∎

11institutetext: Jalpa B Shah 22institutetext: Electronics and Communication
Engineering Department, Amrita School of Engineering, Bengaluru 560035, India
33institutetext: Biswajit Mishra 44institutetext: Dhirubhai Ambani Institute
of Information and Communication Technology, Gandhinagar 382007, India
Tel.: +91 079 30510561
44email<EMAIL_ADDRESS>
# Analytical Equations based Prediction Approach for PM2.5 using Artificial
Neural Network

Jalpa B Shah1 Biswajit Mishra2

(Received: date / Accepted: date)

###### Abstract

Particulate matter pollution is one of the deadliest types of air pollution
worldwide due to its significant impacts on the global environment and human
health. Particulate Matter (PM2.5) is one of the important particulate
pollutants to measure the Air Quality Index (AQI). The conventional
instruments used by the air quality monitoring stations to monitor PM2.5 are
costly, bulkier, time-consuming, and power-hungry. Furthermore, due to limited
data availability and non-scalability, these stations cannot provide high
spatial and temporal resolution in real-time. To overcome the disadvantages of
existing methodology this article presents analytical equations based
prediction approach for PM2.5 using an Artificial Neural Network (ANN). Since
the derived analytical equations for the prediction can be computed using a
Wireless Sensor Node (WSN) or low-cost processing tool, it demonstrates the
usefulness of the proposed approach. Moreover, the study related to
correlation among the PM2.5 and other pollutants is performed to select the
appropriate predictors. The large authenticate data set of Central Pollution
Control Board (CPCB) online station, India is used for the proposed approach.
The RMSE and coefficient of determination (R2) obtained for the proposed
prediction approach using eight predictors are 1.7973 µg/m3 and 0.9986
respectively. While the proposed approach results show RMSE of 7.5372 µg/m3
and R2 of 0.9708 using three predictors. Therefore, the results demonstrate
that the proposed approach is one of the promising approaches for monitoring
PM2.5 without power-hungry gas sensors and bulkier analyzers.

###### Keywords:

Prediction Model, PM2.5, Correlation, Artificial Neural Network, Air Pollution
Monitoring, Machine Learning

##  1 Introduction

Meteorological parameters such as temperature, humidity, light, air velocity
and gaseous pollutants such as Carbon Dioxide (CO2), Carbon Monoxide (CO),
Nitrogen Dioxide (NO2), Sulphur Dioxide (SO2), Volatile Organic Compounds
(VOCs), Suspended Particulate Matter (SPM), and Ozone (O3) express the
environment quality. The main sources of these pollutants are industrial,
residential, transportation, trading, agricultural, and natural activities
such as combustion of fuels, wood fire, and forest fire, etc. airsourcecpcb ;
airsourceepa . In India, the Central Pollution Control Board (CPCB) is
responsible for providing the ambient Air Quality Index (AQI) through the
National Air Quality Monitoring Programme (NAMP). The NAMP NAMP  network
consists of approximately 683 monitoring stations deployed across 300
cities/towns in 29 states and 6 union territories of the country. The
objectives of NAMP are to determine the status and trends of ambient air
quality and check the prescribed upper and lower limits of the air quality and
take corrective measures for the AQI AQIreport . The AQI transforms the air
quality data into a number, nomenclature, color, and a category; Good,
Satisfactory, Moderately Polluted, Poor, Very Poor and Severe based on their
health impacts. The overall AQI AQI  is calculated from a minimum three
pollutants out of which one should be the Particulate Matter (PM2.5) which can
potentially cause serious health problems.

PM2.5 poses a major concern for human health as due to its small size ($<$
2.5µm) they can directly enter into the lungs WHOreport . PM2.5 comes either
from primary sources or from secondary sources. The primary sources can be
vehicles, power plants, wood burning, industrial processes, forest or grass
fires, and agricultural burning processes. The secondary sources are precursor
emissions such as Sulfur dioxide (SO2), Oxides, Volatile Organic Compounds
(VOCs), and Ammonia (NH3) WHOreport ; hodan . Though different methods and
instruments for monitoring PM2.5 exist amaral2015overview , only a few are
used for real-time measurement and monitoring. These instruments for PM2.5
often lack portability and exhibit a slower response time budde2014distributed
. Furthermore, the standard procedure to collect samples through samplers and
analyzing them offline in specialized laboratories is challenging for real-
time monitoring and corrective actions NAAQsample ; pm2.52 . This is because
analyzed data is a delayed response of the current data. Hence real-time
monitoring of PM2.5 can be useful. In this work, we propose a method to
address the issue of the delayed response of data. We propose the PM2.5
prediction model based on analytical equations, which can be ported to a
standard Wireless Sensor Node (WSN). We envisage that such a method not only
provides benefits for real-time monitoring but also enables an existing WSN to
extend its capabilities from monitoring to analyzing.

##  2 Related Work

The classification of both direct and indirect measurements for outdoor
environmental monitoring is shown in Fig. 1. In direct methods, dedicated
instruments such as analyzers NAAQsample , aethalometer Vilcassim2014 ,
samplers gehrig2003characterising ; northcross2010estimating ;
querol2001monitoring ,

and in certain cases Wireless Sensor Nodes (WSNs) hall2012portable ;
mansour2014wireless ; kasar2013wsn ; liu2011developed  are used. Aethalometer
and analyzers provide the pollutants’ values directly but lack portability and
are often expensive. In air pollution monitoring using samplers, offline
analysis is done in specialized laboratories. Whereas in wireless sensor
nodes, the measurement of pollutants is done using on-board gas sensors and is
often a cost-effective solution compared to other monitoring methods
yi2015survey . An example of such a system deployed in a New York subway is
discussed in Vilcassim2014 .

for tree= align=center, parent anchor=south, child anchor=north, font=,
edge=thick, -Stealth[], l sep+=10pt, edge path= [draw, edge] (!u.parent
anchor) – +(0,-10pt) -— (.child anchor)edge label; ,  [Outdoor Monitoring
[Direct Methods [Analyzer
NAAQsample ] [Aethalometer
Vilcassim2014 ] [Sampler
gehrig2003characterising ; northcross2010estimating ; querol2001monitoring ]
[WSN
hall2012portable ; mansour2014wireless ; kasar2013wsn ; liu2011developed ] ]
[Indirect Methods [Prediction model based on
past data of predictand,
meteorological parameters
and other pollutants
Ordieres2005 ; Jef2005 ; emp6 ; nn6 ; lu2006prediction ; Sousa2007 ;
gardner1999neural ; grivas2006artificial ; ann6 ; ann7 ; ann5 ; nc8 ; nc28 ;
A2006 ; diaz2008hybrid ; ann25 ; clusternn ; hybrid5 ; hybrid7 ; hybrid6 ;
regularization ; cgmmodel7 ; deeplearning ; deeplearning2 ; deeplearning6 ]
[Prediction model based on
correlated meteorological parameters
and pollutants
corr27 ; corr7 ; everyaware  [Proposed Method
(Prediction model
based on
correlated pollutants,
as analytical equations)] ] ] ] ]

Figure 1: Direct and Indirect Methods of Prediction of Pollutants for Outdoor
Monitoring

The indirect measurements Ordieres2005 ; Jef2005 ; emp6 ; nn6 ;
lu2006prediction ; Sousa2007 ; gardner1999neural ; grivas2006artificial ; ann6
; ann7 ; ann5 ; nc8 ; nc28 ; A2006 ; diaz2008hybrid ; ann25 ; clusternn ;
hybrid5 ; hybrid6 ; regularization ; cgmmodel7 ; deeplearning ; deeplearning2
; deeplearning6  used prediction approach based on the past data of the
predictand, pollutants and/or meteorological parameters. These pollutants and
meteorological parameters are correlated with the predictand hybrid7 ; corr27
; corr7 ; everyaware . The PM2.5 (predictand) can be forecasted based on the
data of pollutants and meteorological parameters which are correlated with
PM2.5. The performance comparison of different prediction techniques of
greenhouse gas is discussed in predictionmethodsreview . In Ordieres2005 , a
comparison of different topologies of a neural network is presented for a
prediction model of PM2.5. A neural network-based prediction model for PM10
using previous days data for PM10, cloud cover, boundary layer height, wind
direction and day of the week is discussed in Jef2005 . For the prediction of
PM2.5 and O3, the empirical non-linear regression model was designed emp6
using meteorological parameters and past PM2.5 data. In nn6  feed-forward
neural network is used for prediction of PM2.5 based on past values of PM10,
PM2.5 and some observed and forecasted meteorological parameters. In
lu2006prediction ; Sousa2007 , prediction based on ANN using past data of O3
is discussed. A Multilayer Perceptron (MLP) neural network-based prediction
model gardner1999neural  for NO and NO2 pollutants is developed using past
data of pollutants. In grivas2006artificial  prediction model show MLP neural
network has better performance than Multiple Linear Regression (MLR) model.
Results in ann6  demonstrates the better performance of ANN compared to MLR
for prediction of PM2.5 in the agricultural park. Comparison results of MLR
and ANN in ann7 , for prediction of PM2.5 represents the better performance of
ANN. Feed Forward Neural Network (FFNN) with Rolling Mechanism (RM) and
Accumulated Generating Operation (AGO) of Gray model (RM-GM-FFNN) was
developed ann5  for prediction of PM2.5 and PM10 using past data of PM2.5 and
PM10 in addition to meteorological data. Prediction of PM2.5 based on the Back
Propagation (BP) neural network was explored nc8  using satellite-based
Aerosol Optical Depth (AOD), meteorological data and past PM2.5 data. The
optimized version of the BP network using a genetic algorithm is proposed in
nc28 .

Few researchers have also explored the hybrid model approach for prediction. A
hybrid approach based on the autoregressive and nonlinear model for prediction
of NO2 is proposed in A2006 . A hybrid approach based on Autoregressive
Integrated Moving Average Model (ARIMA) and ANN is discussed in diaz2008hybrid
. The Comprehensive Forecasting Model (CFM) was developed based on ARIMA, ANN
and Exponential Smoothing Method (ESM) ann25 . Another cluster-based hybrid
approach using Neural Network Autoregression (NNAR) and the ARIMA model is
discussed in clusternn  for prediction of PM2.5 using past data of PM2.5. A
hybrid-generalized autoregressive conditional heteroskedasticity based
prediction approach proposed in hybrid7  for prediction of PM2.5. In hybrid5
hybrid model was built for PM2.5 by applying the trajectory-based geographic
model and wavelet transformation into the MLP type of neural network. In which
meteorological forecasts and pollutants were used as predictors. Comparison of
a hybrid model consisting of an Ensemble Empirical Mode Decomposition and
General Regression Neural Network (EEMD-GRNN), Adaptive Neuro-Fuzzy Inference
System (ANFIS), Principal Component Regression (PCR), and MLR is discussed in
hybrid6  with best results obtained for EEMD-GRNN model. In regularization
multi-task learning framework is used for the prediction of air pollutants
which reduces model parameters with improved performance. Convolutional
generalization model implemented cgmmodel7  for prediction of PM2.5 using
meteorological data shows MSE of 15.0 µg/m3. A deep learning-based prediction
approach is also implemented for prediction using current and/or previous air
pollutants and meteorological data deeplearning ; deeplearning2 ;
deeplearning6 .

The research work in corr27  focused on Cuckoo Search-Least Squares Support
Vector Machine (CS-LSSVM) based prediction approach for PM2.5 using
correlation and principal component analysis. Previous data of PM2.5 was used
as one of the predictors in addition to correlated parameters. The correlation
analysis of PM2.5 to other meteorological parameters and pollutants using
multivariate statistical analysis method and ANN was implemented in corr7  and
prediction results show RMSE of 24.06 µg/m3 for ANN-based model. Performance
comparison of machine learning approaches such as Random Forests (RF), Support
Vector Machines (SVMs) and ANN is presented in everyaware . Furthermore, a
calibration model is developed using ANN for black carbon in which
meteorological parameter and other correlated pollutants are used as
predictors. The lower RMSE and R2 closeness to 1, also showed the
effectiveness of the ANN.

However, the previously developed prediction model based on past data of
predictand does not eliminate the need for dedicated instruments and in almost
all cases the proprietary tools are used to measure the predictand. This
presents an opportunity for developing a prediction model in the form of
analytical equations based on the correlation. The ANN is adopted in our work,
due to its superior performance discussed in lu2006prediction ; Sousa2007 ;
gardner1999neural ; grivas2006artificial ; ann6 ; ann7 ; everyaware . Primary
results related to the comparison of SVM and ANN are discussed in the results
section and demonstrate the effectiveness of our proposed method.

The contribution of the work is as follows:

  1. 1\.

The study related to correlation of the pollutants with PM2.5 and additionally
the correlation among the pollutants is performed for deciding the predictors.

  2. 2\.

Analytical equations are proposed for prediction of PM2.5 using ANN.

  3. 3\.

Recalibration of the derived prediction model in terms of coefficients and
number of predictors is done to evaluate its performance.

Figure 2: ANN Model of a Neuron

##  3 Introduction to ANN Model

The proposed prediction model to obtain PM2.5 is based on supervised machine
learning. It consists of interconnected computing elements known as neurons
with inputs and outputs. As shown in Fig. 2, the model of a neuron has $P$
inputs each with weight $W$. The sum ($S$) of weighted inputs and bias ($b$)
is fed to the transfer function block ($f$). The output of each neuron is
obtained by subsequently applying the transfer function to the sum of weighted
inputs and bias.

The proposed PM2.5 prediction model using the ANN is derived using the
following steps.

  1. I

Collection of large input data (observations) set for different pollutants.

  2. II

Preprocessing of the input data set to remove outliers.

  3. III

Finding correlation of PM2.5 with other pollutants using preprocessed input
data set.

  4. IV

Based on the correlation results selection of input pollutants (predictors)
for developing the prediction model of PM2.5.

  5. V

Selection of ANN topology for developing the prediction model.

  6. VI

Division of predictors data set into two sets, SET1: 90% of data set or
developing model (training, validation, and testing), SET2: 10% of data set as
unseen data set for further testing.

  7. VII

Developing 100 different ANNs with randomly initialized weights and biases
using SET1.

  8. VIII

Testing of 100 different ANNs using SET2.

  9. IX

Based on performance indices selection of best ANN for the prediction model.

  10. X

Deriving analytical equation for prediction using selected ANN.

  11. XI

Prediction of PM2.5 using derived analytical prediction equation.

|
---|---
|

(a) CO Data

(b) NO Data

(c) NO2 Data

(d) SO2 Data

Figure 3: Original and Smoothed Data of CO, NO and NO2 and SO2

|
---|---
|

(a) O3 Data

(b) Temperature Data

(c) Humidity Data

(d) Benzene Data

Figure 4: Original and Smoothed Data of O3, Temperature, Humidity and Benzene

|
---|---
|

(e) Toluene Data

(f) Ethyl Benzene Data

(g) M-P Xylene Data

(h) O-Xylene Data

Figure 5: Original and Smoothed Data of Toluene, Ethyl Benzene, M-P Xylene and
O-Xylene Figure 6: PM2.5 Data

##  4 Observed Data and Correlation

To select the inputs for the PM2.5 prediction model, it is necessary to obtain
the correlation between PM2.5 and pollutants besides the correlation among the
pollutants. In the proposed study, Step I is the data collection phase: In
this phase, 13 different parameters (pollutants and meteorological parameters)
were collected from a CPCB online station, India (N 23∘ 0’ 16.6287, E 72∘ 35’
48.7816). The data is collected for 41 months, where, the samples of data are
taken every hour. Thirteen different parameters monitored from this online
station includes pollutants; CO, NO, NO2, SO2, O3, VOC (Benzene, Toluene,
Ethyl Benzene, M+P Xylene, O-Xylene), PM2.5 and meteorological parameters;
temperature and humidity. Dataset obtained from CPCB online station for all 13
parameters was containing a total of 29,928 observations. Due to maintenance,
all the parameters data were not available simultaneously for 29,928
observations. After removing maintenance data for each of the parameters,
18,880 observations data set was available simultaneously for all 13
parameters. These 18,880 observations data set was smoothed out to remove the
outliers [Step II] and is treated as the golden standard data. The smoothing
of the data is done by a moving average filter, which was implemented in
MATLAB. The optimum window size for smoothing was found to be 500, resulting
in reasonably smoothed data. After smoothing, the first 500 results were
removed, as the window size was 500. So, smoothed data of size 18,380 was used
for developing the prediction model. Fig. 3 to Fig. 6 shows the original and
smoothed data for all 13 parameters.

Correlation between any two parameters x and y is expressed by the correlation
coefficient $R$ as per Eq. (1).

$R=\dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{(n\sum x^{2}-(\sum x)^{2})*(n\sum
y^{2}-(\sum y)^{2})}}$ (1)

where n is the total number of samples. $R$ takes values in the range of [-1
to +1]. For a strong positive correlation between x and y, the value of $R$
will be close to +1 and vice-versa. For the practical purpose, correlation
greater than 0.8 is assumed as being strong and less than 0.5 as weak corr .

Table 1: Correlation among the Different Parameters

| CO | NO | NO2 | SO2 | O3 | T | RH | Ben | Tol | Eth | M-xyl | O-xyl | PM2.5
---|---|---|---|---|---|---|---|---|---|---|---|---|---
CO | 1 | 0.936 | 0.872 | 0.828 | 0.771 | -0.069 | -0.215 | 0.901 | 0.928 | 0.908 | 0.921 | 0.894 | 0.830
NO | 0.936 | 1 | 0.927 | 0.826 | 0.789 | -0.122 | -0.230 | 0.927 | 0.927 | 0.909 | 0.907 | 0.860 | 0.909
NO2 | 0.872 | 0.927 | 1 | 0.927 | 0.728 | -0.075 | -0.313 | 0.919 | 0.849 | 0.828 | 0.809 | 0.769 | 0.909
SO2 | 0.828 | 0.826 | 0.927 | 1 | 0.714 | 0.009 | -0.328 | 0.881 | 0.817 | 0.790 | 0.766 | 0.769 | 0.845
O3 | 0.771 | 0.789 | 0.728 | 0.714 | 1 | -0.066 | -0.238 | 0.844 | 0.849 | 0.849 | 0.833 | 0.833 | 0.773
T | -0.069 | -0.122 | -0.075 | 0.009 | -0.066 | 1 | 0.294 | -0.126 | -0.158 | -0.191 | -0.217 | -0.127 | -0.080
RH | -0.215 | -0.230 | -0.313 | -0.328 | -0.238 | 0.294 | 1 | -0.318 | -0.297 | -0.323 | -0.315 | -0.324 | -0.222
Benzene | 0.901 | 0.927 | 0.919 | 0.881 | 0.844 | -0.126 | -0.318 | 1 | 0.956 | 0.943 | 0.934 | 0.891 | 0.919
Toluene | 0.928 | 0.927 | 0.849 | 0.817 | 0.849 | -0.158 | -0.297 | 0.956 | 1 | 0.989 | 0.982 | 0.955 | 0.877
Ethyl benzene | 0.908 | 0.909 | 0.828 | 0.790 | 0.849 | -0.191 | -0.323 | 0.943 | 0.989 | 1 | 0.989 | 0.963 | 0.880
M-P Xylene | 0.921 | 0.907 | 0.809 | 0.766 | 0.833 | -0.217 | -0.315 | 0.934 | 0.982 | 0.989 | 1 | 0.964 | 0.855
O-Xylene | 0.894 | 0.860 | 0.769 | 0.769 | 0.833 | -0.127 | -0.324 | 0.891 | 0.955 | 0.963 | 0.964 | 1 | 0.818
PM2.5 | 0.830 | 0.909 | 0.909 | 0.845 | 0.773 | -0.080 | -0.222 | 0.919 | 0.877 | 0.880 | 0.855 | 0.818 | 1

Correlation between PM2.5 and other parameters in addition to the correlation
among the parameters is evaluated [Step III] based on the 18k+ data over a
period of 41 months. The obtained results are shown in Table 1. As can be
seen, the highest correlation of PM2.5 is found with NO, NO2 and Benzene and
low correlation with temperature and humidity. At typical ambient
concentrations, NO is not considered to be hazardous while NO2 can be
hazardous ref1 . Furthermore, NO2 is considered as one of the major pollutants
by world health organizations and environmental agencies ref2 ; ref3 . Hence,
NO2 is considered as one of the predictors for the proposed model and NO is
excluded. A strong correlation ($>$0.8) of CO, NO2, SO2, and VOC (Benzene,
Toluene, Ethyl Benzene, M+P Xylene, O-Xylene) with PM2.5 is observed which is
useful in selecting the inputs for the PM2.5 prediction model.

The proposed prediction model is based on supervised learning, where, both
inputs and target values are provided as a training dataset. So, for the
proposed PM2.5 prediction model, as a training dataset, values of input
pollutants (CO, NO2, SO2, and VOC (Benzene, Toluene, Ethyl Benzene, M+P
Xylene, O-Xylene)) and target (PM2.5) are taken. It is observed that the
training of the ANN will be efficient if each parameter of the training
dataset is normalized within the range [-1:1]. Normalization of the parameters
is done by finding the value of each parameter within the normalized range
using Eq. (2).

$x_{n}=\dfrac{(Y_{max}-Y_{min})*(X-X_{min})}{(X_{max}-X_{min})}+Y_{min}$ (2)

where X is the value of the parameter while Xmax and Xmin are the maximum and
minimum values of the parameter, respectively. For example, in CO data, X is
the smoothed value of CO while Xmax and Xmin are maximum and minimum values of
smoothed CO data, respectively. As normalization range is [-1:1], Ymax is 1
and Ymin is -1. The normalized parameters can be converted back into their
original form using Eq. (3).

$X=\dfrac{(x_{n}-Y_{min})*(X_{max}-X_{min})}{(Y_{max}-Y_{min})}+X_{min}$ (3)

where xn represents normalized data and X is the smoothed data. Xmax and Xmin
are the maximum and minimum values of smoothed data, respectively. For
example, to convert the normalized data of predictand PM2.5 into original
form, Xmax and Xmin values of targeted PM2.5, shown in Fig. 6 are used.

Figure 7: Selected ANN Topology for Prediction

##  5 Prediction model of PM2.5

In the proposed prediction model (see Fig. 7), inputs are selected based on
the correlation results [Step IV]. As can be seen from Table 1, a higher
correlation ($>$0.8) of CO, NO2, SO2, and VOC (Benzene, Toluene, Ethyl
Benzene, M+P Xylene, O-Xylene) with PM2.5 is observed. So, out of 12
parameters 8 parameters; CO, NO2, SO2, and VOC (Benzene, Toluene, Ethyl
Benzene, M+P Xylene, O-Xylene) are selected for developing the PM2.5
prediction model. Additionally, as the number of input parameters is reduced
from 12 to 8, the computation cost of the proposed prediction model is
reduced. The prediction model of PM2.5 shown in Fig. 7 is based on a feed-
forward neural network with a single hidden layer [Step V]. Selected eight
pollutants are the input parameters for each neuron of the hidden layer which
consists of eight neurons.

The weights of the hidden layer and output layer can be represented by a
matrix of size $S\times P$, where, $S$ is equal to the number of neurons in
the layer and $P$ is equal to the number of inputs of the layer. In our case,
the matrix size is 8$\times$8, as both the inputs and hidden layer size are 8.
The matrix size for the output layer is 1$\times$8 as it consists of one
neuron and eight inputs coming from the hidden layer. For the proposed
predicted model, weights of the hidden layer and output layer are represented
by LW1 of (of 8$\times$8 size) and LW2 of size (of 1$\times$8 size)
respectively. The element, LW1(1) represents the first row of LW1 matrix,
which is formed by the weights of inputs going to the first neuron of the
hidden layer. Similarly, LW2(1,1) represents the first row and first column
element of matrix LW2 and so on. Biases of the particular layer can be
represented by a matrix of the size S$\times$1, where S is equal to the number
of neurons in the layer. The bias matrices are  b1 and b2 for hidden layer and
output layer, respectively. As the number of neurons in the hidden layer is 8
and output layer is 1, the bias matrices,  b1 is 8$\times$1 and b2 is
1$\times$1, where b1(1,1) represents the first row and first column element of
matrix b1.

The training function trainlm based on the Levenberg-Marquardt algorithm is
adopted sharma2014comparison ; mathtrain  for training. To train the network
for the nonlinear relationship between input and output and to constrain
output in positive range standard nonlinear transfer function logsig given by
Eq. (4) is used in the hidden layer.

$logsig(m)=\dfrac{1}{(1+e^{-m})}$ (4)

where m is the input to the transfer function. In logsig transfer function,
the output will be in the range of [0:1] for the entire range of inputs. For
nonlinear regression or prediction, purelin is an effective transfer function
for the output layer ref4 . Hence in the proposed model, purelin is used as a
transfer function in the output layer. In purelin, the output will be equal to
the input.

The total available data of 18k+ is divided into two sets the first set (SET1)
includes 90% of data and the second set (SET2) includes 10% of data [Step VI].
The division into two sets is done randomly so that all types of data can be
included in two sets. The SET1 (90% data) is used for designing the neural
network and it is divided in a standard manner widely used by researchers, 70%
for training, 15% for validating and 15% for testing. The SET2 (10% data) is
kept as unseen data for further testing and comparing the performance of
neural networks.

1:Load the data SET1 for developing the network and SET2 to test the Network
for unseen data

2:for i = 1 to 100 do

3: Divide SET1 randomly for training(70%), validating(15%) and testing (15%)

4: Initialize the weights and biases

5: Train the network

6: Validate the network

7: Test the network

8: Evaluate training, validation and testing performance

9: Save the performance results

10: Save Network and its weights and biases

11: Test the Network performance for unseen data using SET2

12: Save the performance results

13:end for

Algorithm 1 Pseudo Code for Developing and Testing 100 different ANNs

For selecting the best ANN for prediction model, 100 different ANNs are
developed and tested as per the pseudo-code in Algorithm 1. This algorithm is
repeated 100 times to get the performance of 100 different ANNs for comparing
training and testing results with good generalization [Step VII, VIII]. The
performance of the ANN is evaluated [Step IX] based on, RMSE and R2, where,
RMSE is the root mean square of the errors, i.e, the difference between the
target value and the predicted value and is given in Eq. (5).

$RMSE=\sqrt{\dfrac{\sum_{i=1}^{n}(A_{i}-P_{i})^{2}}{n}}$ (5)

where Ai represents the actual value, Pi represents the predicted value and n
is the total number of samples. R2 is the coefficient of determination and it
is the square of the correlation R (Eq. (1)). The closeness between target
values and predicted outputs of ANN is represented by R2. The value of R2
equal to 1 represents targets and predicted outputs are very close to each
other.

###  5.0.1 Model Equations

The hidden layer and output layer weights for the proposed model are shown in
Eq. (6) and Eq. (7) respectively. The biases of the model for hidden layer and
output layer are shown in Eq. (8) and Eq. (9) respectively. Matrix B1 is
formed by repeating the hidden layer bias matrix b1, N times, where N is equal
to the size of test dataset (1838 in our case). This operation shown in Eq.
(10), is performed to make bias matrix size B1 equal to the size of product
term matrix $LW_{1}$*$x_{n}$, so that addition operation (B1 \+
$LW_{1}$*$x_{n}$), shown in Eq. (11) can be performed.

$LW_{1}=\left[\begin{matrix}-25.978&-31.063&17.505&38.446&-37.353&97.708&-92.951&65.964\\\
3.295&6.460&0.203&-1.981&10.078&-10.281&3.352&-3.782\\\
-2.661&2.503&-1.075&-1.011&-0.194&1.702&-2.768&1.690\\\
-6.069&6.142&-2.212&-3.593&1.800&-3.002&0.222&2.803\\\
-9.788&-7.748&-4.424&27.227&-4.406&0.016&-6.279&8.460\\\
3.821&-6.233&1.243&-1.449&5.600&1.846&1.801&-5.862\\\
3.149&6.319&0.368&-0.825&10.746&-11.220&2.650&-3.428\\\
-2.127&1.991&-1.116&-0.032&0.038&4.094&-4.882&1.330\\\ \end{matrix}\right]$
(6)

$LW_{2}=\left[\begin{matrix}0.158&-17.591&-6.481&1.614&-0.369&-0.817&17.345&4.950\\\
\end{matrix}\right]$ (7)

$b_{1}=\left[\begin{matrix}34.474\\\ 4.001\\\ -1.015\\\ -2.615\\\ 5.700\\\
-0.148\\\ 4.383\\\ -1.959\\\ \end{matrix}\right]$ (8)

$b_{2}=\left[\begin{matrix}1.593\\\ \end{matrix}\right]$ (9)

$B_{1}=\left[\begin{matrix}b_{1}&b_{1}&b_{1}&b_{1}&.&.&.&.&.&N\end{matrix}\right]$
(10)

The prediction model for deriving PM2.5 [Step X] is given by Eq. (11).

$PM2.5_{n}=b_{2}+LW_{2}*logsig(B_{1}+LW_{1}*x_{n})$ (11)

where PM2.5n is normalized output. The input matrix xn is formed using
normalized values of CO, NO2, SO2, and VOC and the size of xn is $P\times N$
where $P$=8 is the number of inputs and $N$=1838 is the number of values for
each input. Eq. (11) shows the usefulness of the approach to obtain the value
of PM2.5 based on CO, NO2, SO2, and VOC values only. Therefore, low-cost
sensors can be deployed with the derived model that offers the opportunity to
derive PM2.5 through signal processing algorithms. Eq. (12) shows the
conversion to the original value from the normalized one using Eq. (3), in
which Xmax and Xmin are taken as per Fig. 6.

$PM2.5=\dfrac{(PM2.5_{n}+1)*(180.052-2.228)}{2}+2.228$ (12)

The proposed approach based on the above analytical equations eliminates the
need for proprietary tools. The analytical equation for the prediction can be
computed using any low-cost processing tool (e.g. excel sheet etc.). A
screenshot of an example [Step XI] is shown in Fig. 8. In this example, an
input matrix x of size 8$\times$1838 is taken which represents the testing
data set. Eq. (11) is computed as follows.

  1. a.

First, $x_{n}$ is obtained by computing Eq. (2)

  2. b.

Multiplying the two matrices of $LW_{1}$ (Eq. (6)) and $x_{n}$, product term
$LW_{1}$*$x_{n}$ is obtained.

  3. c.

Matrix $B_{1}$, formed using Eq. (10) is added in the product term
$LW_{1}$*$x_{n}$.

  4. d.

Hidden layer activation function (Eq. (4)) is applied to find the output of
the hidden layer.

  5. e.

The output of the hidden layer is multiplied by $LW_{2}$ (Eq. (7)).

  6. f.

Then matrix $b_{2}$ from Eq. (9), is added.

Finally, PM2.5n (marked as A in Fig. 8) is obtained by computing Eq. (11),
which is the normalized value of PM2.5. PM2.5 in the original unit is obtained
by processing Eq. (12) (marked as B in Fig. 8). Predicted values of PM2.5
obtained from Eq. (12) (marked as B in Fig. 8) are close to the actual values
of PM2.5 (marked as C in Fig. 8). Interestingly these computations can be
ported to a wireless sensor node having basic memory along with computational
capability and the algorithms can still perform reliably.

Figure 8: Excel sheet used for processing prediction model equation Figure 9:
Good match of the results obtained from the analytical equation of model with
actual values

The deployment of the developed prediction model needs to consider the
following limitations based on the location, available monitoring stations and
available monitoring parameters as predictors.

  * $\bullet$

Air pollution varies from one location to another based on the few parameters
like human activity, traffic condition, the structure of urban area and
weather conditions. Based on the location, predictors and predictand values as
well as their maximum and the minimum limit will change. So, the application
of the presented prediction model for another location needs model training,
validation, and testing again which provides new coefficients in terms of
weights and biases for accurate prediction with lower RMSE.

  * $\bullet$

Application of prediction model to another location requires a large set of
authentic data for training which is sometimes difficult due to the limitation
on the number of online environment monitoring stations. Due to a few
monitoring parameters, and delay in the availability of data; offline stations
are less preferable than online stations.

  * $\bullet$

Online stations of CPCB monitors pollutants that are greater than the offline
stations. Concentration data for a large set of pollutants is the basic
requirement for a correlation study or developing a prediction model. Due to
the limitation on the online stations available in the city, data were used
from only one online station for training, validation, and testing in the
proposed study. This can be expanded in the future by taking data from
multiple online stations of different cities.

  * $\bullet$

The derived prediction model based on ANN generally shows poor performance for
predicting the sudden large change in predictors. As, sometimes it is
difficult to discriminate between the outliers and sudden change in the value,
applying a smoothing algorithm to remove outliers will also remove the sudden
large change in the value of the predictor. This limitation can be targeted
through different data processing algorithm and is left as part of future work

###  5.0.2 Model Results

In comparison to Support Vector Machine (SVM), the ANN exhibits better
performance in terms of RMSE. The RMSE of 2.862 and 2.823 is obtained during
training and testing respectively for the SVM model (shown in Table 2). While
for ANN, the RMSE of 1.5971 and 1.5121 is obtained (shown in Table 3) during
training and testing for unseen data respectively.

Table 2: Performance of SVM  Performance of |  RMSE
---|---
Training |  2.862
Testing for unseen data |  2.823
Table 3: Performance of Prediction Model  Performance of |  RMSE |  R2
---|---|---
Training |  1.5971 |  0.9987
Validation |  1.6347 |  0.9986
Testing |  1.5843 |  0.9988
Testing for unseen data |  1.5121 |  0.9988

Table 3 shows the best performance of the prediction model obtained from 100
iterations. The value of R2 demonstrates the closeness of the predicted values
with the target values or actual values. The actual values of PM2.5 are
compared (see Fig. 9) with predicted results obtained by Eq. (12). It is found
that the predicted results are in close accordance with actual values, which
confirms the effectiveness of the proposed approach.

Table 4: Summary of previously developed prediction models Reference | Predictand | RMSE | R2
---|---|---|---
lu2006prediction  | O3 (ppb) | 0.30 | 0.69
Sousa2007  | O3 (µg/m3) | 21.78 | 0.73
gardner1999neural  | NO2 (ppb) | 7.3 | 0.91
A2006  | NO2 (µg/m3) | 13.93 | 0.93
grivas2006artificial  | PM 10 (µg/m3) | 12.16 | 0.83
diaz2008hybrid  | PM 10 (µg/m3) | 11.656 | 0.983
nc8  | PM2.5 (µg/m3) | 41.97 | -
ann25  | PM2.5 (µg/m3) | 12.8903 | -
ann5  | PM10 (µg/m3) | 18.4 | 0.895
ann5  | PM2.5 (µg/m3) | 12.7 | 0.954
ann6  | PM2.5 (µg/m3) | 6.77 | 0.99
hybrid6  | PM2.5 (µg/m3) | 5.0324 | 0.79
corr27  | PM2.5 (µg/m3) | 14.47 | -
corr7  | PM2.5 (µg/m3) | 24.06 | -
everyaware  | BC (ng/m3) | 1480.746 | 0.586
This Work | PM2.5 (µg/m3) | 1.7973 | 0.9986

Previously developed prediction models, depend on past data, are often time-
consuming and use dedicated instruments. In the prediction model, we have
eliminated the above requirements and comparison with some researches is shown
in Table 4. As can be seen, the proposed approach has better RMSE and R2
compared to existing methods. The RMSE of 1.7973 µg/m3 and R2 of 0.9986 is
obtained for test dataset of size 1838. We extended the model to accommodate a
reduced test dataset of size 10, which shows RMSE of 146.10 µg/m3 and R2 of
0.9467. The proposed model in the form of the analytical equation thus helps
in predicting PM2.5 using low-cost processing tools or existing WSN.

The proposed prediction model is recalibrated in terms of the number of
predictors, weights, and biases to show the effectiveness of the proposed
approach. Instead of eight predictors, three predictors, CO, NO2, and Benzene
(VOC component) are taken considering the availability of low-cost sensors
mics6814  which includes this type of multiple sensing parameters. The
proposed approach can work for any other three sensing parameters after
recalibrating model. In recalibration, CPCB smoothed data for CO, NO2, and
Benzene (VOC component) are used as it is considered as golden standard data.
For recalibration ANN shown in Fig. 7 is used with the same training and
testing dataset (of three parameters), but the size of the input layer and the
hidden layer is reduced to three. Extracted weights and biases are represented
in Eq. (13) to Eq. (16). Performance results are shown in Table 5. Results
show, during testing RMSE is 7.5372 µg/m3 and R2 is 0.9708.

$LW_{1}=\left[\begin{matrix}26.281&3.456&-12.391\\\ 17.898&-0.863&11.305\\\
-0.996&-0.502&-1.205\\\ \end{matrix}\right]$ (13)

$LW_{2}=\left[\begin{matrix}-1.008&1.379&-1.665\\\ \end{matrix}\right]$ (14)

$b_{1}=\left[\begin{matrix}9.934\\\ 21.939\\\ 1.101\\\ \end{matrix}\right]$
(15)

$b_{2}=\left[\begin{matrix}0.689\\\ \end{matrix}\right]$ (16)

Table 5: Performance of Prediction Model for Three Predictors  Performance of |  RMSE |  R2
---|---|---
Training |  7.9297 |  0.9678
Validation |  8.0954 |  0.9679
Testing |  8.0049 |  0.9672
Testing for unseen data |  7.5372 |  0.9708

##  6 Conclusion and Future Work

In this work, we have studied the correlation of PM2.5 with other pollutants
and correlation among the pollutants, based on the standardized CPCB data. The
prediction model of PM2.5 is based on the correlation and shown to be useful
for online as well as offline measurements. The proposed model is in the form
of analytical equations that enables the use of any low-cost processing tool
and eliminates the need for a proprietary tool for predicting PM2.5 values.
Results obtained using this method with eight predictors ( NO2, SO2, and VOC
(Benzene, Toluene, Ethyl Benzene, M+P Xylene, O-Xylene)) shows RMSE of
1.7973µg/m3 and R2 0.9986 for the test dataset. To show the effectiveness of
the proposed approach, the derived prediction model was recalibrated with
three predictors (CO, NO2, and Benzene (VOC component) due to the possibility
of sensing all three parameters by one or two low-cost sensors. The proposed
approach can work for any other three sensing parameters too after
recalibration. Testing results show RMSE of 7.5372 µg/m3 and R2 of 0.9708. The
obtained results prove the effectiveness of the proposed approach. The
obtained results can be improved in the future by recalibrating prediction
model based on the data available from multiple stations located at the place
of deployment. In comparison to existing methods, the proposed approach
facilitates an efficient method that reduces overall computation cost.
Furthermore, this model can be implemented on the wireless sensor node for
automated measurement of PM2.5.

##  7 Acknowledgement

The authors thank the Central Pollution Control Board (CPCB) and their staff
for their support during this research work.

## Compliance with ethical standards

Conflict of interest: The authors declare that they have no conflict of
interest.

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