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1
A Markov Process-based Approach for Reliability Evaluation of
the Propulsion System in Multi-Rotor Drones
Koorosh Aslansefat, Francisco Marques, Ricardo Mendonça and José Barata
2
Table of Content
What we are going to discuss
Introduction
Brief introduction for drones and the importance of reliability evaluation
Markov Modelling, Simplification and Validation
Markov modelling of drones with different configurations, simplification of models, and model
validation through Monte Carlo Simulations
Numerical Results
Numerical results for reliability and MTTF
Conclusion
A conclusion and suggestions for future works
3
Applications of Drones
Cargo Delivery
Entertainment
Agricultural
Search and
Rescue
UAV Applications
Reliability Definition: The quality of being trustworthy or of performing consistently well.
[3]
4
Drones Market
A quick report
Reference: www.droneii.com
5
Assumptions
CFP Dissemination
At the beginning, system is always operational
There is no common cause failure in the system
During the mission repair is not possible
The failure rates of the components obey an
exponential probability distribution function.
● Probability Distribution Function of Failures
-
( ) 1- t
F t e 

6
Markov Modelling
Hexa-Copter PNPNPN Configuration
7
Simplified Markov Model
Hexa-Copter PNPNPN Configuration
𝜆 = 𝜆 𝑎= 𝜆 𝑏 = 𝜆 𝑐 = 𝜆 𝑑 = 𝜆 𝑒 = 𝜆 𝑓
8
Markov Modelling
Hexa-Copter PPNNPN Configuration
9
Simplified Markov Model
Hexa-Copter PPNNPN Configuration
𝜆 = 𝜆 𝑎= 𝜆 𝑏 = 𝜆 𝑐 = 𝜆 𝑑 = 𝜆 𝑒 = 𝜆 𝑓
10
Model Validation Through Monte Carlo Simulation
Hexa-Copter PNPNPN Configuration
Markov SolutionMonte Carlo (1e06 Iteration)Reliability (Mission Time)
VarianceMean
0.8407211.32e-30.841404R(5)
0.5775021.32e-30.578312R(10)
0.3586761.32e-30.357543R(15)
0.2102881.32e-30.211128R(20)
0.1190511.32e-30.117153R(25)
0.0659571.32e-30.066433R(30)
0.0360631.32e-30.036925R(35)
11
Mean time to failure of hexacopter
vs. failure rate of each rotor
Numerical Results
Reliability and MTTF Evaluation
Reliability evaluation of Multirotors
(Quadcopter and Hexacopter) vs. failure rate
of each rotor at two hours of mission
12
Numerical Results
Reliability and MTTF Evaluation
Reliability evaluation of Multirotors
(Quadcopter and Hexacopter) vs. time with
failure rate of 0.04 failure/hour
Failure Situations
6 M 5 M 4 M* 4 M 3 M
MTTF 13.75 9.58 6.25 8.33 8.33
6 M 5 M -- 4 M --
MTTF 9.17 7.50 -- 6.25 0
Mean time to failure analysis of quadrotor from each
system’s states with failure rate of 0.04 failure/hour
13
Flowchart of the Proposed Markov-based Fault
Detection and Recovery System for Multirotors
14
Conclusion
For the first time, the Markov models of propulsion system in drones with different configurations
and number of rotors have been provided and validated through Monte Carlo Simulation.
Increasing the number of rotors in drones can improve their reliability and also Mean Time To
Failure (MTTF).
In Hexa-Copters, the PNPNPN configuration is more reliable than PPNNPN configuration and it has
a better MTTF.
A systematic mission avoidance and recovery procedure has been defined to reduce the risk of
mission based on MTTF calculation.
15
References
Barr, L. C., Newman, R. L., Ancel, E., Belcastro, C. M., Foster, J. V., Evans, J. K., & Klyde, D. H. (2017). Preliminary Risk
Assessment for Small Unmanned Aircraft Systems. 17th AIAA Aviation Technology, Integration, and Operations Conference.
Denver, Colorado.
Belcastro, C. M., Klyde, D. H., Logan, M. J., Newman, R. L., & Foster, J. V. (2017). Experimental Flight Testing for Assessing the
Safety of Unmanned Aircraft System Safety-Critical Operations. 17th AIAA Aviation Technology, Integration, and Operations
Conference. Denver, Colorado.
Belcastro, C. M., Newman, R. L., Evans, J. K., Klyde, D. H., Barr, L. C., & Ancel, E. (2017). Hazards Identification and Analysis for
Unmanned Aircraft System Operations. 17th AIAA Aviation Technology, Integration, and Operations Conference. Denver,
Colorado.
De Medeiros, I. P., Rodrigues, L. R., Santos, R., Shiguemori, E. H., & Júnior, C. L. (2014). PHM-Based Multi-UAV Task
Assignment. 8th Annual IEEE Systems Conference (SysCon). Ottawa, ON, Canada.
Dubrova, E. (2013). Fault-Tolerant Design. Berlin: Springer.
Juliana de Oliveira Martins Franco, B., & Carlos Sandoval Góes, L. (2007). Failure Analysis Methods in Unmanned Arial Vehicle
(UAV) Applications. 19th International Congress of Mechanical Engineering. Brazil.
Murtha, J. F. (2009). Evidence Theory and Fault-tree Analysis to Cost-effectively Improve Reliability in Small UAV Design. Virginia,
USA: Virginia Polytechnic Institute & State University.
Olson, I., & Atkins, E. M. (2013). Qualitative Failure Analysis for a Small Quadrotor Unmanned Aircraft System. AIAA Guidance,
Navigation, and Control (GNC) Conference. Boston, MA.
Sadeghzadeh, I., Mehta, A., & Zhang, Y. (2011). Fault/Damage Tolerant Control of a Quadrotor Helicopter UAV Using Model
Reference Adaptive Control and Gain-Scheduled PID. AIAA Guidance, Navigation, and Control Conference. Portland, Oregon.
Shi, D., Yang, B., & Quan, Q. (2016). Reliability Analysis of Multicopter Configurations Based on Controllability Theory. IEEE
35th Chinese Control Conference. Chengdu, China.
16
Thanks for Your Attention
If you have any question please fill free to ask

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A markov process based approach for reliability evaluation of the propulsion system in multi-rotor drones presentation

  • 1. 1 A Markov Process-based Approach for Reliability Evaluation of the Propulsion System in Multi-Rotor Drones Koorosh Aslansefat, Francisco Marques, Ricardo Mendonça and José Barata
  • 2. 2 Table of Content What we are going to discuss Introduction Brief introduction for drones and the importance of reliability evaluation Markov Modelling, Simplification and Validation Markov modelling of drones with different configurations, simplification of models, and model validation through Monte Carlo Simulations Numerical Results Numerical results for reliability and MTTF Conclusion A conclusion and suggestions for future works
  • 3. 3 Applications of Drones Cargo Delivery Entertainment Agricultural Search and Rescue UAV Applications Reliability Definition: The quality of being trustworthy or of performing consistently well. [3]
  • 4. 4 Drones Market A quick report Reference: www.droneii.com
  • 5. 5 Assumptions CFP Dissemination At the beginning, system is always operational There is no common cause failure in the system During the mission repair is not possible The failure rates of the components obey an exponential probability distribution function. ● Probability Distribution Function of Failures - ( ) 1- t F t e  
  • 7. 7 Simplified Markov Model Hexa-Copter PNPNPN Configuration 𝜆 = 𝜆 𝑎= 𝜆 𝑏 = 𝜆 𝑐 = 𝜆 𝑑 = 𝜆 𝑒 = 𝜆 𝑓
  • 9. 9 Simplified Markov Model Hexa-Copter PPNNPN Configuration 𝜆 = 𝜆 𝑎= 𝜆 𝑏 = 𝜆 𝑐 = 𝜆 𝑑 = 𝜆 𝑒 = 𝜆 𝑓
  • 10. 10 Model Validation Through Monte Carlo Simulation Hexa-Copter PNPNPN Configuration Markov SolutionMonte Carlo (1e06 Iteration)Reliability (Mission Time) VarianceMean 0.8407211.32e-30.841404R(5) 0.5775021.32e-30.578312R(10) 0.3586761.32e-30.357543R(15) 0.2102881.32e-30.211128R(20) 0.1190511.32e-30.117153R(25) 0.0659571.32e-30.066433R(30) 0.0360631.32e-30.036925R(35)
  • 11. 11 Mean time to failure of hexacopter vs. failure rate of each rotor Numerical Results Reliability and MTTF Evaluation Reliability evaluation of Multirotors (Quadcopter and Hexacopter) vs. failure rate of each rotor at two hours of mission
  • 12. 12 Numerical Results Reliability and MTTF Evaluation Reliability evaluation of Multirotors (Quadcopter and Hexacopter) vs. time with failure rate of 0.04 failure/hour Failure Situations 6 M 5 M 4 M* 4 M 3 M MTTF 13.75 9.58 6.25 8.33 8.33 6 M 5 M -- 4 M -- MTTF 9.17 7.50 -- 6.25 0 Mean time to failure analysis of quadrotor from each system’s states with failure rate of 0.04 failure/hour
  • 13. 13 Flowchart of the Proposed Markov-based Fault Detection and Recovery System for Multirotors
  • 14. 14 Conclusion For the first time, the Markov models of propulsion system in drones with different configurations and number of rotors have been provided and validated through Monte Carlo Simulation. Increasing the number of rotors in drones can improve their reliability and also Mean Time To Failure (MTTF). In Hexa-Copters, the PNPNPN configuration is more reliable than PPNNPN configuration and it has a better MTTF. A systematic mission avoidance and recovery procedure has been defined to reduce the risk of mission based on MTTF calculation.
  • 15. 15 References Barr, L. C., Newman, R. L., Ancel, E., Belcastro, C. M., Foster, J. V., Evans, J. K., & Klyde, D. H. (2017). Preliminary Risk Assessment for Small Unmanned Aircraft Systems. 17th AIAA Aviation Technology, Integration, and Operations Conference. Denver, Colorado. Belcastro, C. M., Klyde, D. H., Logan, M. J., Newman, R. L., & Foster, J. V. (2017). Experimental Flight Testing for Assessing the Safety of Unmanned Aircraft System Safety-Critical Operations. 17th AIAA Aviation Technology, Integration, and Operations Conference. Denver, Colorado. Belcastro, C. M., Newman, R. L., Evans, J. K., Klyde, D. H., Barr, L. C., & Ancel, E. (2017). Hazards Identification and Analysis for Unmanned Aircraft System Operations. 17th AIAA Aviation Technology, Integration, and Operations Conference. Denver, Colorado. De Medeiros, I. P., Rodrigues, L. R., Santos, R., Shiguemori, E. H., & Júnior, C. L. (2014). PHM-Based Multi-UAV Task Assignment. 8th Annual IEEE Systems Conference (SysCon). Ottawa, ON, Canada. Dubrova, E. (2013). Fault-Tolerant Design. Berlin: Springer. Juliana de Oliveira Martins Franco, B., & Carlos Sandoval Góes, L. (2007). Failure Analysis Methods in Unmanned Arial Vehicle (UAV) Applications. 19th International Congress of Mechanical Engineering. Brazil. Murtha, J. F. (2009). Evidence Theory and Fault-tree Analysis to Cost-effectively Improve Reliability in Small UAV Design. Virginia, USA: Virginia Polytechnic Institute & State University. Olson, I., & Atkins, E. M. (2013). Qualitative Failure Analysis for a Small Quadrotor Unmanned Aircraft System. AIAA Guidance, Navigation, and Control (GNC) Conference. Boston, MA. Sadeghzadeh, I., Mehta, A., & Zhang, Y. (2011). Fault/Damage Tolerant Control of a Quadrotor Helicopter UAV Using Model Reference Adaptive Control and Gain-Scheduled PID. AIAA Guidance, Navigation, and Control Conference. Portland, Oregon. Shi, D., Yang, B., & Quan, Q. (2016). Reliability Analysis of Multicopter Configurations Based on Controllability Theory. IEEE 35th Chinese Control Conference. Chengdu, China.
  • 16. 16 Thanks for Your Attention If you have any question please fill free to ask