Adaptive Methane Detection
Transcript of Adaptive Methane Detection
![Page 1: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/1.jpg)
Adaptive Methane DetectionAuthor: Kern Ding
Mentor: David Thompson, Lance Christensen
![Page 2: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/2.jpg)
Outline
Project Overview
Simulate Methane Distribution
Update Hypothesis Probability
Expected Information Gain to start path planning
Demo on real data
![Page 3: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/3.jpg)
Project Object
JPL has developed a hand-held methane sniffer that can be deployed on a flying robot.
To develop an automated system that guides the robot or person carrying the sniffer from first detection to the leak source.
Input: methane concentration and wind vector at detected location
Output: direction to the leak source
![Page 4: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/4.jpg)
Foundation Approach
The approach is a Bayesian ModelFirst, set several hypotheses(leak location,
leak concentration)Using the collocated data to update the
probability of those hypotheses
![Page 5: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/5.jpg)
Outline
Project Overview
Simulate Methane Distribution
Update Hypothesis Probability
Expected Information Gain to start path planning
Demo on real data
![Page 6: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/6.jpg)
Simulate wind turbulence
Src dst
Gaussian Distribution
src dst
![Page 7: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/7.jpg)
Wind turbulence using Gaussian Distribution
![Page 8: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/8.jpg)
Local potential field by obstacle
Calculation Wind Vector = Real wind + Local potential
![Page 9: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/9.jpg)
Build the map model
![Page 10: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/10.jpg)
Build a virtual world for hypothesis
Decompose the map into cells tagged as building, air and ground.
Make a methane leak location cell and its leak concentration as a hypothesis.
Distribute methane from cells to cells using Gaussian distribution by calculated wind.
![Page 11: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/11.jpg)
Outline
Project Overview
Simulate Methane Distribution
Update Hypothesis Probability
Expected Information Gain to start path planning
Demo on real data
![Page 12: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/12.jpg)
Calculated methane concentration under each hypothesis
Concentration plot in 4 Different hypotheses virtual worlds
We normalized the probability for all the hypotheses in the initialized stage:
ππππππππππππππππππππππππ = 1/ππ
For the virtual world according to each hypothesis, calculate the methane concentration in every cell in the map.
We can draw the concentration/coordinate plot as left showing
![Page 13: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/13.jpg)
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12
Con
cent
ratio
n
Coordinate
Real Detection
0
5
10
15
0 5 10 15
Con
cent
ratio
n
Coordinate
Hypothesis#1
0
2
4
6
8
0 5 10 15
Con
cent
ratio
n
Coordinate
Hypothesis#2
-5
0
5
10
15
0 5 10 15Con
cent
ratio
n
Coordinate
Hypothesis#3
Model the likelihood using gamma distribution
![Page 14: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/14.jpg)
Model the likelihood using gamma distribution
ππππππππππ = Concentration under πππ‘π‘π‘ hypothesis
x = Concentration detected in real word
ππππππππππππβππππππππ = Gamma.pdf(ππππππππππ, x)
ππππππππππππππππππππππππππππππ = ππππππππππππππππππππππππππππππ β ππππππππβππππππππ
Repeated the steps for each detection
![Page 15: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/15.jpg)
Model the likelihood using gamma distribution
Hyp#1
Hyp#2
![Page 16: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/16.jpg)
Outline
Project Overview
Simulate Methane Distribution
Update Hypothesis Probability
Expected Information Gain to start path planning
Demo on real data
![Page 17: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/17.jpg)
Entropy for the set of hypotheses
Make probability of hypothesis as variable marked as π₯π₯ππ
Mark the all hypotheses set as ππEntropy of the set of hypotheses is:π»π» ππ = ββππ ππ(π₯π₯ππ)ππππππππππ(π₯π₯ππ)
![Page 18: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/18.jpg)
Update probability in the future under specific assumption
Prepared a location ππ as detected candidate in the future
Assume the πππ‘π‘π‘ hypothesis is true for next detection
Calculate new probability for each hypothesis under that assumption:ππππππππππππβππππππππ,ππ
ππ = πΊπΊπππΊπΊπΊπΊππ. ππππππ ππππππππππππ , ππππππππππππ
ππππππππππππππππππππππππ,ππππ = ππππππππππππππππππππππππ β ππππππππππππβππππππππ,ππ
ππ
![Page 19: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/19.jpg)
Expected Information Gain under specific assumption
The new Entropy for the probability updated hypotheses:π»π» ππππ,ππ =ββi P π₯π₯ππ,ππ
ππ β logbP π₯π₯ππ,ππππ
Expected Information Gain:πΌπΌπΊπΊππ,ππ = π»π» ππ β π»π»(ππππ,ππ)
![Page 20: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/20.jpg)
Sum the Expected Information Gain for each assumption
Assume all the hypotheses are true one hypothesis a time
Sum all the Expected Information Gain under one true hypothesis assumption weighted by its original probability:πΌπΌπΊπΊππ = βππ πΌπΌπΊπΊππ,ππ β ππ(π₯π₯ππ)
![Page 21: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/21.jpg)
Choose candidates by Expected Information Gain
By compared πΌπΌπΊπΊππ for different locations, we can decide which candidate location to move next step in order to get more information.
Itβs a start point for path planning
![Page 22: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/22.jpg)
Outline
Project Overview
Simulate Methane Distribution
Update Hypothesis Probability
Expected Information Gain to start path planning
Demo on real data
![Page 23: Adaptive Methane Detection](https://reader034.fdocuments.in/reader034/viewer/2022051213/55bb0759bb61eb73638b45fa/html5/thumbnails/23.jpg)
A virtualization Demo
Thank David for all his the intelligent ideas and algorithm framework
Thank Lance for his real world knowledge and practical experience to build our model
Here is a Demo running on real data collected by Lance.