Abstract
In this work, we tackle the problem of systematic population of a bank of residual generators for model-based fault diagnosis in Unmanned Aerial Vehicles (UAVs). Intended for detailed, large and non-linear system models, Structural Analysis (SA) is applied to produce a graph-based abstraction of the problem in the form of a bipartite graph. The Branch and Bound Integer Linear Programming (BBILP) algorithm is employed, properly adapted to seek a solution for the constrained graph matching problem. Appropriate causality constraints are formulated, which link the structure of the system graph with the analytical form of the residual generators and certify that all resulting residual generators can be implemented automatically using numerical processes. An extensive performance investigation of the proposed approach is carried out, which is shown to be more efficient than other similar algorithms. Benchmarks of UAV models taken from the literature are presented and a simulated response of the diagnostic system against a fault in the roll-rate sensor is showcased.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
U.S. Standard Atmosphere: Technical report, National Oceanic and Atmospheric Administration, National Aeronautics and Space Adminisration, United States Air Force (1976)
Amato, F., Cosentino, C., Mattei, M., Paviglianiti, G.: A direct/functional redundancy scheme for fault detection and isolation on an aircraft. Aerosp. Sci. Technol. 10(4), 338–345 (2006)
Ascher, U.M., Petzold, L.R.: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, pp. 19104–2688. SIAM, Philadelphia (1998)
Åslund, J., Bregon, A., Krysander, M., Frisk, E., Pulido, B., Biswas, G.: Structural diagnosability analysis of dynamic models. IFAC Proc. Vol. 44(1), 4082–4088 (2011)
Avram, R.C., Zhang, X., Muse, J.: Quadrotor sensor fault diagnosis with experimental results. J. Intell. Robot. Syst.: Theory Appl. 86(1), 115–137 (2017)
Avram, R.C., Zhang, X., Muse, J.: Quadrotor actuator fault diagnosis and accommodation using nonlinear adaptive estimators. IEEE Trans. Control Syst. Technol. 25(6), 2219–2226 (2017)
Beard, R.W., Timothy, W.M.: Small Unmanned Aircraft: Theory and Practice. Princeton University Press (2012)
Bertsimas, D., Tsitsiklis, J.N.: Introduction to Linear Optimization Athena Scientific (1997)
Blanke, M., Hansen, S., Blas, M.R.: Diagnosis for control and decision support in complex systems. In: Conference on Complex Systems: Synergy of Control, Communications and Computing, number 1973, pp. 16–20 (2011)
Blanke, M., Kinnaert, M., Lunze, J., Staroswiecki, M.: Diagnosis and Fault-Tolerant Control, 3rd edn. Springer, Berlin (2016)
Blanke, M., Staroswiecki, M.: Structural design of systems with safe behavior under single and multiple faults. In: Zhang, Z. (ed.) IFAC Safeprocess, pp. 474–479 (2006)
Castaldi, P., Geri, W., Bonfè, M., Simani, S., Benini, M.: Design of residual generators and adaptive filters for the FDI of aircraft model sensors. Control. Eng. Pract. 18(5), 449–459 (2010)
Cen, Z., Noura, H., Susilo, T.B., Al Younes, Y.: Robust fault diagnosis for quadrotor uavs using adaptive Thau observer. J. Intell. Robot. Sys.: Theory Appl. 73(1–4), 573–588 (2014)
Commault, C., Dion, J.-M.: Sensor location for diagnosis in linear systems: A structural analysis. IEEE Trans. Autom. Control 52(2), 155–169 (2007)
Commault, C., Dion, J.-M., Agha, S.Y.: Structural analysis for the sensor location problem in fault detection and isolation. Automatica 44(8), 2074–2080 (2008)
Cormen, T.H., Leiserons, C.E. , Rivest, R.L., Clifford, S.: Introduction to Algorithms, 3rd edn. The MIT Press, London (2009)
Daigle, M.J., Roychoudhury, I., Biswas, G., Koutsoukos, X.D., Patterson-Hine, A., Poll, S.: A comprehensive diagnosis methodology for complex hybrid systems: A case study on spacecraft power distribution systems. IEEE Trans. Syst. Man Cybern. Part A: Syst. Humans 40(5), 917–931 (2010)
Dulmage, A.L., Mendelsohn, N.S.: Coverings of bipartite graphs. Can. J. Math. 10, 517–534 (1958)
Dustegor, D., Cocquempot, V., Staroswiecki, M.: Structural analysis for residual generation: towards implementation. In: Proceedings of the 2004 IEEE International Conference on Control Applications, 2004, vol. 2, pp. 1217–1222. IEEE (2004)
Düstegör, D, Frisk, E., Cocquempot, V., Krysander, M., Staroswiecki, M.: Structural analysis of fault isolability in the DAMADICS benchmark. Control. Eng. Pract. 14(6), 597–608 (2006)
Flaugergues, V., Cocquempot, V., Bayart, M., Pengov, M.: Structural analysis for FDI: A modified, invertibility-based canonical decomposition. In: Proceedings of the 20th International Workshop on Principles of Diagnosis, DX09 (2009)
Flaugergues, V., Cocquempot, V., Bayart, M., Pengov, M.: On non-invertibilities for structural analysis. In: 21st International Workshop on Principles of Diagnosis (DX’10) (2010)
Frank, P.M.: Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy. Automatica 26(3), 459–474 (1990)
Fravolini, M.L., Brunori, V., Campa, G., Napolitano, M.R., La Cava, M.: Structural analysis approach for the generation of structured residuals for aircraft FDI. IEEE Trans. Aerosp. Electron. Syst. 45(4), 1466–1482 (2009)
Fravolini, M.L., Campa, G., Napolitano, M.: Design of redundancy relations for unmanned aerial vehicle FDI. AIAA Guidance, Navigation and Control Conference and Exhibit, pp. 1–12 (2008)
Freddi, A., Longhi, S., Monteriù, A.: A diagnostic Thau observer for a class of unmanned vehicles. J. Intell. Robot. Syst. 67(1), 61–73 (2012)
Freeman, P., Seiler, P., Balas, G.J.: Air data system fault modeling and detection. Control Eng. Pract. 21(10), 1290–1301 (2013)
Frisk, E.: Residual generator design for non-linear, polynomial systems - A Gröbner basis approach. IFAC Proc. Vol. 33(11), 957–962 (2000)
Frisk, E., Bregon, A., Aslund, J., Krysander, M., Pulido, B., Biswas, G.: Diagnosability analysis considering causal interpretations for differential constraints. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 42(5), 1216–1229 (2012)
Frisk, E., Krysander, M., Jung, D.: A toolbox for analysis and design of model based diagnosis systems for large scale models. In: IFAC World Congress (2017)
Gertler, J.: Fault detection and isolation using parity relations. Control. Eng. Pract. 5(5), 653–661 (1997)
Gertler, J.: Fault Detection and Diagnosis in Engineering Systems. CRC Press (1998)
Gertler, J.: All linear methods are equal and extendible to (some) nonlinearities. Int. J. Robust Nonlinear Control 12(8), 629–648 (2002)
Hansen, S., Blanke, M.: Diagnosis of airspeed measurement faults for unmanned aerial vehicles. IEEE Trans. Aerosp. Electron. Syst. 50(1), 224–239 (2014)
Hansen, S., Blanke, M., Adrian, J.: A framework for diagnosis of critical faults in unmanned aerial vehicles. IFAC Proc. Vol. 19(3), 10555–10561 (2014)
Hopcroft, J.E., Karp, R.M.: An nˆ{5/2} algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2(4), 225–231 (1973)
Izadi-Zamanabadi, R.: Structural analysis approach to fault diagnosis with application to fixed-wing aircraft motion. In: Proceedings of the 2002 American Control Conference, vol. 5, pp. 3949–3954. IEEE (2002)
Izadi-Zamanabadi, R., Staroswiecki, M.: A structural analysis method formulation for fault-tolerant control system design. In: Proceedings of the 39th IEEE Conference on Decision and Control, vol. 5, pp. 4901–4902. IEEE (2000)
Jung, D., Frisk, E: Residual selection for fault detection and isolation using convex optimization. Automatica 97, 143–149 (2018)
Jung, D., Sundstrom, C.: A combined data-driven and model-based residual selection algorithm for fault detection and isolation. IEEE Trans. Control Syst. Technol., 1–15 (2017)
Klein, V., Morelli, E.A.: Aircraft system identification: Theory and practice. AIAA (2006)
Krysander, M., Frisk, E.: Sensor placement for fault diagnosis. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 38(6), 1398–1410 (2008)
Krysander, M., Aslund, J.: An efficient algorithm for finding over-constrained sub-systems for construction of diagnostic tests. In: 16th International Workshop on Principles of Diagnosis (DX-05), vol. 3, pp. 1–17 (2005)
Krysander, M., Aslund, J., Frisk, E.: A structural algorithm for finding testable sub-models and multiple fault isolability analysis. In: 21st International Workshop on the Principles of Diagnosis (2010)
Kuhn, H.W.: The Hungarian method for the assignment problem. Naval Res. Logist. Q. 2(1-2), 83–97 (1955)
Marzat, J., Piet-Lahanier, H., Damongeot, F., Walter, E.: Model-based fault diagnosis for aerospace systems: a survey. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 226(10), 1329–1360 (2012)
Mulaire, W.M.M.: Department of Defense: World geodetic system 1984. Technical report, National Imagery and Mapping Agency (2000)
Munkres, J.: Algorithms for the assignment and transportation problems. J. Soc. Ind. Appl. Math. 5(1), 32–38 (1957)
Murty, K.G.: Letter to the editor - An algorithm for ranking all the assignments in order of increasing cost. Oper. Res. 16(3), 682–687 (1968)
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization - Algorithms and Complexity. Dover Publications (1998)
Patton, R.J., Chen, J.: Review of parity space approaches to fault diagnosis for aerospace systems. J. Guid. Control. Dyn. 17(2), 278–285 (1994)
Patton, R.J., Clark, R.N., Frank, P.M.: Issues of Fault Diagnosis for Dynamic Systems. Springer (2000)
Qi, X., Qi, J., Theilliol, D., Zhang, Y., Han, J., Song, D., Hua, C.: A review on fault diagnosis and fault tolerant control methods for single-rotor aerial vehicles. J. Intell. Robot. Syst.: Theory Appl. 73(1–4), 535–555 (2014)
Raghuraj, R., Bhushan, M., Rengaswamy, R.: Locating sensors in complex chemical plants based on fault diagnostic observability criteria. AIChE J 45(2), 310–322 (1999)
Rosich, A., Frisk, E., Aslund, J., Sarrate, R., Nejjari, F.: Fault diagnosis based on causal computations. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 42(2), 371–381 (2012)
Rotondo, D., Cristofaro, A., Johansen, T.A., Nejjari, F., Puig, V.: Diagnosis of icing and actuator faults in UAVs using LPV unknown input observers. J. Intell. Robot. Syst.: Theory Appl. 91(3–4), 651–665 (2018)
Staroswiecki, M., Comtet-Varga, G.: Analytical redundancy relations for fault detection and isolation in algebraic dynamic systems. Automatica 37(5), 687–699 (2001)
Stevens, B.L., Lewis, F.L., Johnson, E.N.: Aircraft Control and Simulation, 3 edn. Wiley (2016)
Svard, C., Nyberg, M., Frisk, E., Svärd, C, Nyberg, M., Frisk, E.: Realizability constrained selection of residual generators for fault diagnosis with an automotive engine application. IEEE Trans. Syst. Man Cybern. Syst. 43(6), 1354–1369 (2013)
Svärd, C., Nyberg, M., Svard, C., Nyberg, M., Svärd, C., Nyberg, M.: Residual generators for fault diagnosis using computation sequences with mixed causality applied to automotive systems. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 40(6), 1310–1328 (2010)
Unger, J., Kröner, A., Marquardt, W.: Structural analysis of differential-algebraic equation systems—theory and applications. Comput. Chem. Eng. 19(8), 867–882 (1995)
Vaiopoulos, P., Zogopoulos-Papaliakos, G., Kyriakopoulos, K.J.: On-line aerodynamic model identification on small fixed-wing UAVs with uncertain flight data. In: IEEE International Conference on Robotics and Automation, 2018. Proceedings. ICRA ’18 2018 (2018)
Venkatasubramanian, V., Rengaswamy, R., Kavuri, S.N.: A review of process fault detection and diagnosis. Comput. Chem. Eng. 27(3), 313–326 (2003)
Venkatasubramanian, V., Rengaswamy, R., Yin, K., Kavuri, S.N.: A review of process fault detection and diagnosis. Comput. Chem. Eng. 27(3), 293–311 (2003)
Yang, X., Warren, M., Arain, B., Upcroft, B., Gonzalez, F., Mejias, L.: A UKF-based estimation strategy for actuator fault detection of UASs. In: 2013 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 516–525. IEEE (2013)
Zhang, Y., Jiang, J.: Bibliographical review on reconfigurable fault-tolerant control systems. Annu. Rev. Control. 32(2), 229–252 (2008)
Zogopoulos-Papaliakos, G., Kyriakopoulos, K.J.: Generating semi-explicit DAEs with structural index 1 for fault diagnosis using structural analysis. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), pp. 5812–5817. IEEE (2017)
Zogopoulos-Papaliakos, G., Kyriakopoulos, K.J.: Parity-based diagnosis in UAVs detectability and robustness analyses. In: IEEE International Conference on Robotics and Automation, 2019. Proceedings. ICRA ’19 2019. Available at http://www.controlsystemslab.gr/index/publications/zogopoulos2019.pdf (2019)
Funding
This research work was partially funded by the ”Hellenic Civil Unmanned Arial Vehicle (HCUAV)” project, sponsored by the Greek Secretariat of Research and Technology.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zogopoulos-Papaliakos, G., Kyriakopoulos, K.J. An Efficient Approach for Graph-Based Fault Diagnosis in UAVs. J Intell Robot Syst 97, 553–576 (2020). https://doi.org/10.1007/s10846-019-01061-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10846-019-01061-7