance of the multi-step ahead air quality early-warning system, which is highly desirable for conducting in-depth investigations for engineering applications; (3) Most previous studies merely focused on modeling individual air quality signals centered on PM2.5 or PM10, while ignoring the importance of developing an early-warning system for all the air quality signals in practical application; (4) Most previous studies employed single-objective optimization algorithms to improve forecasting accuracy or stability in air quality forecasting, while ignoring the significance of these two issues. However, both accuracy and stability are crucial to the performance of a forecasting model. Clearly, to reach both forecasting accuracy and stability contemporaneously is a multi-objective optimization problem (MOP) instead of a single-objective problem (SOP). Fortunately, several multi-objective optimization techniques have been developed to solve this problem, such as the multi-objective particle swarm optimization (MOPSO) [31], the multi-objective ant lion optimizer (MOALO) [32] and the multi-objective dragonfly algorithm (MODA) [33], etc. In many other fields, the multi-objective optimization method has been successfully employed, including in the fields of mechanical engineering [34], chemistry [35], civil engineering [36], etc. Therefore, given the limitations of previous studies of air quality prediction discussed above, a novel multi-step ahead air quality early-warning system, based on the data preprocessing module, the optimization module, the forecasting module and the evaluation module, is proposed in this paper. More specifically, the data preprocessing module developed modified complete ensemble empirical mode decomposition with adaptive noise (MCEEMDAN) to decompose the original series, which uses VMD to decompose the high frequencies from complete ensemble empirical mode decomposition with adaptive noise (CEEMADN). Moreover, a multi-objective optimization algorithm named multi-objective salp swarm algorithm (MOSSA) is applied to optimize the initial weights and thresholds of the Elman neural network (ENN), which effectively achieves both high forecasting accuracy and 




















































stability at the same time. The hybrid MOSSA-ENN model is developed for air quality forecasting in the forecasting module. Finally, the reasonable and scientific evaluation module is an integral part of a complete early-warning system, which can verify the forecasting effectiveness using typical evaluation metrics and statistical perspective; in this study, several evaluation metrics are used in this module to test the forecasting ability. Moreover, the main differences between the proposed system and the related published work (take the latest literature [28] as an example) can be summarized as: (1) A modified data preprocessing method is employed in the
data preprocessing module, which combined CEEMDAN, and VMD is used to decompose the original data.
In contrast, a simple data preprocessing method called ICEEMDAN is used in [28]; (2) In the optimization module, a multi-objective optimization algorithm is introduced to optimize parameters of neural networks, while in the literature [28], only a single-objective optimization algorithm was used; (3) While only main pollution contaminants were forecasted in [28], multi-step forecasting for atmospheric contaminants and one important air quality indicator are all considered in the forecasting module; (4) A more comprehensive evaluation module is employed including
a
stability test, nonparametric tests, etc. T he major contributions of this paper are as follows: (1) Air quality early-warning plays a vital role in improving air quality and human health. However, despite its significance, few studies focus on the forecasting of all air quality signals, including six main pollutant concentrations (PM2.5, PM10, SO2, NO2, CO and O3) and one important air quality indicator named the air quality index (AQI). However, most previous studies center on modeling single air quality signals. Therefore, in order to conduct effective air quality forecasting, a novel air quality early-warning system is successfully developed in this paper. The effectiveness of the system is well-validated in three cities of China, indicating that the developed system is applicable and effective for air quality early-warning. (2) Development of a modified data decomposition technique. Most prior studies employed simple data preprocessing to decompose the original data, while the simple data decomposition cannot completely obtain the primary features of the original data. Thus, a modified data decomposition technique named MCEEMDAN is proposed in this study. The prediction validity of the proposed air quality early-warning system demonstrates its superiority, compared with forecasting models based on simple data decomposition. (3) Use of a multi-objective algorithm in an air quality early-warning system. Most previous studies use single-objective optimization algorithms aimed to improve forecasting accuracy or stability, while not improve these two goals simultaneously. Therefore, an algorithm called the multi-objective salp swarm algorithm is initially used in air quality forecasting, which can achieve superior accuracy and stability in air quality prediction simultaneously. (4) Aiming to achieve effective performance in both one-step and multi-step air quality early-warning. Multi-step air quality early-warning can effectively capture the dynamic behavior of the data of air quality in the future, which is more 






 
 
 
 
 
 
 


 


beneficial to air-quality forecasts than one-step forecasting. The air quality single-step forecasting is insufficient for obtaining early-warning information for air quality as much as possible. Thus, this study builds an
early-warning system to achieve accurate results for multi-step ahead air quality early-warning. (5) The focus of this study was not only on the forecasting of six main pollutant concentrations and the air quality index but also on the discussion of the fuzzy comprehensive evaluation for air quality. Moreover, the forecasting results of pollutant concentration and AQI, combined with the air quality level published by fuzzy comprehensive evaluation, will provide more useful information for people's daily lives.

 
 
 
 
 


The remainder of this study is structured as follows. Section 2 illustrates the framework of the proposed air quality early-warning system. The details of the developed early-warning system are introduced in Section 3. Section 4 provides the experimental study and analysis. Further discussion is presented in Section 5, and finally, a conclusion is provided in Section 6.

 


2 F ramewor k of the proposed air quality early-warning system

 




 
























A new multi-step ahead air quality early-warning system is proposed, which exhibits greater effectiveness in air quality forecasting. It employs a modified data decomposition technique to overcome the weaknesses of simple data decomposition; meanwhile it addresses the drawbacks of single objective optimization algorithms that only enhance either accuracy or stability. The main procedures of the developed system for air quality early warning are displayed in F igure 1, and include the following four steps: Step 1. Data preprocessing: A modified data preprocessing technique named MCEEMDAN is developed to decompose the raw air quality series into several subseries and to adequately extract the primary features of the raw data, which successfully improves the forecasting performance. Step 2. Optimization: The multi-objective salp swarm algorithm is used to optimize the parameters of the ENN model, aimed to make the ENN model achieve the two aims of higher accuracy and strong stability at the same time. Step 3. Forecasting: The ENN model optimized by the MOSSA method is developed to forecast each subseries from the MCEEMDAN. Then, the final air quality forecast value can be gained by adding the forecast results of each subseries. Step 4. Evaluating: Evaluating the forecasting performance of the developed system by comparing the forecasting results of the proposed system and other models through a scientific evaluation module. In addition, five discussions are established, including the performance of the proposed early-warning system, evaluating the superiority of the proposed early-warning system based on nonparametric tests, t

   












superiority of the proposed early-warning system, the stability of the proposed early-warning system and the fuzzy comprehensive evaluation for air quality to further test the effectiveness and practicability of the developed early-warning system.





F igure 1. Flowchart of the developed early-warning system framework.




3 Details of the proposed air quality early-warning system






To obtain accurate and stable forecasting results, the proposed air quality early-warning system is developed in this paper and includes four modules: data preprocessing, optimization, forecasting and evaluation.




3.1 Module 1: Data preprocessing






In this paper, a modified data decomposition method named MCEEMDAN, which uses the VMD to decompose the high frequency intrinsic mode functions of CEEMDAN, is established in the data preprocessing module.









3.1.1 Complete ensemble empirical mode decomposition with adaptive noise The CEEMDAN method was developed by Torres. et al. [37] and is used to further develop the decomposition methods of the EMD family. The EMD technique was proposed by Huang et al. [38] and can decompose the original sequences into intrinsic mode functions (IMFs). EMD is capable of decomposing complex data, such as nonlinear data; however, one drawback is mode mixing. The EEMD method [39]















has been proposed to solve this drawback. However, EEMD causes two difficulties, which are that the reconstructed signal still has residual noise, and the quantities of IMFs are likely to differ with the same decomposition. To solve the mode mixing problem, while maintaining the capacity to solve these additional difficulties, the method CEEMDAN was developed [37]. The major discrimination of CEEMDAN is the introduction of adaptive noise when compared with EEMD. Therefore, this paper employs the CEEMDAN algorithm for data preprocessing in phase I. The detailed steps of CEEMDAN are displayed in [37].
















3.1.2 Variational mode decomposition The VMD approach was proposed by Dragomiretskiy et al. [40] and is a nonrecursive data preprocessing method. This method is used to decompose a data series into a set of modes mn
  and each mode has a center pulsation cn, which is controlled with the decomposition process. The process to obtain the bandwidth of each mode can be described as follows: Step 1: Obtaining the unilateral frequency spectrum of each mode, through employing the Hilbert transform to calculate the linked analytic signal. Step 2: Shifting the frequency spectrum of each mode to baseband, through an exponential tuned to the several estimated frequencies. Step 3: Estimating the bandwidth of each mode, using the H 1 Gaussian smoothness of the demodulated signal. Then, the constrained variational problem is represented as Equation (1):

       min   
     
                




    





 

 
    

(1)








where f(s) represents the initial signal, the as implies the Dirac distribution and
is a convolution. Equation (1) is changed into an unconstrained problem through Equation (2):




   
                                        








where  represents the Lagrangian multipliers and implies the balancing parameter of the data-fidelity. The alternate direction method of multipliers (ADMM) is employed to deal with Equation (2). Based on ADMM method, the optimization of mn and cn can be obtained by Equation (3) and Equation (4), respectively:




 







   
 



 
     







(2)

(3)






  




  
 


  









  



  

 

(4)




    where 
 , 
 ,
 , 
  are the Fourier transforms of f(c), mt(c), 
,   ,




respectively, and k is the iteration number.






3.2 Module 2: Optimization In this section, the multi-objective optimization method named MOSSA is introduced.


 
 
 
 
 


3.2.1 The theory of multi-objective optimization problem The single-objective optimization problems can only deal with one objective, which cannot solve problems that need multiple objectives. However, multi-objective optimization can solve more than one objective and all of the objectives can be optimized contemporaneously. The multi-objective optimization problems can be represented as follows: min L (v )  l1 (v ), l2 (v ),..., lo (v )  k i (v )  0, i  1, 2,..., n  s.t . hi (v )  0, i  1, 2,..., m  L v U , i  1, 2,..., p i i  i

 


(5)

 


 
 
 
 
 
 


where p, o, n and m represent the variable number, objective functions, inequality constraints and equality constraints, respectively. k i and hi represent the i -th inequality and equality constraints. The upper and lower bounds of the i -th variable are represented by L i and U i, respectively. There are four definitions, which are Pareto Dominance, Pareto optimality, Pareto optimal set, and Pareto optimal front. With these definitions, the multi-objective problems can be easily solved. A more particular description of these definitions can be represented as follows: Definition 1. Pareto Dominance [41]:

 


Two vectors a   a1 , a2 ,..., ak  and b  b1 , b2 ,..., bk   Supposing a
dominates b (a b) if:
j  1, k , l  a j  l  b j   j  1, k : l ( a j )  l  b j 

 




 


Definition 2. Pareto optimality [42]: Supposing that  
and a is a Pareto optimality if:




Definition 3. Pareto optimal set:

b  A s.t. b






(7)

a


       




Definition 4. Pareto optimal front: A set consisting of the objective values in the Pareto solutions set: 



(6)

(8)






   


  















3.2.2 Multi-objective salp swarm algorithm The MOSSA algorithm is a multi-objective method of the salp swarm algorithm proposed by Mirjalili et al. in 2017 [43], and the major steps of this algorithm are displayed as follows: Step 1. Initialize the population of salps based on the upper and lower bounds of the variables. Step 2. Figure the impersonal values for every salp and obtain the nondominated solutions. If the repository is not full, then the archive will add the nondominated solutions. In contrast, the repository maintenance will expurgate the solutions with congesting neighborhood. Step 3. Update the repository through the nondominated
salp. Step 4. Update a coefficient a1 by employing Equation (10):




   



   

(9)

(10)







where t represents the current iteration and T represents the maximum number of iterations. Step 5. Update the position of leading and follower salps, employing Equations (11) and (12), respectively:





   


 


               
 

 





 where  , P i, ui, l i are 

 
  , the position of the food source, upper





bound and lower bound of the i -th dimension, respectively. a1, a2, a3 are random numbers.






   
   

(11)

(12)




 where    and  displays the position of j -th follower salp in i -th dimension.




Step 6. Repeat steps 2-5 until the optimal solutions
are obtained.







3.3 Module 3: F orecasting In this paper, a novel hybrid ENN model optimized by the MOSSA algorithm (MOSSA-ENN) is developed in the forecasting module, which simultaneously achieves both high forecasting accuracy and stability.








3.3.1 E lman neural network The ENN is a two-layer network that was developed by Elman in 1990 [44]. The ENN model is composed of four parts, namely: the input layer, hidden layer, output layer, and context layer. Compared to the traditional neural networks, ENN achieves better prediction results for time series.
The details of ENN can be seen in [45]. 



























3.3.2 Optimization of Elman neural network The initial weights and thresholds of the ENN model are generated randomly, by which they fall into the locally optimal solution, overfitting and low convergence speed [46]. Fortunately, the intelligent optimization algorithms can solve these issues. Therefore, to solve the shortcomings of the ENN model and to obtain the two aims including high accuracy and stability contemporaneously, the MOSSA algorithm is used to optimize the initial weights and thresholds of the ENN model, and then the hybrid MOSSA-ENN model, with high accuracy and strong stability, is developed. The main steps of MOSSA-ENN are represented as follows: Step 1. Parameter initialization. The parameters both of MOSSA and ENN model should be initialized. Step 2. Identify the objective functions of the MOSSA method. In this paper, f1 and f2 are the objective functions of MOP, which can be used as the criteria for setting the initial weight and threshold of ENN for achieving high accuracy and stability simultaneously. More specifically, the error criteria mean square error (MSE), which is widely employed in the single-objective algorithm as the function f1, is used to achieve high prediction accuracy; In addition, the standard deviation (std) can be used to evaluate the prediction stability; thus, the std of prediction errors as the other objective function f2 in the multi-objective optimization is used to demonstrate the prediction stability. Therefore, two objectives are defined as:





 


 
      
   


      
 














(13)

where O t represents the observed value, P t is the predictive value and T is the number of testing sets. Step 3. Update the position of the salps based on the objective functions, then obtain the next generation. Step 4. Identify the stop situation of this method and then optimize. Step 5. Stop optimizing and achieve the optimal parameters of the ENN model. The pseudocode of the MOSSA-ENN is shown as A lgorithm 1. Algorithm 1: MOSSA-ENN Objective functions: 
 


 
      
   


      
 





Input:




Ot
0  O
0
1 , O
0
2  ,..., O
0
p 

 -the training data




O
f 0  O
0
p  1 , O
0
p  2  ,..., O
0
p  l 

Output: 



 -
the testing data






Pf
0  P
0
p  1 , P
0
p  2  ,..., P
0
p  l 

1 2 3 4 5 6 7 8 9 10 11 12

 the forecasting data

Parameters: T the maximum iterations n the number of salp F ithe fitness of i-th salp [l i, u i] the boundaries of each salp yithe position of i-th salp tthe current number of iteration dthe dimension of the optimized problem /*Set the basic parameters of MOSSA. */ /*Initialize the salp population yi (i 

n) in regard to l i and u i. */ W H I L E (t < T ) D O /*Calculate the fitness values of each salp. */ /*Find the nondominated salps. */ /*Update the repository in regard to the obtained nondominated salps. */ I F the repository is full D O /* Omit one repository resident using the repository maintenance. */ /* Add the nondominated salp to the repository. */ END IF Choose a food source from repository: F = SelectFood(repository) /*Update the most important parameter a1. */    

13

   

14 15 16

F O R E A C H salp D O I F (i = =1) D O /*Update the position of the leading salp. */

17 18 19 20


         


          
          


E LSE /*Update the position of the follower salp. */     

       

END IF 21 END F OR 22 /*Amend the salps in regard to l i and u i. */ 23 t =t +1 24 25 E N D W H I L E 26 R E T U R N repository. 27 Obtain X
according to repository. 28 Set the initial weight and threshold of E N N according to X*. 






29 Use X* to train and update the weight and threshold of E N N. 30 Input the historical data into E N N to forecast the future changes . 











3.4 Module 4: Evaluation It is requisite to test the prediction effectiveness of the early-warning system through appropriate metrics. In this paper, six common evaluation metrics are adopted to evaluate the performance of the early-warning system, including mean absolute error (MAE), root mean square error (RMSE), mean absolute average error (MAPE), index of agreement (IA), Theil U statistic 1 (U1) and Theil U statistic 2 (U2). The equations to compute these metrics are provided as Table 1, where O i represents the observed value, P i is the predictive value and I is the number of testing sample. Table 1 Evaluation metrics.

M etric

Definition

MAE

The mean absolute error of I forecasting results

R MSE

The root mean square error of I forecasting results

M APE

The mean absolute percentage error of I forecasting results

E quation

MAE  R MSE 

M AP E 

1 I  Oi  Pi I i 1 1 I  ( Oi  Pi )2 I i 1

1 I  (Oi  Pi ) Oi 100% I i 1

IA

The index of agreement of forecasting results

I A  1   i 1 ( Oi  pi )2

U1

The
theil U statistic 1 of forecasting results

U1 

U2

The theil U statistic 2 of forecasting results

I

U2 

1

I

1 I 2  
O  P  I i 1 i i I


P O  O O  I

2

1

I

I

 
( Oi 1  Pi ) / Oi  i 1




4 E xperimental study
and analysis




 


In this section, three experiments are established to verify the effectiveness of the proposed multi-step ahead air quality early-warning system. Moreover, it should be noted that all experiments are conducted in MATLAB R2015a on Windows 10 with a 2.60 GHz Intel Core i7-6700HQ CPU, 64-bit and 8 GB RAM.

 
 
 
 
 
 




4.1 Study area Jinan, which is the capital of Shandong Province in China, is located at 36°40' North latitude and 117°00' East longitude. Jinan is a famous national tourist city because it has 72 springs and is called the spring city. In addition, the city is located in the mid-latitude zone, due to solar radiation, atmospheric circulation and geographical environment and is a temperate monsoon climate. Shanghai, which is a municipality as well as the national center city of China, is located on the Pacific West Bank and east of the Asian continent.
Shanghai is part of 



2

i

 1 I 2 1 I 2   Oi  P I i 1 i

I i 1

 
( Oi 1  Pi 1 ) / Oi  i 1

i

i 1

2




 
 
 
 
 
 
 
 



the alluvial plain in the Yangtze River Delta, which averages approximately 2.19 meters above sea level. Due to its special geographical location, the city is a subtropical monsoon climate with four distinct seasons. Harbin, which lies between 125° 42'~ 130°10' East longitude and 44°04 '~ 46°40° North latitude, is located in the northeast of China and is also the capital of Heilongjiang Province in China. The city is the first important hub of the Eurasian Continental Bridge and the air corridor and is also a historical, tourist and cultural city in China. In addition, Harbin is China's highest latitude and lowest temperature metropolis, with long winters and cooler weather in summer.




 
















4.2 Data description In this study, the daily concentrations of six air pollutants including PM2.5, PM10, SO2, NO2, CO and O3, and the important air quality indicator named AQI, collected from three cities in China including Jinan, Shanghai and Harbin, are adopted as illustrative case studies to test the performance of the proposed early-warning system in application. All the experimental data are divided into training datasets and testing datasets. For each city, the experimental data extending from January 1, 2015 to June 30, 2016 are adopted as a training dataset to develop the air quality early warning system, while the data extending from July 1, 2016 to August 31, 2016 are selected as testing data to verify the effectiveness of the proposed early-warning system. F igure 2 displays the observed six air pollutants and AQI series, including training data and testing data from the three cities. More specifically, in this study, 89.82% of the data is selected as training data and the remaining 10.18% of the data is used as testing data. The descriptive statistics of all datasets used in this paper are shown in Table 2, which reveals that the experimental data collected from three different cities shows different characteristics.





Table 2 Descriptive statistics of the data used for the simulation. P M 2.5(
/m3)

P M 10(
/m3)

SO 2(
/m3)

N O 2(
/m3)

C O(mg/m3)

O 3(
/m3)

AQI

16 419 82.2600 51.2460

32 609 154.3700 78.1190

9 186 43.2500 28.3220

15 156 47.4400 20.5300

1 6 1.3100 0.6350

5 172 67.5800 39.3910

33 475 121.8200 58.8240

6 219 50.8342 32.3229

8 259 68.7340 38.4314

6 74 14.9409 8.6166

4 142 42.8539 20.5245

0.38 2.21 0.8175 0.2843

9 174 73.5517 29.9675

23 270 78.6535 37.9368

7 650 58.1970 62.2122

15 668 90.0772 75.3554

2 222 32.6962 40.8123

13 145 44.6141 21.4509

0.37 4.38 1.0647 0.4556

6 139 43.6470 21.7627

16 466 86.4581 66.2469

Jinan Minimum Maximum Mean Standard Shanghai Minimum Maximum Mean Standard H arbin Minimum Maximum Mean Standard












Figure 2. Detailed information on the studied data.

























4.3 E xperimental design To demonstrate the effectiveness of the developed air quality early-warning system, three experiments are designed in this study. More specifically, in Experiment I, the dataset collected from Jinan is used to test the superiority of the multi-objective optimization algorithm used in this study. In Experiment II, the air pollutant concentrations and AQI series collected in Jinan are employed, and in addition, four comparison models, including autoregressive integrated moving average (ARIMA), ENN, MOSSA-ENN, CEEMDAN-MOSSA-ENN, are used to verify the performance of the developed air quality early-warning system. To further evaluate the superiority of the developed system, the datasets collected from Shanghai and Harbin are employed as another experiment, called Experiment III. Moreover, if the developed air quality early-warning system performs better than other compared models in both Experiment II and Experiment III, we can safely conclude the effectiveness and universal applicability because of the different environments of the three selected study areas including economic development, geographical location and climatic factors, etc. Furthermore, the main experimental parameters are listed in Table 3.





Table 3 Main experimental parameters. Experimental parameters

ENN

CEEMDAN

VMD

M OSSA

Default value AQI

P M 10

P M 2.5

SO 2

N O2

O3

Input number

8

8

8

8

8

8

8

Hidden number

17

17

17

17

17

17

17

Output number

1

1

1

1

1

1

1

Noise standard deviation

0.2/0.1/0.2*

0.2/0.1/0.2*

0.2/0.2/0.1*

0.1

0.1

0.1

0.3

Number of realizations

200

200

200

200

200

200

200

Max_Iter

5000

5000

5000

5000

5000

5000

5000




2000/1000/2000*

1000

1000

1000/1000/2000*

1000

1000

1000

Number of modes

8

8

8

8

8

8

8

Max_Iter

100

100

100

100

100

100

100

The number of salp

50

50

50

50

50

50

50

li

-2

-2

-2

-2

-2

-2

-2

ui

2

2

2

2

2

2

2




*












4.4 E xperiment I: Test of multi-objective optimization algorithm In this experiment, the data of six air pollutants and AQI from Jinan are selected to evaluate the forecasting effectiveness of the developed system. More specifically, for the first comparison (I), MCEEMDAN-SSA-ENN is used in this section, which is employed to test the forecasting performance of multi-objective optimization; for the second comparison (II), two well-known multi-objective optimizations: MODA and multi-objective grey wolf optimizer (MOGWO) are employed to verify the prediction accuracy of the developed early-warning system. In addition, all the performance results for each model are shown in Tables 4 and 5 (the bold values depicted the best

refers to the experimental parameters of Jinan, Shanghai and Harbin, respectively.





CO









values of each performance metrics in all the models used), and F igure 3 which displays the one-step to three-step prediction result of all air pollutants series and AQI.





F igure 3. Forecasting results of the developed system and other compared models.











From Tables 4 and 5, and F igure 3, we can conclude that: (1) In comparison I, the multi-objective optimization model (MCEEMDAN-MOSSA-ENN) is superior to the single-objective model (MCEEMDAN-SSA-

 
 
 


 

MCEEMDAN- MOSSA-ENN model exhibits the minimum MAPE at 3.8218%, 5.6585%, and 6.0907% for 1-step to 3-step forecasting, respectively, while the MCEEMDAN-SSA-ENN achieves a larger MAPE at 4.7085%, 7.0908%, and 7.7962% for one-step to three-step forecasting, respectively. The forecasting 



























 
 
 
 
 
 
 



differences of the results between these two models imply that the prediction validity of the developed system based on multi-objective optimization is superior to that of the single-objective optimization model. (2) In comparison II, upon comparing the developed early-warning system with the MCEEMDAN-MODA-ENN model and the MCEEMDAN-MOGWO-ENN model, it can be clearly found that
the developed system significantly outperforms the MCEEMDAN-MODA-ENN model and the MCEEMDAN-MOGWO-ENN model because it performs better for all air pollutants and AQI. For example, it can be observed that the MAPE values of the developed system for the all air pollutants and AQI listed in Table 5 are 3.8218% (AQI), 5.3440% (PM2.5), 4.2233% (PM10), 3.3662% (SO2), 3.6423% (NO2), 4.0396% (CO) and 5.7193% (O3), respectively, which are smaller than those of other two models at 1-step forecasting. In the 2-step and 3-step predictions, the proposed early-warning system also achieves minimum MAPE values. From the detailed analysis, it is obvious that the MOSSA algorithm achieves the best performance compared with the other two well-known algorithms (MODA and MOGWO), which proves the superiority of the developed early warning system in air pollutant concentration and AQI forecasting. (3) Moreover, from Figure 3, it can be clearly seen that the developed system has better forecasting performance than other compared models for all air six pollutants and AQI series, which further demonstrates the developed system is effective for air quality early-warning. Remar k : Based on the above experiment, including all air pollutants and AQI, the developed early-warning system MCEEMDAN-MOSSA-ENN, exhibits superior performance in almost all forecasting error indexes, which can be widely employed in air pollutant concentration and AQI forecasting. Due to the outstanding performance of the MOSSA algorithm compared with other considered algorithms, this paper employs the MOSSA-based model for air quality early-warning.









Table 4 
Comparison of prediction performances of a single-objective optimization-based model and a multi-objective optimization-based model. MCEEMDAN-SSA-ENN

AQI

PM 2.5

PM 10

SO 2

NO 2

CO

O3

MCEEMDAN-MOSSA-ENN

MAE

RMSE

MAPE

IA

U1

U2

MAE

RMSE

MAPE

IA

U1

U2

1-step

3.5688

4.3900

4.7085

0.9929

0.0254

0.1916

2.9205

3.7718

3.8218

0.9948

0.0218

0.1876

2-step

5.0167

6.3568

7.0908

0.9847

0.0366

0.2782

4.1188

5.5445

5.6585

0.9883

0.0322

0.2549

3-step

5.7122

7.7956

7.7962

0.9744

0.0448

0.3520

4.3186

5.8344

6.0907

0.9873

0.0337

0.2687

1-step

2.7350

3.4383

6.6785

0.9947

0.0305

0.2202

2.1919

3.0592

5.3440

0.9959

0.0272

0.1718

2-step

4.0722

5.2801

10.2973

0.9870

0.0467

0.2971

3.3577

4.3091

8.1684

0.9916

0.0382

0.2362

3-step

4.5493

5.9135

11.6171

0.9815

0.0517

0.3285

3.0574

4.5582

7.0424

0.9907

0.0405

0.2552

1-step

4.6914

5.8485

5.6511

0.9940

0.0277

0.2094

3.7206

5.1020

4.2233

0.9955

0.0242

0.1607

2-step

7.2178

9.0774

9.0448

0.9851

0.0430

0.2601

5.8367

7.7315

7.0652

0.9892

0.0366

0.2360

3-step

6.8824

8.8458

9.3217

0.9857

0.0415

0.2879

6.8417

8.9661

8.1615

0.9852

0.0426

0.2795

1-step

0.8285

1.0878

4.0527

0.9868

0.0258

0.2284

0.6826

0.9448

3.3662

0.9901

0.0223

0.1885

2-step

1.0837

1.4483

5.2644

0.9771

0.0343

0.2952

0.8712

1.2373

4.2800

0.9825

0.0291

0.2522

3-step

1.1189

1.5174

5.5055

0.9730

0.0359

0.3303

1.0032

1.4223

4.9822

0.9765

0.0337

0.3077

1-step

1.2248

1.5157

3.9592

0.9934

0.0212

0.1662

1.1460

1.4433

3.6423

0.9941

0.0202

0.1538

2-step

1.6797

2.1553

5.4858

0.9865

0.0301

0.2404

1.5799

1.9993

5.0651

0.9884

0.0279

0.2205

3-step

1.9830

2.6274

6.5655

0.9788

0.0367

0.3065

1.8902

2.4232

6.1358

0.9821

0.0338

0.2772

1-step

0.0420

0.0561

4.3027

0.9915

0.0266

0.1785

0.0387

0.0512

4.0396

0.9930

0.0243

0.1587

2-step

0.0605

0.0789

6.2203

0.9828

0.0376

0.2606

0.0547

0.0713

5.7522

0.9859

0.0339

0.2310

3-step

0.0728

0.0980

7.6468

0.9724

0.0468

0.3301

0.0680

0.0915

7.2278

0.9763

0.0433

0.3021

1-step

4.0228

4.9336

6.3576

0.9906

0.0290

0.2432

3.5808

4.7931

5.7193

0.9911

0.0283

0.2146

2-step

4.7744

5.9451

7.4581

0.9860

0.0349

0.2883

4.0162

5.3978

6.6187

0.9886

0.0318

0.3080

3-step

5.5064

7.2795

9.4976

0.9781

0.0427

0.4996

4.6333

6.1721

7.7376

0.9847

0.0363

0.3714












Table 5 
Comparison of prediction performances of different multi-objective optimization algorithms-based models. MCEEMDAN-MODA-ENN MAE RMSE MAPE IA U1

AQI 1-step 2-step 3-step PM2.5 1-step 2-step 3-step PM10 1-step 2-step 3-step SO2 1-step 2-step 3-step NO2 1-step 2-step 3-step CO 1-step 2-step 3-step O3 1-step 2-step 3-step

U2

MCEEMDAN-MOGWO-ENN MAE RMSE MAPE IA U1

U2

3.8680 4.7904 5.0545 0.9914 0.0277 0.2118 3.8607 4.6617 5.1013 0.9917 0.0269 0.2010 2.9205 3.7718 3.8218 0.9948 0.0218 0.1876 4.8381 6.0201 6.6418 0.9860 0.0348 0.2615 5.2930 6.8418 7.2002 0.9815 0.0396 0.2949 4.1188 5.5445 5.6585 0.9883 0.0322 0.2549 6.0738 7.7560 8.2407 0.9756 0.0449 0.3553 5.9471 7.6912 8.0864 0.9761 0.0444 0.3670 4.3186 5.8344 6.0907 0.9873 0.0337 0.2687 2.9429 3.8206 6.8872 0.9936 0.0337 0.2176 2.9156 3.7227 6.8926 0.9939 0.0329 0.2049 2.1919 3.0592 5.3440 0.9959 0.0272 0.1718 4.1118 5.2287 9.8028 0.9878 0.0460 0.2817 4.2803 5.5080 10.3744 0.9860 0.0487 0.3008 3.3577 4.3091 8.1684 0.9916 0.0382 0.2362 4.7228 6.1729 11.2470 0.9824 0.0540 0.3288 5.5491 7.5576 14.4654 0.9658 0.0646 0.4063 3.0574 4.5582 7.0424 0.9907 0.0405 0.2552 4.7512 6.2644 5.5083 0.9930 0.0296 0.1805 4.6879 6.1368 5.5636 0.9933 0.0289 0.1851 3.7206 5.1020 4.2233 0.9955 0.0242 0.1607 6.2672 7.9408 7.5365 0.9881 0.0375 0.2463 6.2148 8.1311 7.6879 0.9879 0.0384 0.2474 5.8367 7.7315 7.0652 0.9892 0.0366 0.2360 7.1052 9.3213 8.3970 0.9834 0.0441 0.3030 8.1570 10.9206 10.2761 0.9769 0.0512 0.3444 6.8417 8.9661 8.1615 0.9852 0.0426 0.2795 0.7542 1.0144 3.6873 0.9885 0.0241 0.2204 0.8065 1.1266 3.8846 0.9854 0.0267 0.2324 0.6826 0.9448 3.3662 0.9901 0.0223 0.1885 1.0405 1.5372 4.9939 0.9731 0.0366 0.3041 1.1450 1.5934 5.6268 0.9705 0.0377 0.3472 0.8712 1.2373 4.2800 0.9825 0.0291 0.2522 1.2125 1.7106 5.9968 0.9646 0.0405 0.3646 1.3770 1.8146 6.7024 0.9571 0.0429 0.3852 1.0032 1.4223 4.9822 0.9765 0.0337 0.3077 1.6793 2.0182 5.4317 0.9875 0.0279 0.2265 1.3401 1.6677 4.3429 0.9920 0.0232 0.1852 1.1460 1.4433 3.6423 0.9941 0.0202 0.1538 2.1094 2.6693 6.7228 0.9786 0.0370 0.2952 1.7980 2.2844 5.8482 0.9844 0.0318 0.2573 1.5799 1.9993 5.0651 0.9884 0.0279 0.2205 2.3681 3.0579 7.8081 0.9710 0.0423 0.3556 2.2877 2.9528 7.5473 0.9730 0.0411 0.3466 1.8902 2.4232 6.1358 0.9821 0.0338 0.2772 0.0446 0.0585 4.6218 0.9907 0.0278 0.1934 0.0452 0.0578 4.7868 0.9908 0.0273 0.1877 0.0387 0.0512 4.0396 0.9930 0.0243 0.1587 0.0572 0.0750 5.9915 0.9843 0.0356 0.2539 0.0636 0.0836 6.7569 0.9798 0.0394 0.2772 0.0547 0.0713 5.7522 0.9859 0.0339 0.2310 0.0735 0.0994 7.7665 0.9714 0.0472 0.3304 0.0775 0.1030 8.2408 0.9681 0.0485 0.3449 0.0680 0.0915 7.2278 0.9763 0.0433 0.3021 3.8947 5.1406 5.8449 0.9899 0.0305 0.2403 5.0194 6.1083 7.3860 0.9853 0.0362 0.2939 3.5808 4.7931 5.7193 0.9911 0.0283 0.2146 5.1824 7.3135 7.8752 0.9788 0.0435 0.3312 5.4301 6.7569 8.1863 0.9809 0.0399 0.3296 4.0162 5.3978 6.6187 0.9886 0.0318 0.3080 6.7026 9.1804 10.4101 0.9655 0.0546 0.4622 7.3698 9.7782 11.5809 0.9543 0.0572 0.5181 4.6333 6.1721 7.7376 0.9847 0.0363 0.3714





U2

MCEEMDAN-MOSSA-ENN MAE RMSE MAPE IA U1




 
 
 
 




 






































4.4 E xperiment I I: Case in Jinan To test the validity of the proposed multi-step ahead air quality early-warning system, the air pollutant concentrations and AQI series selected in Jinan are addressed in this section. Four benchmark models including ARIMA, ENN, MOSSA-ENN, and CEEMDAN-MOSSA-ENN, as well as six evaluation criteria
such as the MAE, RMSE, MAPE, IA, U1 and U2, are chosen to verify the validity of the developed model. Three different model comparisons are chosen in this section. Comparison I (ENN vs. MOSSA-ENN) aims to test the superiority of the multi-objective optimization method. Comparison II (i.e., MOSSA-ENN vs. CEEMDAN-MOSSA-ENN, and CEEMDAN-MOSSA-ENN vs. MCEEMDAN-MOSSA-ENN) is used to emphasize the importance of the data decomposition method in the hybrid forecasting model. Moreover, comparison III is employed to compare the proposed prediction model with the traditional forecasting method (ARIMA), in order to express the prediction capability of the proposed early-warning system in this study. In addition, the forecasting results are depicted in Tables 6 and 7, where the bold values are the optimal value of each index among the studied models. Moreover, for the sake of showing the detailed forecasting results, F igure 4 displays the prediction results of AQI for all models.
More detailed forecasting results are displayed below: (1) In Comparison I, through comparing the ENN model with the MOSSA-ENN model, it can be gained that the MOSSA-ENN model outperforms the ENN model, which demonstrates the superiority of the MOSSA method. For example, in Tables 6 and 7, the MAPE values of the MOSSA-ENN model for all air pollutants and AQI are 27.2807% (AQI), 41.3475% (PM2.5), 34.4053% (PM10), 17.5729% (SO2), 24.2840% (NO2), 26.0214% (CO) and 27.1739% (O3), respectively, which is smaller than for the ENN model at 1-step forecasting. In the 2-step and 3-step predictions, the developed early-warning system still has minimum MAPE values in almost all air pollutant concentrations series. (2) Comparison II is used to testify the contribution of data decomposition techniques through comparing MOSSA-ENN with CEEMDAN-MOSSA-ENN and CEEMDAN-MOSSA-ENN with MCEEMDAN-MOSSA-ENN (MOSSA-ENN vs. CEEMDAN-MOSSA-ENN and CEEMDAN-MOSSA-ENN vs. MCEEMDAN-MOSSA-ENN). According to the results displayed in Tables 6 and 7, it can be concluded that employing data decomposition methods can improve the forecasting accuracy significantly. Taking PM2.5 as an example, the MAE, RMSE, MAPE, IA, U1 and U2 values of MCEEMDAN -MOSSA-ENN are 2.1919, 3.0592, 25.3440%, 0.9959, 0.0272 and 0.1718 at 1-step forecasting, respectively, which achieves the best values at all evaluation criteria among the compared models. More specifically, from the above analysis, the data decomposition technique is a significant tool to improve prediction effectiveness and the MCEEMDAN performs better than the original CEEMDAN. (3) In comparison III, in order to compare the forecasting performance of the proposed early-warning system with the traditional forecasting model, the 


























ARIMA model is selected as a benchmark model. It is clear that the developed model outperforms the ARIMA model. For example, the MCEEMAN-MOSSA-ENN model exhibits the best MAPE vales of PM10 at 4.2233%, 7.0652%, and 8.1615% for 1-step to 3-step prediction, respectively. (4) To depict the detailed forecasting results, the AQI results for 1-step to 3-step prediction are displayed in F igure 4. From Figure 4, it can be observed that the developed early-warning system is superior to all selected compared models in 1-step to 3-step forecasting. Moreover, the prediction values of the developed system are closer to the actual data, which also verifies that the developed system is reliable for air quality early-warning. Remar k : According to the above analysis, the developed early-warning system has the best values in almost all evaluation criteria (including MAE, RMSE, MAPE, IA, U1 and U2) at all air pollutant concentrations and AQI. Therefore, it can be concluded that the proposed early-warning system has better performance than other models. More specifically, the data decomposition technique MCEEMDAN and multi-objective optimization MOSSA successfully improve the air quality forecasting performance and can be widely used in air quality forecasting, as well as in other fields.




F igure 4. Forecasting results of AQI in Jinan.









Table 6 
Results of the proposed early-warning system and other compared models. ARIMA ENN Indices 1-step 2-step 3-step 1-step 2-step 3-step MAE 18.7474 23.5993 25.4423 20.2318 24.2952 26.6326 RMSE 25.1793 32.7288 36.5268 24.0724 29.4099 32.6111 MAPE 23.5603 31.1835 35.0364 28.3582 34.4839 39.3461 AQI IA 0.7305 0.5181 0.3296 0.6857 0.5106 0.4228 U1 0.1459 0.1901 0.2116 0.1339 0.1617 0.1764 U2 0.7510 0.6592 0.8860 0.7687 0.7899 0.9339 MAE 16.2043 19.3427 20.7924 16.9275 20.5240 22.6657 RMSE 21.9258 27.4426 29.7450 20.7443 24.9268 27.5084 MAPE 36.3437 45.6856 51.4159 43.8858 53.5649 61.2098 PM 2.5 IA 0.7538 0.5707 0.4414 0.7172 0.5330 0.4505 U1 0.1951 0.2451 0.2648 0.1779 0.2115 0.2292 U2 0.8076 0.6258 0.8912 0.7757 0.8023 0.9144 MAE RMSE MAPE IA U1 U2

PM 10

29.2778 38.2857 32.1789 0.6979 0.1807 0.7493

35.5000 47.0159 41.2737 0.4970 0.2224 0.6312

38.7087 51.9468 47.5832 0.3131 0.2472 0.8846

28.1998 34.7091 35.3436 0.6775 0.1595 0.7537

32.9770 40.9075 42.1057 0.5208 0.1857 0.7275

36.6702 45.4780 48.9766 0.3898 0.2039 0.9168

MOSSA-ENN CEEMDAN-MOSSA-ENN MCEEMDAN-MOSSA-ENN 1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step 19.9398 24.0860 26.2659 8.7978 10.0052 11.9036 2.9205 4.1188 4.3186 23.7072 29.1266 31.8694 10.6462 11.7236 14.6227 3.7718 5.5445 5.8344 27.2807 33.2889 38.5161 11.3674 13.7461 15.8299 3.8218 5.6585 6.0907 0.7144 0.5392 0.4452 0.9535 0.9411 0.8966 0.9948 0.9883 0.9873 0.1323 0.1605 0.1728 0.0619 0.0678 0.0845 0.0218 0.0322 0.0337 0.7393 0.7889 0.9309 0.5633 0.6275 0.7670 0.1876 0.2549 0.2687 16.1418 19.5904 21.4848 8.6346 8.5326 9.5805 2.1919 3.3577 3.0574 20.2416 24.4506 26.5501 11.0134 11.0576 12.5409 3.0592 4.3091 4.5582 41.3479 50.4940 57.8210 19.5079 20.5068 22.0371 5.3440 8.1684 7.0424 0.7305 0.5371 0.4614 0.9426 0.9412 0.9215 0.9959 0.9916 0.9907 0.1753 0.2101 0.2242 0.0991 0.0992 0.1119 0.0272 0.0382 0.0405 0.7512 0.7576 0.9081 0.6739 0.6834 0.7171 0.1718 0.2362 0.2552 27.3045 31.8999 35.4016 13.7557 14.6350 16.8856 3.7206 5.8367 6.8417 33.7423 38.8913 43.6584 17.1295 18.0632 20.8572 5.1020 7.7315 8.9661 34.4053 40.4077 46.7333 15.7568 17.4457 19.9701 4.2233 7.0652 8.1615 0.7047 0.5567 0.4169 0.9396 0.9301 0.8995 0.9955 0.9892 0.9852 0.1550 0.1771 0.1966 0.0811 0.0857 0.0988 0.0242 0.0366 0.0426 0.7473 0.7683 0.9371 0.6438 0.6301 0.7707 0.1607 0.2360 0.2795












Table 7 
Results of the proposed early-warning system and other compared models. Indices MAE RMSE MAPE SO 2 IA U1 U2 MAE RMSE MAPE NO 2 IA U1 U2 MAE RMSE MAPE CO IA U1 U2 MAE RMSE MAPE O3 IA U1 U2

1-step 3.9000 5.1785 18.4971 0.6079 0.1239 0.8814 7.1303 9.5051 21.0523 0.7146 0.1336 0.6852 0.2583 0.3218 26.2855 0.6772 0.1529 0.7917 19.8642 24.8675 28.1206 0.7366 0.1478 0.8346

ARIMA 2-step 3.4304 4.9091 16.3156 0.6031 0.1196 0.9362 8.9771 12.0165 28.0340 0.5739 0.1666 0.7355 0.2790 0.3365 29.0196 0.6165 0.1599 0.8088 20.9720 26.4958 31.4884 0.6818 0.1597 1.0317

3-step 3.7403 5.3631 17.1134 0.5149 0.1337 0.9406 10.7950 13.5108 34.6720 0.3677 0.1900 0.8854 0.2751 0.3631 28.2750 0.4785 0.1766 0.9237 25.0669 31.7591 39.7345 0.5865 0.1940 1.1221

1-step 3.5729 4.6616 18.3909 0.5939 0.1071 0.8984 7.2974 8.7109 24.5313 0.5846 0.1212 0.8103 0.2510 0.2999 26.8954 0.5943 0.1414 0.8514 18.2491 22.3989 29.0829 0.7350 0.1319 0.7462

ENN 2-step 3.7305 4.8077 19.5411 0.5681 0.1096 0.9449 8.3632 9.9400 28.6575 0.4809 0.1368 0.8655 0.2706 0.3170 29.8770 0.4941 0.1486 0.8926 19.4932 24.5474 33.0561 0.6558 0.1443 1.0961

3-step 4.0009 5.1232 21.0620 0.5105 0.1164 0.9120 9.0580 10.7946 31.6083 0.3504 0.1483 0.8992 0.2880 0.3462 31.6928 0.2891 0.1635 0.9648 21.5196 26.5883 37.8495 0.5943 0.1558 1.0836

MOSSA-ENN 1-step 2-step 3-step 3.3977 3.5285 3.7301 4.5685 4.6971 4.9239 17.5729 18.5640 19.6991 0.5722 0.5406 0.4808 0.1059 0.1082 0.1132 0.8990 0.9460 0.9181 7.1059 8.1011 8.7363 8.7279 9.7658 10.5359 24.2840 28.1271 30.7274 0.5863 0.4983 0.4132 0.1210 0.1338 0.1443 0.8314 0.8851 0.9203 0.2449 0.2624 0.2804 0.2922 0.3104 0.3377 26.0214 28.7035 30.6442 0.6063 0.5083 0.2974 0.1383 0.1460 0.1602 0.8330 0.8733 0.9465 17.2547 19.2243 21.8118 22.0936 24.9111 27.2303 27.1739 32.6353 38.6882 0.7535 0.6599 0.5815 0.1305 0.1466 0.1594 0.7448 1.1449 1.1109








CEEMDAN-MOSSA-ENN 1-step 2-step 3-step 1.6796 1.8520 2.1009 2.1397 2.4506 2.7700 8.5723 9.1305 10.1928 0.9447 0.9247 0.8941 0.0499 0.0576 0.0654 0.6456 0.6702 0.7548 3.9735 4.2974 4.6121 5.2440 5.5301 5.8331 13.0635 13.5950 14.3859 0.9140 0.8958 0.8787 0.0730 0.0778 0.0821 0.8623 0.8244 0.9071 0.1286 0.1459 0.1602 0.1536 0.1748 0.1929 13.5728 15.3723 16.8061 0.9164 0.8933 0.8684 0.0730 0.0826 0.0910 0.6384 0.6367 0.7029 8.4226 10.1645 11.8717 10.7595 12.7380 14.4739 12.5229 14.8158 19.0540 0.9535 0.9280 0.8992 0.0635 0.0752 0.0851 0.7739 0.8271 1.0948

MCEEMDAN-MOSSA-ENN 1-step 2-step 3-step 0.6826 0.8712 1.0032 0.9448 1.2373 1.4223 3.3662 4.2800 4.9822 0.9901 0.9825 0.9765 0.0223 0.0291 0.0337 0.1885 0.2522 0.3077 1.1460 1.5799 1.8902 1.4433 1.9993 2.4232 3.6423 5.0651 6.1358 0.9941 0.9884 0.9821 0.0202 0.0279 0.0338 0.1538 0.2205 0.2772 0.0387 0.0547 0.0680 0.0512 0.0713 0.0915 4.0396 5.7522 7.2278 0.9930 0.9859 0.9763 0.0243 0.0339 0.0433 0.1587 0.2310 0.3021 3.5808 4.0162 4.6333 4.7931 5.3978 6.1721 5.7193 6.6187 7.7376 0.9911 0.9886 0.9847 0.0283 0.0318 0.0363 0.2146 0.3080 0.3714























 
 
 
 
 
 
 




4.5 E xperiment I I I: Additional case in Shanghai and H arbin To further
demonstrate the effectiveness and applicability of the developed early-warning system, the air pollutant concentrations and AQI collected from Shanghai and Harbin are chosen as an additional case. All of the forecasting results of this experiment are shown in Tables 8-11 (the best values of each evaluation criteria are shown in boldface) and F igure 5. More specifically, Tables 8 and 9 display the  
 

  
 

 



F igure 5 shows the forecasting results of all air pollutant concentrations and AQI at 3-step prediction. Based on the prediction results displayed in Tables 8-11, similar conclusions to those in Jinan can be determined: the developed early-warning system achieves the best forecasting ability among all of the models (i.e., ARIMA model, MOSSA-ENN model, CEEMDAN-MOSSA-ENN model). Taking the prediction results of   
3 as an example, in 1-step forecasting, the developed early-warning system exhibits the least forecasting errors, with MAE, RMSE, MAPE, IA, U1 and U2 values of 3.6627, 4.6785, 5.4552%, 0.9947, 0.0272 and 0.2479, respectively. The better performance to improve prediction ability is based on the data decomposition technique MCEEMDAN and multi-objective optimization MOSSA as well. From F igure 5, it is observed that the proposed system has superior forecasting ability than other compared models, which further supports the results that show the proposed system is superior in terms of air quality early-warning. Remar k : The experimental results of Shanghai and Harbin revealed that the proposed early-warning system obtains the best performance compared with other models in this study, which indicates that MCEEMDN and the MOSSA play a significant role in improving prediction ability. Furthermore, in all experiments, the developed system achieves excellent prediction performance compared with other considered models, which proves that the system has universal utility for multi-step ahead air quality early-warning in different environments.









Table 8 
Results of the proposed early-warning system and other compared models (Shanghai).
ARIMA ENN MOSSA-ENN CEEMDAN-MOSSA-ENN MCEEMDAN-MOSSA-ENN Indices 1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step MAE 13.6099 14.3727 16.1562 20.6915 24.0363 26.9381 19.4249 22.6375 25.9558 6.3159 7.3379 7.9379 2.4092 3.7024 4.2952 RMSE MAPE AQI IA U1 U2 MAE RMSE MAPE PM 2.5 IA U1 U2

18.7757 24.9074 0.8496 0.1495 0.7351 8.3046 12.2649 32.3765 0.8483 0.1859 0.7387

18.1558 27.8751 0.8409 0.1475 0.7931 9.3132 12.7831 37.3440 0.8178 0.1980 0.8482

19.6858 33.7684 0.7828 0.1586 0.8561 9.1680 12.3107 39.9873 0.8116 0.1883 0.8132

23.3523 50.0471 0.6940 0.1743 0.9301 14.6369 16.5724 83.9107 0.6794 0.2252 0.9517

28.3360 61.9877 0.5999 0.2057 1.0036 17.7968 20.8204 107.3624 0.5759 0.2707 0.9983

31.7468 69.7462 0.5254 0.2261 1.0147 20.0228 23.1098 120.2206 0.5232 0.2920 1.0093

21.5833 45.9405 0.7405 0.1626 0.9067 11.7304 13.7373 62.5573 0.7635 0.1941 0.8476

26.1399 57.5884 0.6439 0.1922 0.9931 13.5949 15.9392 77.8675 0.6983 0.2200 0.9137

29.9469 66.3953 0.5603 0.2153 1.0108 15.8845 18.2653 91.7416 0.6178 0.2459 0.9503

8.4746 11.0737 0.9712 0.0686 0.4666 3.3943 4.7608 12.8482 0.9793 0.0720 0.4505

10.2683 12.8087 0.9576 0.0830 0.4585 4.0786 5.6697 15.6311 0.9702 0.0859 0.5307

10.4639 14.1934 0.9562 0.0846 0.5633 4.4385 6.0584 16.1749 0.9657 0.0923 0.5562

3.0986 4.5480 0.9965 0.0247 0.1873 1.6451 2.1221 7.9772 0.9960 0.0320 0.2456

5.3393 6.5721 0.9894 0.0428 0.2465 2.1578 2.7888 9.6639 0.9930 0.0422 0.2674

5.7585 8.0010 0.9876 0.0462 0.3498 2.7526 3.5778 12.0075 0.9883 0.0538 0.3817

MAE RMSE MAPE IA U1 U2

9.7965 13.8750 22.2502 0.8617 0.1365 0.7958

10.6244 15.5328 24.8494 0.8162 0.1541 0.8378

12.0563 15.4266 30.4460 0.7929 0.1504 0.8460

14.3717 16.6098 40.4493 0.7459 0.1542 0.8863

16.8248 19.7209 49.4180 0.6608 0.1793 0.9561

19.2800 22.2602 57.6573 0.6085 0.1974 0.9803

12.1473 14.8757 32.9668 0.8149 0.1399 0.8405

13.9569 16.7994 39.5138 0.7526 0.1563 0.9086

16.1140 18.6476 46.9112 0.7078 0.1695 0.9433

5.4350 8.8459 10.7905 0.9470 0.0895 0.5517

5.6287 8.8284 11.3473 0.9480 0.0887 0.5389

5.9226 8.9688 11.7678 0.9433 0.0908 0.6335

1.9780 2.4594 4.6705 0.9963 0.0244 0.1959

3.0355 4.0434 7.3493 0.9900 0.0401 0.2867

3.7893 5.0086 8.9126 0.9844 0.0495 0.3663

PM 10












Table 9 
Results of the proposed early-warning system and other compared models (Shanghai).
Indices MAE RMSE MAPE SO 2 IA U1 U2 MAE RMSE MAPE NO 2 IA U1 U2 MAE RMSE MAPE CO IA U1 U2 MAE RMSE MAPE O3 IA U1 U2

1-step 1.2784 1.5965 13.7476 0.8351 0.0837 0.8518 6.2632 8.6955 26.2136 0.8332 0.1568 0.5458 0.0666 0.0928 9.6050 0.8792 0.0655 0.5685 17.4437 23.8111 25.5573 0.8549 0.1382 0.9695

ARIMA 2-step 1.3986 1.7818 14.8404 0.7414 0.0942 0.8640 7.9365 11.3568 33.0360 0.6931 0.2047 0.5977 0.0797 0.1116 11.3783 0.8171 0.0789 0.6159 20.4427 26.0445 30.9883 0.8233 0.1538 1.0185

3-step 1.4284 1.9915 14.5422 0.6682 0.1060 0.8706 8.6451 10.9693 37.0897 0.6464 0.2027 0.7055 0.0836 0.1108 12.0722 0.7874 0.0794 0.6793 18.0868 22.7210 29.0922 0.8314 0.1315 0.8651

1-step 1.3319 1.6557 15.2844 0.7731 0.0840 0.8857 7.2741 9.1040 35.1622 0.7743 0.1580 0.6812 0.0832 0.1072 12.6977 0.7320 0.0748 0.7764 17.8835 22.0540 26.0780 0.8381 0.1313 1.0268

ENN 2-step 1.6008 1.9252 18.3259 0.6604 0.0970 0.9275 8.9745 11.3423 44.0806 0.6358 0.1932 0.7899 0.0966 0.1259 14.9271 0.6004 0.0873 0.8839 19.4260 23.3972 28.4714 0.7997 0.1423 1.0049

3-step 1.7911 2.1186 20.5638 0.5983 0.1058 0.9157 9.9262 12.0767 49.4250 0.5532 0.2049 0.9188 0.1100 0.1371 16.8915 0.5013 0.0950 0.9391 20.7649 24.4537 30.6871 0.7520 0.1485 0.9846

MOSSA-ENN 1-step 2-step 3-step 1.2002 1.4323 1.5029 1.5474 1.7975 1.9466 13.3919 15.9155 16.7400 0.8072 0.6968 0.6171 0.0799 0.0926 0.0996 0.8713 0.9107 0.8872 6.9997 8.4371 9.6861 9.0362 11.2461 12.2336 32.0974 39.5786 46.2113 0.7807 0.6402 0.5374 0.1584 0.1941 0.2094 0.6369 0.7594 0.8696 0.0777 0.0928 0.1068 0.1055 0.1234 0.1358 11.6744 14.2200 16.3674 0.7624 0.6377 0.5351 0.0737 0.0855 0.0939 0.7228 0.8355 0.8930 17.3931 18.9389 20.0440 22.3992 23.4775 24.2824 24.7590 26.7231 28.1548 0.8397 0.8115 0.7666 0.1340 0.1443 0.1497 1.0576 1.0315 0.9810








CEEMDAN-MOSSA-ENN 1-step 2-step 3-step 0.5111 0.6196 0.7144 0.6705 0.8158 0.9548 5.2909 6.5864 7.5173 0.9730 0.9605 0.9467 0.0354 0.0429 0.0506 0.4964 0.6234 0.6951 4.4810 4.5094 4.3418 6.3175 6.1891 5.7483 19.9999 19.7271 19.1626 0.9293 0.9273 0.9362 0.1093 0.1078 0.1016 1.2000 1.1438 0.9639 0.0549 0.0536 0.0584 0.0780 0.0750 0.0786 7.8374 7.6836 8.4554 0.9197 0.9198 0.9077 0.0554 0.0532 0.0554 1.1568 1.0006 0.8019 8.7380 10.4714 11.6350 11.5716 13.5374 14.5155 12.9119 15.4560 16.6112 0.9653 0.9494 0.9396 0.0667 0.0783 0.0851 0.7381 0.8056 0.7799

MCEEMDAN-MOSSA-ENN 1-step 2-step 3-step 0.2613 0.3697 0.4541 0.3390 0.4897 0.5857 2.9068 4.1648 4.9355 0.9939 0.9873 0.9811 0.0177 0.0256 0.0306 0.2104 0.3397 0.3903 1.6443 1.9756 2.0756 2.2642 2.6531 2.8844 8.2243 9.6351 10.3401 0.9904 0.9866 0.9841 0.0400 0.0468 0.0507 0.3802 0.4026 0.4261 0.0122 0.0175 0.0219 0.0154 0.0235 0.0317 1.8090 2.6060 3.2233 0.9969 0.9928 0.9868 0.0108 0.0165 0.0223 0.1885 0.2786 0.3435 3.6627 5.0900 6.1238 4.6785 6.4773 7.8931 5.4552 7.8911 9.3574 0.9947 0.9893 0.9834 0.0272 0.0377 0.0460 0.2479 0.3325 0.3702





Table 10 
Results of the proposed early-warning system and other compared models (Harbin).
ARIMA ENN MOSSA-ENN CEEMDAN-MOSSA-ENN MCEEMDAN-MOSSA-EN Indice 1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step MAE 10.290 10.870 11.469 10.186 11.069 12.576 9.4129 9.8353 11.657 4.5186 5.1063 6.4080 2.2903 3.1553 4.0620 RMSE 13.212 13.290 13.952 12.991 14.031 15.237 12.344 12.738 14.203 5.5854 6.9837 8.7061 2.8739 4.1137 MAPE 25.739 27.991 29.916 28.330 31.762 36.041 25.458 27.964 33.049 12.265 13.626 16.604 5.8562 7.8708 AQI IA 0.6765 0.6063 0.5697 0.6001 0.4913 0.4493 0.6623 0.5713 0.5029 0.9462 0.9157 0.8654 0.9878 0.9740 0.1450 0.1480 0.1523 0.1384 0.1486 0.1585 0.1326 0.1364 0.1491 0.0608 0.0759 0.0952 0.0315 U2 0.7068 0.8920 0.8367 0.7015 0.9318 0.9728 0.6374 0.8496 0.9300 0.6248 0.5974 0.7119 0.2363 MAE 8.7897 9.8521 10.210 8.4787 9.4022 10.969 8.2364 9.3162 11.448 3.7380 4.4526 5.3570 1.6290 RMSE 11.487 12.694 13.543 11.353 12.313 13.543 11.350 12.739 14.111 5.2645 6.1989 6.9754 2.1057 MAPE 46.357 53.500 56.147 49.634 58.154 69.134 45.597 55.129 67.941 19.657 22.897 27.900 8.8205 IA 0.6722 0.5651 0.5049 0.6558 0.5527 0.4988 0.6528 0.5274 0.4409 0.9331 0.9102 0.8773 0.9913 U1

PM 2. 5

U1 U2

PM 10

0.0614

0.3533 2.6162 3.6220

0.4829 3.3021 4.6347

14.0812 17.2008 0.9743

0.9563

0.2336 0.2637 0.2728 0.2201 0.2382 0.2520 0.2238 0.2519 0.2702 0.1077 0.1262 0.1445 0.0428 0.0728 0.8734 0.9923 0.8695 0.7379 0.9219 0.9378 0.7135 0.8931 0.9438 0.6742 0.6747 0.7374 0.2340 0.3944

0.0939

0.1851 0.1882 0.1937 0.1749 0.1902 0.2022 0.1675 0.1745 0.1869 0.0590 0.0985 0.1112 0.0336 0.0560 0.7575 0.9442 0.8896 0.7167 0.9659 1.0100 0.6696 0.9003 0.9652 0.4607 0.5416 0.6575 0.1870 0.3359








0.9525

0.0451

MAE 13.022 13.676 13.823 12.895 14.200 16.018 11.798 12.350 14.239 4.3178 6.5926 7.5634 2.3812 3.7674 RMSE 16.392 16.329 16.925 16.180 17.774 19.385 15.260 15.966 17.452 5.2463 8.8049 9.9250 3.0032 5.0240 MAPE 35.258 37.850 38.304 39.830 45.801 51.586 35.901 39.650 45.223 13.171 19.173 21.561 6.5576 10.8277 IA 0.6508 0.5842 0.5275 0.5805 0.4767 0.4454 0.6059 0.5197 0.4722 0.9676 0.9089 0.8739 0.9909 0.9748 U1 U2

5.5563 9.9325

0.5372 4.1535 5.7688 11.7215 0.9641 0.0648 0.4312





Table 11 
Results of the proposed early-warning system and other compared models (Harbin).
Indices MAE RMSE MAPE SO 2 IA U1 U2 MAE RMSE MAPE NO 2 IA U1 U2 MAE RMSE MAPE CO IA U1 U2 MAE RMSE MAPE O3 IA U1 U2

1-step 1.4825 1.9693 25.5249 0.8049 0.1445 0.8796 6.8230 8.5632 23.4763 0.6324 0.1388 0.8240 0.1137 0.1521 12.4771 0.7240 0.0816 0.7302 13.7970 17.5692 28.3469 0.7204 0.1549 0.8697

ARIMA 2-step 1.7320 2.1474 30.3956 0.7631 0.1573 0.9106 8.4433 10.2505 29.4387 0.4936 0.1666 0.9346 0.1262 0.1567 13.6508 0.6641 0.0854 0.8672 15.8032 18.5956 32.5579 0.6153 0.1655 0.8363

3-step 1.7917 2.2024 32.8635 0.7780 0.1610 0.8665 7.0413 8.5988 24.7233 0.5939 0.1405 0.9689 0.1328 0.1634 14.3537 0.5887 0.0879 0.8550 13.2823 16.2608 29.4335 0.6701 0.1444 0.9064

1-step 1.2083 1.4867 21.6066 0.8604 0.1100 0.7666 6.0154 7.5408 22.9935 0.5507 0.1202 0.7858 0.1155 0.1467 13.0078 0.6721 0.0775 0.7392 12.8761 16.1611 28.4365 0.7027 0.1425 0.8702

ENN 2-step 1.3919 1.7514 25.9245 0.7938 0.1291 0.9113 6.8721 8.2798 26.7654 0.4092 0.1311 0.9189 0.1228 0.1503 13.9456 0.5749 0.0796 0.8967 14.0420 16.6518 31.1887 0.6052 0.1472 0.9449

3-step 1.4182 1.7405 26.8828 0.8021 0.1276 0.9640 6.5584 8.0998 25.8594 0.4215 0.1280 0.9643 0.1422 0.1667 16.4868 0.4878 0.0872 0.9018 12.9860 15.8707 30.8496 0.6086 0.1400 1.0037

MOSSA-ENN 1-step 2-step 3-step 1.1733 1.3326 1.4033 1.5115 1.7134 1.7325 18.7575 21.9106 22.7142 0.8566 0.8031 0.7971 0.1163 0.1333 0.1361 0.7622 0.8425 0.8962 5.7831 6.5567 6.7225 7.4157 8.0962 8.1853 22.1686 25.5721 26.1488 0.5252 0.3722 0.3560 0.1189 0.1294 0.1303 0.7801 0.9218 0.9621 0.1099 0.1144 0.1369 0.1425 0.1416 0.1594 12.1598 12.6598 15.4872 0.7057 0.6272 0.5190 0.0757 0.0756 0.0842 0.7274 0.8766 0.8922 12.2718 13.7098 12.7304 15.7780 16.2945 15.5065 26.8436 29.8102 29.6895 0.7272 0.6419 0.6622 0.1396 0.1447 0.1367 0.8782 1.0360 1.1002








CEEMDAN-MOSSA-ENN 1-step 2-step 3-step 0.7884 0.8969 0.9300 0.9672 1.1426 1.2198 14.6885 16.5234 16.1486 0.9490 0.9305 0.9253 0.0690 0.0812 0.0866 0.7261 0.7400 0.6979 3.5566 3.8964 4.0903 4.3940 4.8316 5.0667 13.0994 14.2688 15.0703 0.8837 0.8514 0.8321 0.0716 0.0785 0.0821 0.6783 0.6863 0.7180 0.0537 0.0603 0.0672 0.0738 0.0858 0.0882 5.9386 6.7169 7.4355 0.9249 0.9030 0.9000 0.0396 0.0459 0.0472 0.6236 0.5682 0.6505 6.6763 7.5399 8.2604 9.2319 10.3567 11.0121 14.1563 16.0283 17.5734 0.9245 0.8995 0.8887 0.0820 0.0922 0.0986 0.6618 0.6813 0.8827

MCEEMDAN-MOSSA-ENN 1-step 2-step 3-step 0.5113 0.6946 0.6463 0.6195 0.8407 0.8321 8.8163 12.2825 11.5029 0.9813 0.9657 0.9663 0.0450 0.0608 0.0606 0.3425 0.5027 0.5117 1.0816 1.3270 1.7015 1.3442 1.7093 2.1745 3.8724 4.8090 6.0625 0.9916 0.9862 0.9768 0.0218 0.0277 0.0354 0.1398 0.1970 0.2543 0.0191 0.0284 0.0319 0.0259 0.0380 0.0429 2.1202 3.1427 3.5327 0.9925 0.9837 0.9787 0.0139 0.0204 0.0231 0.1807 0.2501 0.2983 1.8045 2.5563 2.4432 2.3200 3.1186 3.2744 3.9346 5.6333 5.4413 0.9957 0.9919 0.9911 0.0206 0.0277 0.0292 0.1154 0.1513 0.1794








Figure 5. Illustration of MAPE for 3-step forecasting in Shanghai and Harbin.























4.6 Summary Based on the results of Experiments I
III, we can obtain the following conclusions: (a) The developed air quality early-warning system based on the MCEEMADN method and MOSSA algorithm achieves better forecasting effectiveness than other considered models, and significantly improved the forecasting accuracy of the developed system. (b) As for all six air pollutant concentrations and AQI series, the developed system achieves better prediction performance than other compared models, indicating that the developed system has great effectiveness for air quality early-warning. (c) In all of the data series including Jinan, Shanghai and Harbin, the developed system obtains superior performance compared with the compared models. Thus, it can be concluded that the developed system can be widely employed for air quality early-warning system.




5 Discussion






To further verify the effectiveness and practicability of the developed early-warning system, the forecasting performance, stability and air quality evaluation are discussed in this section.

























5.1 Discussion I: The performance of the proposed early-warning system The forecasting effectiveness (FE) [47] and grey relational analysis (GRA) [48] can be considered as effective tools for estimating the forecasting performance. In GRA, grey relational degrees (GRD) are used to display the relevance between prediction results and actual results. To verify the accuracy of the proposed early-warning system, FE and GRA are employed in this section. The results of FE and GRD are depicted in Table 12 and the best values of each metric are shown in boldface. Furthermore, FE1 indicates the one-order forecasting effectiveness and FE2 indicates the two-order forecasting effectiveness. Through the results of FE and GRD, the conclusion can be clearly drawn that the proposed system has better forecasting accuracy as compared to other benchmark models. Using Experiment I as an example, for 1-step forecasting, by the results of the developed system and other models including MCEEMDAN-SSA-ENN, MCEEMDA-MODA-ENN and MCEEMDAN-MOGWO-ENN, the FE1 values of the three benchmark models and proposed system are 0.9531, 0.9505, 0.9533 and 0.9579; the FE2 values are 0.9149, 0.9093, 0.9131 and 0.9184; and the GRD values are 0.9265, 0.9233, 0.9289 and 0.9337, respectively, which means that the proposed system has better prediction accuracy than other models. In addition, the proposed system still achieves better forecasting accuracy through the results of FE and GRD at 2-step and 3-step forecasting. Based on the above analysis in this section, the proposed early-warning system achieves better prediction performance compared with other models, which is highly valid for air quality prediction. 







Table 12 
Results for FE and GRD. Experiment

Model

 


MCEEMDAN-SSA-ENN MCEEMDAN-MODA-ENN MCEEMDAN-MOGWO-ENN MCEEMDAN-MOSSA-ENN

 


 

(Shanghai)

Experim

( Harbin)

FE1

FE2

1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step 0.9531 0.9505 0.9533 0.9579

0.9315 0.9348 0.9377 0.9406

0.9257 0.9203 0.9288 0.9350

0.9149 0.9093 0.9131 0.9184

0.8646 0.8765 0.8825 0.8829

0.8466 0.8447 0.8638 0.8665

0.9265 0.9233 0.9289 0.9337

0.9184 0.9223 0.9267 0.9290

0.9272 0.9221 0.9248 0.9295

ARIMA

0.7430 0.7162 0.6931 0.5870 0.5487 0.5213 0.6982 0.7213 0.7238

ENN

0.7205 0.6858 0.6605 0.5643 0.5170 0.4835 0.6916 0.7096 0.7013

MOSSA-ENN

0.7304 0.6945 0.6682 0.5714 0.5231 0.4904 0.6959 0.7137 0.7066

CEEMDAN-MOSSA-ENN

0.8675 0.8535 0.8365 0.7698 0.7438 0.7139 0.8187 0.8355 0.8350

MCEEMDAN-MOSSA-ENN

0.9579 0.9406 0.9350 0.9184 0.8829 0.8665 0.9337 0.9290 0.9295

ARIMA ENN MOSSA-ENN CEEMDAN-MOSSA-ENN MCEEMDAN-MOSSA-ENN

0.7875 0.6670 0.7016 0.8896 0.9511

0.7553 0.6296 0.6636 0.8819 0.9341

0.7420 0.5947 0.6254 0.8762 0.9215

0.6413 0.5185 0.5533 0.7931 0.9086

0.6019 0.4729 0.5056 0.7783 0.8765

0.5886 0.4436 0.4733 0.7802 0.8549

0.7352 0.7319 0.7318 0.8376 0.9265

0.7413 0.7098 0.7213 0.8498 0.9159

0.7317 0.6752 0.6961 0.8372 0.9001

ARIMA

0.7286 0.6898 0.7001 0.5687 0.5382 0.5412 0.7081 0.6625 0.6726

ENN

0.7330 0.7090 0.6863 0.5659 0.5352 0.5144 0.7105 0.6706 0.6679

MOSSA-ENN

0.7478 0.7254 0.6924 0.5838 0.5572 0.5318 0.7142 0.6773 0.6683

CEEMDAN-MOSSA-ENN

0.8705 0.8480 0.8305 0.7612 0.7203 0.7002 0.8384 0.8168 0.8000

MCEEMDAN-MOSSA-ENN

0.9450 0.9195 0.9117 0.9000 0.8509 0.8313 0.9190 0.8883 0.8817








GRD

























5.2 Discussion I I: Evaluating the superiority of the proposed early-warning system based on
nonparametric tests To evaluate the proposed early warning system, using the statistical best-performing approach in all considered models, three nonparametric tests including Friedman, Friedman Aligned Ranks and Quade tests [49] are employed in this study. The results of the nonparametric tests based on the MAPE values of each model are displayed in Table 13, which lists the average ranks, statistics and related p-values. Based on the results of Friedman, Friedman Aligned Ranks and Quade tests, it can be clearly seen that the proposed system is significantly superior to other compared models, because it has the minimum ranks and the related p-values are less than 0.0001. Using Experiment II as an example, the ranks of the proposed system by Friedman, Friedman Aligned Ranks and Quade tests are 1.0000, 11.5714 and 1.0000, respectively, which are the best ranks in all cases; in addition, the related p-value is 0.0000, which means that the proposed system significantly outperforms the other models. Moreover, the proposed system still achieves the best ranking for Friedman, Friedman Aligned Ranks and Quade tests in Experiment I and Experiment III and is significantly superior to other models at the 1% level. Based on the results and analysis of this section, the proposed system is the statistical best-performing model in all considered models and can be widely used for air quality prediction.









Table 13 
Results for nonparametric tests. Experiment

Statistics tests

MCEEMDANSSA-ENN

MCEEMDANMODA-ENN

MCEEMDANMOGWO-ENN

MCEEMDANMOSSA-ENN

Statistic

p-value

 


Friedman Friedman Aligned Quade

2.6191 44.9524 2.5844

2.7381 49.3571 2.7836

3.6429 64.1191 3.6320

1.0000 11.5714 1.0000

52.8324 40.2774 25.1477

0.0000 0.0000 0.0000

Statistics tests Friedman  
Friedman Aligned Quade Statistics tests Friedman  
(Shanghai) Friedman Aligned Quade Statistics tests Friedman  
Friedman Aligned (Harbin) Quade

ARIMA

ENN

MOSSA-ENN

3.5238 67.8095 3.4805

4.8095 80.1429 4.8139

3.6667 74.0476 3.7056

ARIMA

ENN

MOSSA-ENN

3.2381 52.5238 3.1558

4.9524 86.4286 4.9610

3.8095 79.8571 3.8831

ARIMA

ENN

MOSSA-ENN

3.8571 73.5714 3.6580

4.6667 78.6191 4.7533

3.4762 69.8095 3.5887








CEEMDAN- MCEEMDANStatistic MOSSA-ENN MOSSA-ENN 2.0000 1.0000 178.6487 30.3810 12.6191 67.9372 2.0000 1.0000 44.9659 CEEMDAN- MCEEMDANStatistic MOSSA-ENN MOSSA-ENN 2.0000 1.0000 400.0000 28.0000 18.1905 67.9246 2.0000 1.0000 57.0922 CEEMDAN- MCEEMDANStatistic MOSSA-ENN MOSSA-ENN 2.0000 1.0000 138.6331 28.7619 14.2381 65.1500 2.0000 1.0000 42.3932

p-value 0.0000 0.0000 0.0000

p-value 0.0000 0.0000 0.0000

p-value 0.0000 0.0000 0.0000
















 
 
 
 
 
 
 


 
 
 
 
 


5.3 Discussion I I I 


  
  


  
 -warning system A novel hybrid air quality early-warning system is developed in this study, to evaluate the performance of the data preprocessing module, optimization module and forecasting module. Three improvement percentages [50] of error criteria, including MAE, RMSE and MAPE are introduced in this section. The results for the improvement percentages are listed in Table 14 and are the average results of 1-step to 3-step forecasting. Based on the results of MOSSA-ENN and MCEEMDN-MOSSA-ENN used for the Shanghai dataset, it is clear that the MCEEMDAN-MOSSA-ENN model has significant improvements compared with the MOSSA-ENN model. It can be concluded that the data preprocessing module proposed in this study can improve the forecasting ability of air quality. In addition, through the results of ENN and MOSSA-ENN used in the Harbin datasets, the effectiveness of the optimization module can be calculated: it improves the MAPE by 10.1315%, 5.0210%, 11.8757%, 14.7253% 2.3091%, 7.2676% and 4.5941% for AQI, PM2.5, PM10, SO2, NO2, CO and O3, respectively, which reveals the superior performance of the optimization module. Moreover, by comparing MCEEMDAN-MODA-ENN with MCEEMDAN-MOSSA-ENN used the Jinan datasets, it significantly improves the MAE, RMSE and MAPE in all air pollutant concentrations and AQI series, which demonstrates the effectiveness of the forecasting module proposed in this study. In summary, main modules of the proposed early-warning system, including the data preprocessing module, optimization module and forecasting module, have superior performance compared with other models and can be employed as an effective approach for air quality early-warning. Table 14 Results for the improvement percentages.

Improvement percentages MAE R MSE M APE

AQI

P M 10

P M 2.5

84.8981 81.9962 88.8791

84.2582 82.4892 87.2497

79.4842 77.5130 82.7449

8.6855 6.9938 10.1315

-0.1980 -2.5402 5.0210

10.8818 8.6097 11.8757

Improvement percentages MAE R MSE M APE Improvement percentages MAE R MSE M APE  
 
 


SO 2

N O2

CO

O3

M OSSA-E N N vs. M C E E M D N-M OSSA-E N N 74.0686 73.5867 74.2143

77.2217 75.9244 75.8857

81.6491 81.0081 82.1616

73.8380 73.0062 71.7341

5.1302 4.3678 7.2676

3.0091 2.2703 4.5941

E N N vs. M OSSA-E N N 2.7369 0.3196 14.7253

1.9826 0.9409 2.3091

M C E E M D A N-M O D A-E N N vs. M C E E M D N-M OSSA-E N N 22.7537 17.9797 21.7610

26.3740 21.2247 25.4879

10.7563 8.3340 10.7955

14.3421 14.4081 13.3076

25.6800 24.7807 26.3397

8.3608 8.4532 7.8423

20.4786 21.9076 14.5921

5.4 Discussion I V: The stability of the proposed early-warning system In this study, the proposed early-warning system is aimed to achieve better accuracy and stability, synchronously. The prediction stability, which is a significant 










 













indicator in forecasting models, should be employed to assess the ability of the proposed system. The variance (VAR) is an important metric that is used to evaluate the forecasting stability and a smaller VAR indicates stronger stability. Therefore, the VAR is employed to assess the forecasting stability of the proposed system in this study. The VAR results are displayed in Table 15, and the best values of each experiment are in bold. It can be seen that the proposed system has smaller VAR values for all experiments, which means the proposed system achieves better forecasting stability compared with other benchmark models. Moreover, the forecasting stability of the proposed system is not only superior to the single-objective optimization model (MCEEMDAN-SSA-ENN), but it is also better than other multi-objective optimization models. In summary, the developed early-warning system achieves the best stability. Table 15 Results for VAR. Model

 


MCEEMDAN-SSA-ENN MCEEMDAN-MODA-ENN MCEEMDAN-MOGWO-ENN MCEEMDAN-MOSSA-ENN

 


 

(Shanghai)

E xperim

( H arbin)










VAR

E xperiment

1-step

2-step

3-step

11.4223 13.0546 11.3530 10.1243

25.0504 21.5082 19.1794 19.0060

25.1280 28.4920 25.5568 23.6273

ARIMA

481.1162

710.1764

884.0265

ENN

361.0159

485.5253

571.3731

MOSSA-ENN

355.6512

475.5887

558.0106

CEEMDAN-MOSSA-ENN

93.7843

108.1567

144.0642

MCEEMDAN-MOSSA-ENN

10.1243

19.0060

23.6273

ARIMA ENN MOSSA-ENN CEEMDAN-MOSSA-ENN MCEEMDAN-MOSSA-ENN

194.4310 180.8550 175.3535 45.3680 6.1883

222.6030 228.9440 208.3041 56.5898 13.4637

194.6603 261.5261 237.1241 59.1214 18.6619

ARIMA

139.4405

153.6706

145.4719

ENN

115.3771

129.0316

130.1421

MOSSA-ENN

113.4400

124.5554

130.8074

CEEMDAN-MOSSA-ENN

25.2796

39.9961

50.5176

MCEEMDAN-MOSSA-ENN

3.8927

9.2483

13.7290

5.5 Discussion V: The fuzzy comprehensive evaluation for air quality Based on the future changes of main air pollutant concentrations, air quality evaluation and grading can be performed as in future research to release alert information in the form of air quality level. To do this, the fuzzy comprehensive evaluation for air quality, based on the multiple super-scale weighting method, is discussed in this section and can be used to visualize the forecasting result of six main pollutant concentrations. And the details of the fuzzy comprehensive evaluation 
























Data point 01/07/2016 03/07/2016 05/07/2016 07/07/2016 09/07/2016 11/07/2016 13/07/2016 15/07/2016 17/07/2016 19/07/2016 21/07/2016 23/07/2016 25/07/2016 27/07/2016 29/07/2016 31/07/2016 01/08/2016 03/08/2016 05/08/2016 07/08/2016 09/08/2016 11/08/2016 13/08/2016

method for air quality can be seen in [51]. The fuzzy comprehensive evaluation results for air quality are represented in Table 16. I-V denotes different air quality 



!"
! "
! "
!
"

!


"
 


A ctual is the air quality level evaluated by actual data, while the 1-step, 2-step and 3-step are the air quality levels calculated by forecasting data. Moreover, the metric called hit rate is used in [51], which indicates the uniformity ratio of different !"

  

 


 
 
forecasting air quality level equals the actual level, almost at the data point at 1-3 step forecasting, which can be quantified: the hit rate for 1-step, 2-step and 3-step are 59/62, 58/62, 56/62, respectively. Moreover, the forecasting results obtained by the developed system have no negative influence on publishing the effective alert information by air quality level. Therefore, we can safely and reasonably draw the conclusion that the developed early-warning system can meet the requirements for practical application. The forecasting results of pollutant concentration and AQI, combined with the air quality level published by the fuzzy comprehensive evaluation, will provide more useful information for people's daily lives. Table 16 Typical air quality evaluation results of the three study areas. Jinan

Shanghai

H arbin

A ctual

1-step

2-step

3-step

A ctual

1-step

2-step

3-step

A ctual

1-step

2-step

3-step

II III IV III II II III II IV III II II II II II II I III II II II II II

II III IV III II II III II IV III II II II II III II I III II I II II II

II III IV III II II III II IV III II II II II III II I III III II II II II

II III IV III II II III III IV III II II II II II II I III III II II II II

II II I I I I II II III II II II I II III I I I I I I I I

II II I I I I III II III II II II II II III I I I I I I I I

II II I I I I III II III II II II II II III I I I I I I I I

II II II I I II III II III II II II II II III I I I II I I I I

I I I II II II I I I II II I I I I II II II I I I II II

I I I II II II I I I II II I I I I II II II I I I II II

I I I II II II I I I II II I I I I II II I II I I III II

I I I II II II I I I II II I I I II II II II I I I II II








15/08/2016 17/08/2016 19/08/2016 21/08/2016 23/08/2016 25/08/2016 27/08/2016 29/08/2016 31/08/2016

II II II II II II II II II

II II II II II II II I II

II II II II II II II II II

II II II II II II II II II

I I I II I I I I II

I I I II I II I I II

I I I II I II I I II

I I I II I II I I II

I I I I I I I I I

I I I I II I I I I




6 Conclusion



































Air quality early-warning plays a vital role in improving air quality and protecting human health and is significant for containing deteriorating air quality. However, air pollutant series are nonstationary, which makes it difficult to obtain an accurate forecasting result. To solve such a difficult problem and to achieve high accuracy and stability simultaneously, a new air quality early-warning system is initially proposed for multi-step ahead air quality early-warning. Three datasets, collected from Jinan, Shanghai and Harbin, were employed as case studies to verify the effectiveness of the proposed air quality early-warning system. The experimental results reveal that the proposed system is superior in both forecasting accuracy and stability, compared with all of the comparison models. Moreover, through the results of the experiments in this paper, the developed early-warning system exhibits some superiority as follows: First, a modified data decomposition method named the modified complete ensemble empirical mode decomposition with adaptive noise is successfully developed for air quality forecasting, which successfully reduces the nonstationary feature of the original data, is superior to the complete ensemble empirical mode decomposition with adaptive noise method, and further improves the prediction ability of the proposed system. Second, a multi-objective optimization method called the multi-objective salp swarm algorithm is used to optimize the Elman neural network model in this paper. This is superior to the single-objective optimization method (i.e., salp swarm algorithm) and two popular multi-objective optimization methods (i.e., multi-objective grey wolf optimizer and multi-objective dragonfly algorithm), and can simultaneously achieve superior forecasting accuracy and stability. Finally, the proposed early-warning system not only
achieves effective performance in single-step forecasting but also outperforms other compared models in all experiments for multi-step air quality early-warning. More specifically, in Experiment I of testing of the multi-objective optimization algorithm, the averaged MAPE values of the proposed system are reduced 11.7869%, 7.8022% and 13.6190%
in one-step to three-step prediction, compared with other optimization algorithm-based models; In Experiment II of the case in Jinan, the proposed system improves the MAPE 78.5668%, 81.1935%, 79.3183%, 71.6724%, 77.8528%, 76.0691% and 73.8964% for AQI, PM2.5, PM10, SO2, NO2, CO and O3, respectively; For Experiment III, the developed system 



I I I I II I I I I

I I I I II I I I I


















achieves the smallest MAPE values in both the Shanghai and Harbin data series. Overall, based on the above comparative studies, the developed system has been proven superior in terms of air quality early warning compared with other models. With the advantage of the proposed early-warning system discussed above, the proposed system can be used as a reasonable tool for predicting air quality signals, and it can also be used as a promising method to predict other complex data series, such as electrical load forecasting, wind speed forecasting, electricity price forecasting, etc.
Moreover,
in the future, it will be significant for the development an interval forecasting model to quantify the uncertainty for air quality early-warning.
Additionally, designing more effective deep-learning-based models to improve the performance of
air quality early-warning is another important subject for future research.






A cknowledgements This work was supported by Major Program of National Social Science Foundation of China (Grant No.17ZDA093).






Conflicts of Interest The authors declare that there is no conflict of interest regarding the publication of this paper.




























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