1) The document discusses using a Markov chain model to analyze and predict air quality index (AQI) levels in several areas of Bangalore, India.
2) Data on AQI levels from 7 areas over 215 days was categorized into 4 states and transition probability matrices were calculated for each area.
3) Steady state and mean return time matrices were then used to analyze long-term AQI levels and predict probabilities of future states. Results showed areas like Mysore Road had higher chances of moderate AQI while areas like Nisarga Bhavan had very low chances of poor AQI.
4. ● The Markov chain is a special case of the stochastic process.
Markov is a stochastic process with the Markov property that
was named after Andrei Andreevich Markov, a Russian
mathematician.
● Recently, the methods have been used to estimate the matrix
of transition from the observing states of the system. It is a
random process where all information about the future is
contained in the present state.
● In addition, the main components in developing the Markov
chain model are state transition matrix and probability; both of
which will summarize all the essential parameters of dynamic
change.
WHAT IS MARKOV CHAIN?
5. ● Markov chain is a discrete time discrete state space stochastic process.
● A Markov chain is a stochastic process containing random variables
transitioning from one state to another depending only on certain
assumptions and definite probabilistic rules.
● The Markov property is a simple statement where we say:
"Given the Present, the Future is independent of the past."
● It is a property belonging to a memoryless process as it is solely dependent on
the current state and the randomness transitioning to the next states
WHAT IS MARKOV CHAIN?
6. MARKOV STATE:
All the states (occurrences) are within the state – space 's' of the dynamical system.
TRANSITION MATRIX:
State transition matrix, N, as defined by the Markov chain, indicates the observed frequency of
transition or jump from one state to another state. Thus,
TRANSITION PROBABLITY MATRIX:
Where, nij is the number of transitions in a sequence for state i followed by state j. Let P be a transition
matrix or stochastic matrix that describes all the transition probabilities for each state of the Markov
chain model. Hence, P is denoted as below,
COMPONENTS OF MARKOV CHAIN
7. STEADY STATE MATRIX
The n-step State Transition Probability pij(n) is the conditional probability that the system will be in state j
after exactly n transitions, given that it is presently in state i.
The n-step transition probability can be obtained by multiplying the transition probability matrix by itself n
times.
For the class of Markov Chain in which the limit exists we define the limiting state probabilities as:
MEAN RETURN TIME MATRIX:
Mean return time matrix(mij) is the inverse of the steady state matrix that depicts the return time of a
particular state in the given time.
INITIAL VECTOR:
Initial vector describes the probability distribution of starting at each of the possible states.
COMPONENTS OF MARKOV CHAIN
8. ● Frequently used to describe consumer behavior
● Sales forecasting
● Useful in the prediction of brand switching
● Effects on individual's market share
● Brand loyalty and consumer behavior can be analyzed
● Ranking website web searches
● Weather forecasting
APPLICATIONS OF MARKOV CHAINS:
9. ● A Markov chain is commonly used in stock market analysis, manpower planning, and in
many other areas because of its efficiency in predicting long run behavior. However, the
Air Quality Index (AQI) suffers from not using a Markov chain in its forecasting approach.
● Using Markov chains , AQI states for every hour ,day , month, year can be calculated
hence it is very convenient and flexible.
● Our study aims at using Markov chains to calculate the future probabilities as well as
quantify how often these states occur in the particular area.
● Our literature review directed us towards several articles about understanding Markov
chains and Air quality index. which we have fused together in our analysis and applied it
to Bengaluru
MARKOV CHAIN AND AIR QUALITY
12. An air quality index (AQI) is used by government agencies to communicate to the public
how polluted the air currently is or how polluted it is forecasted to become public health risks
increase as the AQI rises.
AIR QUALITY INDEX (AQI)
Source of the index: Environmental Protection Agency(EPA)
13. • To determine air quality in an area, pollutant concentrations are physically
measured and reported. The AQI is calculated based on the average
concentration of a particular pollutant measured over a standard time
interval (24 hours for most pollutants, 8 hours for carbon monoxide and
ozone). For example, the AQI for PM2.5 is based on 24-hour average
concentration.
• It is severe (400+) if 24-hour averages are greater than 250
microgram/m3, and if concentrations are 380 microgram/m3 or more, they
get reported as 500, the maximum possible.
• In a similar manner, the AQI is calculated separately for each of several
pollutants.
14. DATASET
Source
Karnataka State
Pollution Control Board
Type of Data
Secondary Data
Areas under Consideration
7 prominent areas of Bangalore
spread across the city
Time Frame
1st July,2021 to 31st
January,2022 (215 days)
Tools Used
MS Excel, R
16. 1. To do a deep dive into the Air quality levels of
prominent areas in Bengaluru using Markov
chains.
2. To predict the future AQI levels using Markov
chains.
3. To find Mean return times for each of the states
in the particular area.
OBJECTIVES
17. OUR APPROACH
Calculate state transition
matrix and probability
Calculate steady state and
mean return time matrix
Forecast the values
01 02 03 04
Define states
19. CATEGORIZING DATASET TO MARKOV STATES
51-100
1=Good
0-50
4=Poor
201-300
3=Moderate
101-200
2=Satisfactory
Minimal effect
Breathing problem for
sensitive people
Breathing problem for
people with lung and heart
disease
Breathing discomfort for
most of the people
23. TRANSITION PROBABLITY MATRIX FOR MYSORE ROAD
TPMMR Good Satisfactory Moderate Poor
Good 0.666667 0.3333333 0 0
Satisfactory 0.123967 0.768595 0.09917355 0.008264
Moderate 0 0.3076923 0.64102564 0.051282
Poor 0 0 0.5 0.5
PRESENT
STATE
FUTURE STATE
24. STEADY STATE MATRIX, MEAN RETURN TIME MATRIX
STEADY STATE MATRIX
Good Satisfactory Moderate Poor
0.2097087 0.5638834 0.1968933 0.029515
MEAN RETURN TIME MATRIX
Good Satisfactory Moderate Poor
4.768519 1.773416 5.078894 33.88154
INITIAL VECTOR:
good satisfactory moderate poor
0 0 1 0
25. FORECASTING FOR NEXT WEEK
31st Jan 2020 was the 215th day therefore the forecasted values are:
Day Prediction
Good Satisfactory Moderate Poor
216(1st Feb 2022) 0.03814366 0.4337294 0.4670698 0.0610571
217(2nd Feb 2022) 0.0791972 0.4897906 0.3729467 0.0580654
218(3rd Feb 2022) 0.113516 0.5176025 0.3166754 0.052206
219(4th Feb 2022) 0.1398429 0.5331039 0.2804325 0.0466205
220(5th Feb 2022) 0.1593158 0.5426422 0.2559445 0.0420972
221(6th Feb 2022) 0.1734802 0.5489295 0.2389313 0.0386586
222(7th Feb 2022) 0.1837026 0.5532486 0.2269297 0.0361188
30. KEY TAKEAWAYS FROM OUR ANALYSIS
Chance of having
moderate level AQI
in Mysore road on
1st Feb 2022
Chance of having
moderate, poor, very
poor and severe AQI
states in Nisarga
bhavan
For a poor level AQI
to return in Mysore
road
Is the probability of
having a good state in
the long run according
to steady state matrix
for HSR layout
0% 64% 34 days 0.176
31. Is the probability of
having good state in the
long run according to
steady state matrix of
Nisarga bhavan
For a good state to
return to HSR layout
At least one day is
an intermediate level
of AQI in Hebbal
and Shalini grounds
Chance of having a
good level of AQI in
Nisarga bhavan on
10th Feb 2022
5 days 0.708 Every week 71%
KEY TAKEAWAYS FROM OUR ANALYSIS
33. When compared with other cities in India, Bangalore is doing a lot better with respect to
AQI levels which is about 64.5. The most polluted area in Bangalore is the Mysore
Road area which sees an average of 81 while the least polluted area is Nisarga
Bhavan which sees an average of 42 AQI.
We see that the steady state matrices show a very low value for the poor state and
0 for very poor and severe which is encouraging as this says Bangalore will not see
poor, very poor or severe states anytime soon.
Most of the areas in Bangalore have a mean return time of less than 2 days for
good states which is a positive sign as it says that a good day returns every
alternate days in most areas.
34. Stricter policies need to be introduced in and around Mysore road for the vehicles
travelling and recommend industries to keep a check at how much it is polluting,
as the steady state matrix point at high chances of moderate AQI
The reason for Nisarga Bhavan having such low levels of AQI is because it is surrounded
by trees, which helps reduce the pollution levels in that area and hence planting more
trees could reduce the risk of having high AQI levels.
Bangalore hits peak levels of air pollution that is high levels of AQI in the month of
December and this is due to something called as the winter inversion effect and
hence having a check on the pollution levels and enforcing strong rules during this
period is important.
Vehicular Pollution need to be managed better in Silk board(HSR layout) as the mean return
time matrix points at a moderate AQI level returning almost twice every week.
39. LIMITATIONS
The number of decimal places considered for the analysis majorly affects
the results.
This Project has collected data which includes days during which Covid 19 was hit
in Bangalore hence it is not a good representation of the reality.
Markov chain helps to predict the probability of the future states but not the exact
values of the AQI for the forecasted values.
40. FUTURE SCOPE
Our study concludes at finding the current state of the air quality in some
areas of Bangalore, but all these areas have distinctive problems and features
in them that explain as to why these areas have that much AQI hence
identifying these problems and creating a relationship between these features
and air quality could really help identify solutions as well as problems.
Comparison of accuracy of the Markov chain model for prediction of AQI as
compared to methods such as Seasonal ARIMA(SARIMA).
The data included in this report is only 7 areas and these are Randomly
distributed. This can further be done to all areas in the city and classify
multiple areas as industrial and residential and see the impact
41. BIBLIOGRAPHY
1.towardsdatascience.com
2. Markov Chain Model Development for Forecasting Air Pollution Index of Miri, Sarawak- a research paper
3. kspcb.karnataka.gov.in
4. EasyStat YouTube channel
5. Predicting the Air Quality Index of Industrial Areas in an Industrialized City in India Using Adopting Markov
Chain Model- a research paper
42. ACKNOWLEDGEMENT
We would like to express our special thanks to our mentor Prof.
Suma ma'am. who helped us for our project and to whom we are so
thankful for learning new things through the project.
We would like to thank our Chairperson Dr. Santosha C. D. sir for
giving us this golden opportunity.
Finally, we would like to thank one and all present in the presentation,
we hope we made everyone aware and inspired all present here to do
their part in saving the earth and making it better for us and the future
generations.
Good afternoon, L and Gentlemen. Today I Kuhu Dixit, along with my project mates Akarsh Avinash and Deepak Kumar are here to present on our topic AQI Levels Prediction for Bangalore using Markov Chain.
Ambient air pollution accounts for an estimated 4.2 million deaths per year due to stroke, heart disease, lung cancer and chronic respiratory diseases. Around 91% of the world's population lives in places where air quality levels exceed WHO limits. I would like to request you all to focus on the slide in front of you L and G. News clippings like ..... shows that ever since humans got familiar with industrialiazation, our greed for advancement has put the future of the earth and the next generations in danger. I ,myself born and brought up from Kanpur, an industrial city, suffer from mild asthma since birth. I probably knew how to operate a nebulizer even before I knew how to ride a bicycle. Even though as I grew up my lungs adjusted, still at times when I am doing strenuous activites like trekking,running or even climbing a flight of stairs, I still feel out of breath and feel mild to severe pressure on my chest. This isn’t just my story, but every 1 in 12 child has suffered from these problems, increasingly since the past 25 years. All of this motivated us to study and examine the AQI levels presently and try to predict how it will be in the future and how we can make sure that the aqi levels are low and what we can do to ensure the same. Now I’ll be handing it over to Deepak.
the tools used for our project are Microsoft excel and R studio. The data was available monthwise on the government website hence we had to import it monthwise and join them together on excel. these numbers were then colour coded for each state and rewritten for each state and hence analysed on R using three main packages that is readexcel , markovchain and diagram.
As of 2021, around 8,00,000 vehicles use the road daily, in its presently operation section starting from Electronic City ending at Tumkur Road.At least 58,804 passenger vehicles move between Bangalore and Mysore every day
At least 58,804 passenger vehicles move between Bangalore and Mysore every day(mysore road)
* There is a park in Nisarga Bhavan sanegurvanahalli which is basaveshwar nagar tree park. which controls the polltution in the area and it is a residental area where most of the people leave and there is a central pollution control boardin the park(nisarga bhavan)
*There are more it parks in hsr layout near silk board. Now it has emerged into a leading residential area due to its proximity to IT Parks in Bangalore(hsr) * There are two high ways one is outer ring road and other one is airport road on NH 44 which causes more pollution. And it is prime residental area(hebbal)
*The 4th Block area is known for its many South Indian restaurants while 5th Block is lined with sari shops. Close by, Lalbagh Botanical Garden has popular walking trails and an 1889-built greenhouse. Jayanagar is a residential neighborhood, with traditional-style single-story homes and several local places of worship.(jayanagar)
* It is a place where all the trains and buses from other states enter into Bangalore . it is the gate way of Bangalore to enter from northern states to banglore(majestic)
*Jayaprakash Nagar, officially Jayaprakash Nagara, is an established posh upmarket residential area located in the south of the Bangalore it contains industries and it has more traffic (shalini grounds)
