An Uncertainty Quantification Framework for Autonomous System Tracking and Health Monitoring
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Published
Mar 29, 2021
Matteo Corbetta
Chetan Kulkarni
Portia Banerjee
Elinirina Robinson
Abstract
This work proposes a perspective towards establishing a framework for uncertainty quantification of autonomous system tracking and health monitoring. The approach leverages the use of a predictive process structure, which maps uncertainty sources and their interaction according to the quantity of interest and the goal of the predictive estimation. It is systematic and uses basic elements that are system agnostic, and therefore needs to be tailored according to the specificity of the application. This work is motivated by the interest in low-altitude unmanned aerial vehicle operations, where awareness of vehicle and airspace state becomes more relevant as the density of autonomous operations grows rapidly. Predicted scenarios in the area of small vehicle operations and urban air mobility have no precedent, and holistic frameworks to perform prognostics and health management (PHM) at the system- and airspace-level are missing formal approaches to account for uncertainty. At the end of the paper, two case studies demonstrate implementation framework of trajectory tracking and health diagnosis for a small unmanned aerial vehicle.
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Keywords
Uncertainty Quantification, Autonomous System Tracking, Health Monitoring
References
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Celaya, J. R., Saxena, A., Kulkarni, C. S., Saha, S., & Goebel,
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Crestaux, T., Maıˆtre, O. L., & Martinez, J.-M. (2009). Polynomial chaos expansion for sensitivity analysis. Reliability Engineering & System Safety, 94(7), 1161 - 1172. (Special Issue on Sensitivity Analysis)
Daigle, M., & Kulkarni, C. (2013). Electrochemistry-based battery modeling for prognostics. In Annual conference of the prognostics and health management society 2013 (p. 249-261).
Davis, J. D., & Chakravorty, S. (2007). Motion planning under uncertainty: application to an unmanned helicopter. Journal of Guidance, Control, and Dynamics, 30(5), 1268–1276.
Drozeski, G. R., Saha, B., & Vachtsevanos, G. J. (2005). A fault detection and reconfigurable control architecture for unmanned aerial vehicles. In 2005 ieee aerospace conference (pp. 1–9).
Eldred, M., & Burkardt, J. (2009, Jan). Comparison of nonintrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition. Retrieved from http://dx.doi.org/10.2514/6.2009-976 doi: 10.2514/6.2009-976
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Frew, E., & Sengupta, R. (2004). Obstacle avoidance with sensor uncertainty for small unmanned aircraft. In 2004 43rd ieee conference on decision and control (cdc) (ieee cat. no. 04ch37601) (Vol. 1, pp. 614–619).
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Gordon, N. J., Salmond, D. J., & Smith, A. F. (1993). Novel approach to nonlinear/non-gaussian Bayesian state estimation. 140(2), 107–113.
Gorospe, G. E. J., Kulkarni, C. S., Hogge, E., Hsu, A., Ownby, N. (2017). A study of the degradation of electronic speed controllers for brushless dc motors. In Asia pacific conference of the prognostics and health management society 2017.
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Hoffmann, G., Huang, H., Waslander, S., & Tomlin, C. (2007). Quadrotor helicopter flight dynamics and control: Theory and experiment. In Aiaa guidance, navigation and control conference and exhibit (p. 6461).
Holtz, J. (1992). Pulsewidth modulation-a survey. IEEE Transactions on Industrial Electronics, 39(5), 410–420.
Jing, D., & Haifeng, W. (2013). System health management for unmanned aerial vehicle: conception, state-of-art, framework and challenge. In 2013 IEEE 11th international conference on electronic measurement & instruments (Vol. 2, pp. 859–863).
Johry, A., & Kapoor, M. (2016). Unmanned aerial vehicle (UAV): Fault tolerant design. International Journal of Engineering Technology Science and Research, 3(6), 1–7.
Jun, M., & D’Andrea, R. (2003). Path planning for unmanned aerial vehicles in uncertain and adversarial environments. In Cooperative control: models, applications and algorithms (pp. 95–110). Springer.
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of basic Engineering, 82(1), 35–45.
Kaminer, I., Pascoal, A., Hallberg, E., & Silvestre, C. (1998). Trajectory tracking for autonomous vehicles: An integrated approach to guidance and control. Journal of Guidance, Control, and Dynamics, 21(1), 29–38.
King, D.W., Bertapelle, A., & Moses, C. (2005). UAV failure rate criteria for equivalent level of safety. In International helicopter safety symposium, Montreal (Vol. 9).
Kopardekar, P., Rios, J., Prevot, T., Johnson, M., Jung, J., Robinson, J. E. (2016). Unmanned aircraft system traffic management (UTM) concept of operations. In AIAA aviation forum.
Krish nakumar, K. S., Kopardekar, P. H., Ippolito, C. A., Melton, J., Stepanyan, V., Sankararaman, S., Nikaido, B. (2017). Safe autonomous flight environment (safe50) for the notional last “50 ft” of operation of “55 lb” class of uas. In Aiaa information systems. AIAA infotech@ aerospace (p. 0445).
Langelaan, J. W., Alley, N., & Neidhoefer, J. (2011). Wind field estimation for small unmanned aerial vehicles. Journal of Guidance, Control, and Dynamics, 34(4), 1016–1030.
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Pillay, P., & Krishnan, R. (1989). Modeling, simulation, and analysis of permanent-magnet motor drives. i. the permanent-magnet synchronous motor drive. IEEE Transactions on industry applications, 25(2), 265–273.
Radmanesh, M., Kumar, M., & Sarim, M. (2018). Grey wolf optimization based sense and avoid algorithm in a bayesian framework for multiple uav path planning in an uncertain environment. Aerospace Science and Technology, 77, 168–179.
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Sankararaman, S., & Goebel, K. (2015). Uncertainty in prognostics and systems health management. International Journal of Prognostics and Health Management, 6.
Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2009). Uncertainty quantification in fatigue damage prognosis. In Annual conference of the prognostics and health management society (pp. 1–13).
Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., Schwabacher, M. (2008). Metrics for evaluating performance of prognostic techniques. In Prognostics and health management, 2008. PHM 2008. International conference on (pp. 1–17).
Smith, R. C. (2013). Uncertainty quantification: theory, implementation, and applications (Vol. 12). Society for Industrial and Applied Mathematics (SIAM).
Stevens, B. L., Lewis, F. L., & Johnson, E. N. (2015). Aircraft control and simulation: dynamics, controls design, and autonomous systems. John Wiley & Sons.
Sujit, P., Saripalli, S., & Sousa, J. B. (2014). Unmanned aerial vehicle path following: A survey and analysis of algorithms for fixed-wing unmanned aerial vehicles. IEEE Control Systems Magazine, 34(1), 42–59.
Tessem, B. (1992). Interval probability propagation. International Journal of Approximate Reasoning, 7(3), 95 - 120. doi: https://doi.org/10.1016/0888-613X(92)90006-L
Walker, M. (2010). Next generation prognostics and health management for unmanned aircraft. In 2010 IEEE aerospace conference (pp. 1–14).
Adams, B. M., Bohnhoff, W., Dalbey, K., Eddy, J., Eldred, M., Gay, D., Swiler, L. P. (2009). Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: version 5.0 user’s manual. Sandia National Laboratories, Tech. Rep. SAND2010-2183.
Alba ker, B., & Rahim, N. (2009). A survey of collision avoidance approaches for unmanned aerial vehicles. In 2009 international conference for technical postgraduates (techpos) (pp. 1–7).
Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking. Signal Processing, IEEE Transactions on, 50(2), 174–188.
Balaban, E., Roychoudhury, I., Spirkovska, L., Sankararaman, S., Kulkarni, C. S., & Arnon, T. (2017). Dynamic routing of aircraft in the presence of adverse weather using a pomdp framework. In 17th AIAA aviation technology, integration, and operations conference (p. 3429).
Banerjee, P., & Corbetta, M. (2020). In-time uav flight-trajectory estimation and tracking using Bayesian filters. In 2020 IEEE aerospace conference (pp. 1–9).
Cacuci, D. (2003). Sensitivity & uncertainty analysis: Theory, volume 1. Chapman and Hall/CRC. doi: 10.1201/9780203498798
Celaya, J. R., Saxena, A., Kulkarni, C. S., Saha, S., & Goebel,
K. (2012, Jan). Prognostics approach for power MOSFET under thermal-stress aging. In Proceedings annual reliability and maintainability symposium.
Chen, Z. (2003). Bayesian filtering: From Kalman filters to particle filters, and beyond. Statistics, 182(1), 1–69.
Corbetta, M., Banerjee, P., Okolo, W., Gorospe, G., Luchinsky, D. (2019). Real-time uav trajectory prediction for safety monitoring in low-altitude airspace. In AIAA aviation forum, UAS traffic management IV session.
Corbetta, M., & Kulkarni, C. S. (2019, September). An approach towards uncertainty quantification and management of unmanned aerial vehicle health. In S. Clements (Ed.), Annual conference of the prognostic and health management society.
Crestaux, T., Maıˆtre, O. L., & Martinez, J.-M. (2009). Polynomial chaos expansion for sensitivity analysis. Reliability Engineering & System Safety, 94(7), 1161 - 1172. (Special Issue on Sensitivity Analysis)
Daigle, M., & Kulkarni, C. (2013). Electrochemistry-based battery modeling for prognostics. In Annual conference of the prognostics and health management society 2013 (p. 249-261).
Davis, J. D., & Chakravorty, S. (2007). Motion planning under uncertainty: application to an unmanned helicopter. Journal of Guidance, Control, and Dynamics, 30(5), 1268–1276.
Drozeski, G. R., Saha, B., & Vachtsevanos, G. J. (2005). A fault detection and reconfigurable control architecture for unmanned aerial vehicles. In 2005 ieee aerospace conference (pp. 1–9).
Eldred, M., & Burkardt, J. (2009, Jan). Comparison of nonintrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition. Retrieved from http://dx.doi.org/10.2514/6.2009-976 doi: 10.2514/6.2009-976
FAA. (2018). Unmanned aerial system (uas) traffic management (utm), concept of operations (Tech. Rep.). Federal Aviation Administration.
Fong, T. (2018). Autonomous systems: Nasa capability overview.
Freeman, P., & Balas, G. J. (2014). Actuation failure modes and effects analysis for a small uav. In American control conference (acc), 2014 (pp. 1292–1297).
Frew, E., & Sengupta, R. (2004). Obstacle avoidance with sensor uncertainty for small unmanned aircraft. In 2004 43rd ieee conference on decision and control (cdc) (ieee cat. no. 04ch37601) (Vol. 1, pp. 614–619).
Ghanem, R. G., & Spanos, P. D. (1991). Stochastic finite elements: A spectral approach. Springer New York. doi: 10.1007/978-1-4612-3094-6
Ginart, A., Brown, D., Kalgren, P., & Roemer, M. (2009). Online ringing characterization as a diagnostic technique for igbts in power drives igbts in power drives. In IEEE transactions on instrumentation and measurement (Vol. 58).
Glasheen, K., Pinto, J., Steiner, M., & Frew, E. W. (2019). Experimental assessment of local weather forecasts for small unmanned aircraft flight. In AIAA scitech 2019 forum (p. 1193).
Goebel, K. (2017). Prognostics, the science of making prediction. CreateSpace Independent Publishing Platform (1).
Gordon, N. J., Salmond, D. J., & Smith, A. F. (1993). Novel approach to nonlinear/non-gaussian Bayesian state estimation. 140(2), 107–113.
Gorospe, G. E. J., Kulkarni, C. S., Hogge, E., Hsu, A., Ownby, N. (2017). A study of the degradation of electronic speed controllers for brushless dc motors. In Asia pacific conference of the prognostics and health management society 2017.
Haug, A. (2005). A tutorial on Bayesian estimation and tracking techniques applicable to nonlinear and non-gaussian processes. MITRE Corporation, McLean.
Hoffmann, G., Huang, H., Waslander, S., & Tomlin, C. (2007). Quadrotor helicopter flight dynamics and control: Theory and experiment. In Aiaa guidance, navigation and control conference and exhibit (p. 6461).
Holtz, J. (1992). Pulsewidth modulation-a survey. IEEE Transactions on Industrial Electronics, 39(5), 410–420.
Jing, D., & Haifeng, W. (2013). System health management for unmanned aerial vehicle: conception, state-of-art, framework and challenge. In 2013 IEEE 11th international conference on electronic measurement & instruments (Vol. 2, pp. 859–863).
Johry, A., & Kapoor, M. (2016). Unmanned aerial vehicle (UAV): Fault tolerant design. International Journal of Engineering Technology Science and Research, 3(6), 1–7.
Jun, M., & D’Andrea, R. (2003). Path planning for unmanned aerial vehicles in uncertain and adversarial environments. In Cooperative control: models, applications and algorithms (pp. 95–110). Springer.
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of basic Engineering, 82(1), 35–45.
Kaminer, I., Pascoal, A., Hallberg, E., & Silvestre, C. (1998). Trajectory tracking for autonomous vehicles: An integrated approach to guidance and control. Journal of Guidance, Control, and Dynamics, 21(1), 29–38.
King, D.W., Bertapelle, A., & Moses, C. (2005). UAV failure rate criteria for equivalent level of safety. In International helicopter safety symposium, Montreal (Vol. 9).
Kopardekar, P., Rios, J., Prevot, T., Johnson, M., Jung, J., Robinson, J. E. (2016). Unmanned aircraft system traffic management (UTM) concept of operations. In AIAA aviation forum.
Krish nakumar, K. S., Kopardekar, P. H., Ippolito, C. A., Melton, J., Stepanyan, V., Sankararaman, S., Nikaido, B. (2017). Safe autonomous flight environment (safe50) for the notional last “50 ft” of operation of “55 lb” class of uas. In Aiaa information systems. AIAA infotech@ aerospace (p. 0445).
Langelaan, J. W., Alley, N., & Neidhoefer, J. (2011). Wind field estimation for small unmanned aerial vehicles. Journal of Guidance, Control, and Dynamics, 34(4), 1016–1030.
Lawler, G. F. (2010). Stochastic calculus: An introduction with applications. American Mathematical Society.
Liu, Y., & Goebel, K. (2018). Information fusion for national airspace system prognostics. In PHM society conference (Vol. 10).
Luttinen, J., & Ilin, A. (2012, 21–23 Apr). Efficient gaussian process inference for short-scale spatio-temporal modeling. In N. D. Lawrence & M. Girolami (Eds.), Proceedings of the fifteenth international conference on artificial intelligence and statistics (Vol. 22, pp. 741–750). La Palma, Canary Islands: PMLR.
Najm, H. N. (2009, Jan). Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics. Annual Review of Fluid Mechanics, 41(1), 35–52. doi: 10.1146/annurev.fluid.010908.165248
Physical Sciences 2, H. U. (2013). A summary of error propagation. Harvard University Lecture Notes.
Pillay, P., & Krishnan, R. (1989). Modeling, simulation, and analysis of permanent-magnet motor drives. i. the permanent-magnet synchronous motor drive. IEEE Transactions on industry applications, 25(2), 265–273.
Radmanesh, M., Kumar, M., & Sarim, M. (2018). Grey wolf optimization based sense and avoid algorithm in a bayesian framework for multiple uav path planning in an uncertain environment. Aerospace Science and Technology, 77, 168–179.
Rasmussen, C. E., & Williams, C. K. (2006). Gaussian processes for machine learning (Vol. 2) (No. 3). MIT Press Cambridge, MA.
Rogers, D. F. (2000). An introduction to nurbs: with historical perspective. Elsevier.
Roy, C. J., & Oberkampf, W. L. (2011). A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing. Computer methods in applied mechanics and engineering, 200(25-28), 2131–2144.
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Tarantola, S. (2008). Global sensitivity analysis: the primer. John Wiley & Sons.
Saltelli, A., Tarantola, S., Campolongo, F., & Ratto, M. (2004). Sensitivity analysis in practice: a guide to assessing scientific models. Chichester, England.
Sankararaman, S. (2015). Significance, interpretation, and quantification of uncertainty in prognostics and remaining useful life prediction. Mechanical Systems and Signal Processing, 52, 228–247.
Sankararaman, S. (2017). Towards a computational framework for autonomous decision-making in unmanned aerial vehicles. In Aiaa information systems-aiaa infotech@ aerospace (p. 0446).
Sankararaman, S., & Goebel, K. (2015). Uncertainty in prognostics and systems health management. International Journal of Prognostics and Health Management, 6.
Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2009). Uncertainty quantification in fatigue damage prognosis. In Annual conference of the prognostics and health management society (pp. 1–13).
Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., Schwabacher, M. (2008). Metrics for evaluating performance of prognostic techniques. In Prognostics and health management, 2008. PHM 2008. International conference on (pp. 1–17).
Smith, R. C. (2013). Uncertainty quantification: theory, implementation, and applications (Vol. 12). Society for Industrial and Applied Mathematics (SIAM).
Stevens, B. L., Lewis, F. L., & Johnson, E. N. (2015). Aircraft control and simulation: dynamics, controls design, and autonomous systems. John Wiley & Sons.
Sujit, P., Saripalli, S., & Sousa, J. B. (2014). Unmanned aerial vehicle path following: A survey and analysis of algorithms for fixed-wing unmanned aerial vehicles. IEEE Control Systems Magazine, 34(1), 42–59.
Tessem, B. (1992). Interval probability propagation. International Journal of Approximate Reasoning, 7(3), 95 - 120. doi: https://doi.org/10.1016/0888-613X(92)90006-L
Walker, M. (2010). Next generation prognostics and health management for unmanned aircraft. In 2010 IEEE aerospace conference (pp. 1–14).
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