For the successful operation of an autonomous unmanned vehicle, also known as AUV, it is imperative to have an apt design of its hull and other components such as seals and housings to prevent all possible failures due to increasing atmospheric pressure at greater depths below sea level. Thus, each phase, right from the design to the termination phase involves a series of crucial steps. These steps are sequentially arranged by implementing a mathematical model known as Markov Chains. Based on heuristic and experimental data we analyzed the reliability of the seals used in the propulsion module of the vehicle, by assigning transition probabilities to each step whether recurring, non-recurring, or terminating. The proposed model consists of a total of seven states. These states are then plotted in a square matrix also known as the ‘Distribution Matrix’. Successive iterations are then obtained based on an initial probability vector. This quantitative analysis of the iterations explores the pattern in which the entire procedure unfolds with time and predicts the success rate and the risk involved in the process when the system attains a steady state vector.

2. Hello.

3. Dedicated to…

5. Reliability Analysis of Seals used in Propulsion
Module of an Autonomous Unmanned Vehicle
using Markov Chains

6. Disclaimer
This presentation has been prepared exclusively for the “INTERNATIONAL
CONFERENCE ON INTELLIGENT MANUFACTURING AND AUTOMATION”, organized
on July 20-21, 2018 at Dwarkadas J. Sanghavi College of Engineering, Mumbai. The
presentation is intended solely for the benefit of attendees and its contents and
conclusions are confidential and may not be disclosed to any other persons or
companies without the prior written permission of the Author. The information upon
which this presentation is based from own experience, knowledge and databases and
few other references. The use of this research content was authorized in advance and
any further use or redistribution of it is strictly prohibited without written permission by
the Author. The opinions expressed herein have been achieved internally and are being
shared for the purpose of discussions at the presentation, which are merely directional
and not for any commercial purpose or decisions, and subject to changes as per
market dynamics. The Author does not accept any liability or claims for your reliance
upon them.

7. Presentation Outline
Project Adamya AUV
Problem Definition
Introduction to Markov Chains
Preparation of stochastic model

8. Larsen & Toubro Defense IC
One of India’s largest manufacturer of defense equipment and systems for more
than 30 years
Offers customized turnkey projects for the Indian Armed Forces to improvise and
innovate the weaponry used in modern day warfare
Collaboration with companies in allied nations like Russia, South Korea, United
States, France and Japan

9. The Adamya Autonomous Unmanned
Vehicle (AUV)

10. Adamya – impossible to subdue or defeat
The ​Adamya is an underwater unmanned marine surveillance
prototype, also called as AUV currently being developed in-
house by Larsen and Toubro
It can be launched from the torpedo tube of a submarine
carry out predefined mission objectives independent of manual
control.
Indeed a globally pioneering feat

11. The Propulsion Module
Cone shaped component to provide housing for the fin motors, rotary
propellers and other electrical and electronic components
Fin motors are synchronized to tilt or turn the AUV whereas propellers
are used to provide forward thrust
Pressure test in a specially designed fixture is conducted to check the
ability of seals to withstand the rising pressure at varying sea levels

12. The Problem Statement
“To evaluate and analyse the risk involved in the selection of the
appropriate seals to prevent leakage in the propulsion module
of an unmanned marine surveillance prototype and predict the
behaviour in its failure and the overall accomplishment of the
critical task using Markov chains.”

13. The Approach
Identify the critical activity from the project plan
Study different types of seals and their applications
Study the type of seals suitable for marine application
Study the different types of greases used for lubrication of seals, and
suitable for marine application
Mount the seals along with the fin motors on the designated fixture
and conduct the pressure test (Hydraulic: Static and dynamic)

14. The Approach
Conduct each test by increasing the pressure proportionate to the
pressure at that depth of sea level
If any of the seals fail during the test, analyse the type of failure,
redesign the seal as per the new recommendations, and then conduct
further experiments

15. Test setup

16. There’s something more…

18. The Markov Chain

19. Basic Concept
Concept introduced by Andrey Markov, a Russian Mathematician
A stochastic model to analyse the behaviour of a system as it changes its state
The successor’s phase is dependant on its predecessor’s phase
An effective tool for analysing risk
Can be applied to any industrial operation which involves risk

20. Types of Markov Chains
Discrete Markov Chain Continuous Markov Chain

21. What is a Stochastic Model?

22. What is Risk?

23. Using Markov Chains to simulate a
lecture hall

24. Arriving
Playing on Phone
Paying attention
Kicked out
Writing Notes
Listening
0.5
0.5
0.99
0.8
0.01
1
0.2
1 1

25. The Transition Matrix ‘M’
We have,
M = 0 0.5 0.5 0 0 0
0 0 0.99 0 0 0.01
0 0.8 0 0.2 0 0
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1
Playing on phone
Arriving
Paying attention
Kicked out
Writing notes
Listening

26. Initial Probability Vector ‘𝜋’
𝜋(0) = {1 0 0 0 0 0 }

27. Iterations
n = 0 . Mn
1 = {0 0.5 0.5 0 0 0 }
10 = {0 0.4 0.495 0.1 0 0.005 }
100 = {0 0.157 0.195 0.331 0.288 0.028 }
180= {0 0 0 0.48 0.47 0.05 } (Steady State Vector)

28. Markov Chain to assess the reliability of
seals

29. Design phase
Pressure Test 1
Pressure Test 2
Pressure Test 3
Pressure Test 4 Pressure Test 5 Dispatch (Termination)
0.7
0.3
0.4
0.25
0.35
0.350.3
0.45
0.25
0.55
0.2
0.65
1

30. 0.70 0.30 0.00 0.00 0.00 0.00 0.00
0.35 0.40 0.25 0.00 0.00 0.00 0.00
0.30 0.00 0.35 0.35 0.00 0.00 0.00
M = 0.25 0.00 0.00 0.30 0.45 0.00 0.00
0.20 0.00 0.00 0.00 0.25 0.55 0.00
0.15 0.00 0.00 0.00 0.00 0.20 0.65
0.00 0.00 0.00 0.00 0.00 0.00 1.00
𝜋0 = { 1.00 0.00 0.00 0.00 0.00 0.00 0.00 }
Predecessors
Successors
S1 S2 S3 S4 S5 S6 S7
S1 S2 S3 S4 S5 S6 S7
S1
S2
S3
S4
S5
S6
S7

31. Iterations
1 = { 0.700 0.300 0.000 0.000 0.000 0.000 0.000 }
100 = { 0.126 0.065 0.026 0.013 0.008 0.006 0.756 }
200 = { 0.020 0.011 0.004 0.002 0.001 0.001 0.950 }
210 = { 0.020 0.011 0.004 0.002 0.001 0.001 0.950 }
(steady state vector)

33. Limitations of FMEA
Error in severity rating
Limited scope
Multiple ways in which a system can fail
Detailed analysis
Not easily changeable

34. Smart
Easy to use
Not – so – smart
Not – so – easy
to use
Markov
chain
Regular
FMEA
Analysis

35. Inference
Failure of experiments can be observed at each phase
In case the prototype fails at the site, the Markov Chain can be modified easily
and new results can be obtained
Once the prototype clears the test at the site it can be manufactured on a large
scale
Reduction in time loss in excessive brainstorming

36. Some interesting applications
Supply Chain Management
Defence Logistics
Pharmaceutical industry
Study of Continental drifts
Analysis of complex surgical procedures

37. And many more …

38. Software used for analysis
Microsoft Excel 2010
MS Project 2010
SciLab version 6.0.1

39. Acknowledgements

40. Dr. Vijay S. Bilolikar
(Internal guide and Dean, student affairs)

41. Mr. Vivekanand Hegde
(Assistant General Manager – PMG Defence)