Abstract
Intensive research in the field of mathematical modeling of hydraulic servo systems has shown that their mathematical models have many important details which cannot be included in the model. Due to impossibility of direct measurement or calculation of dimensions of certain components, leakage coefficients or friction coefficients, it was supposed that parameters of the hydraulic servo system are random. On the other side, it has been well known that the hydraulic servo system can be approximated by a linear model with time-varying parameters. An estimation of states and time-varying parameters of linear state-space models is of practical importance for fault diagnosis and fault-tolerant control. Previous works on this topic consider estimation in Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of parameter–state robust estimation of linear state-space models in the presence of all possible faults and non-Gaussian noises. Because of its good features in robust filtering, Masreliez–Martin filter represents a cornerstone for realization of the robust algorithm. The good features of the proposed robust algorithm to identification of the hydraulic servo system are illustrated by intensive simulations.
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References
Filipovic, V., Nedic, N., Stojanovic, V.: Robust identification of pneumatic servo actuators in the real situations. Forschung im Ingenieurwesen—Eng. Res. 75(4), 183–196 (2011)
Stojanovic, V., Nedic, N.: Identification of time-varying OE models in presence of non-Gaussian noise: application to pneumatic servo drives. Int. J. Robust Nonlinear Control 26(18), 3974–3995 (2016)
Kalman, R.E.: New approach to linear filtering and prediction problems. Trans. ASME – J. Basic Eng. 82(1), 35–45 (1960)
Ding, B., Fang, H.: Fault estimation and prediction for nonlinear stochastic system with intermittent observations. Int. J. Robust Nonlinear Control (2017). https://doi.org/10.1002/rnc.3925
Chang, Y.H., Hu, Q., Tomlin, C.J.: Secure estimation based Kalman filter for cyber–physical systems against sensor attacks. Automatica 95, 399–412 (2018)
Chang, L., Zha, F., Qin, F.: Indirect Kalman filtering based attitude estimation for low-cost attitude and heading reference systems. IEEE/ASME Trans. Mechatron. 22(4), 1850–1858 (2017)
Liu, W.-Q., Wang, X.-M., Deng, Z.L.: Robust fusion time-varying Kalman estimators for multisensor networked systems with mixed uncertainties. Int. J. Robust Nonlinear Control (2018). https://doi.org/10.1002/rnc.4226
Nosrati, K., Shafiee, M.: Kalman filtering for discrete-time linear fractional-order singular systems. IET Control Theory Appl. 12(9), 1254–1266 (2018)
Khan, R., Williams, P., Riseborough, P., Rao, A., Hill, R.: Fault detection and identification—a filter investigation. Int. J. Robust Nonlinear Control (2017). https://doi.org/10.1002/rnc.3989
Viegas, D., Batista, P., Oliveira, P., Silvestre, C.: Discrete-time distributed Kalman filter design for formations of autonomous vehicles. Control Eng. Pract. 75, 55–68 (2018)
Walle, A., Naets, F., Desmet, W.: Virtual microphone sensing through vibro-acoustic modelling and Kalman filtering. Mech. Syst. Signal Process. 104, 120–133 (2018)
Maes, K., Iliopoulos, A., Weijtjens, W., Devriendt, C., Lombaert, G.: Dynamic strain estimation for fatigue assessment of an offshore monopile wind turbine using filtering and modal expansion algorithms. Mech. Syst. Signal Process. 76–77, 592–611 (2016)
Cavallo, A., De Maria, G., Natale, C., Pirozzi, S.: Slipping detection and avoidance based on Kalman filter. Mechatronics 24(5), 489–499 (2014)
Rodriguez, M.T., Banks, S.P.: Linear, Time-Varying Approximations to Nonlinear Dynamical Systems. Springer, Berlin (2010)
Cox, H.: On the estimation of state variables and parameters for noisy dynamic systems. IEEE Trans. Autom. Control 9(1), 5–12 (1964)
Ljung, L.: Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems. IEEE Trans. Autom. Control 24(1), 36–50 (1979)
Aksoy, S., Muhurcu, A., Kizmaz, H.: State and parameter estimation in induction motor using the extended Kalman filtering algorithm. In: Proceedings of the International Symposium Modern Electric Power Systems, 1–5, Wroclaw, Poland, September (2010)
Plett, G.L.: Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: part 3. State and parameter estimation. J. Power Sources 134(2), 277–292 (2004)
Carrassi, A., Vannitsem, S.: State and parameter estimation with the extended Kalman filter: an alternative formulation of the model error dynamics. Q. J. R. Meteorol. Soc. 137(655), 435–451 (2011)
Isermann, R.: Fault-Diagnosis Applications: Model-Based Condition Monitoring: Actuators, Drives, Machinery, Plants, Sensors, and Fault-Tolerant Systems. Springer, Berlin (2011)
Arulampalam, M.S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 50(2), 174–188 (2002). https://doi.org/10.1109/78.978374
Chatzi, E.N., Smyth, A.W.: Nonlinear system identification: particle-based methods. In: Beer, M., Kougioumtzoglou, I., Patelli, E., Au, I.K. (eds.) Encyclopedia of Earthquake Engineering. Springer, Berlin, Heidelberg (2014)
Nemeth, C., Fearnhead, P., Mihaylova, L.: Sequential Monte Carlo methods for state and parameter estimation in abruptly changing environments. IEEE Trans. Signal Process. 62(5), 1245–1255 (2014). https://doi.org/10.1109/tsp.2013.2296278
Olivier, A., Smyth, A.W.: Particle filtering and marginalization for parameter identification in structural systems. Struct. Control Health Monit (2017). https://doi.org/10.1002/stc.1874
Stojanovic, V., Nedic, N.: Joint state and parameter robust estimation of stochastic nonlinear systems. Int. J. Robust Nonlinear Control 26, 3058–3074 (2016). https://doi.org/10.1002/rnc.3490
Aggarwal, C.: Outlier Analysis, 2nd edn. Springer, New York (2017)
Huber, P.J., Ronchetti, E.M.: Robust Statistics, 2nd edn. Wiley, New York (2009)
Maronna, R.A., Martin, R.D., Yohai, V.J., Barrera, M.S.: Robust Statistics: Theory and Methods, 2nd edn. Wiley, New York (2019)
Chen, J., Patton, R.J.: Robust Model-Based Fault Diagnosis for Dynamic Systems. Springer, Berlin (1999)
Stojanovic, V., Nedic, N.: Robust identification of OE model with constrained output using optimal input design. J. Frankl. Inst. 353(2), 576–593 (2016)
Masreliez, C.J., Martin, R.D.: Robust Bayesian estimation for the linear model and robustifying the Kalman filter. IEEE Trans. Autom. Control 22(3), 361–371 (1977)
Blackburn, J.F., Reethof, G., Shearer, J.L.: Fluid Power Control. The MIT Press, Cambridge (1960)
M. Jelali, A. Kroll, “Hydraulic Servo-systems: Modelling, Identification and Control”, Springer, 2003
Barnet, V., Lewis, T.: Outliers in Statistical Data, 3rd edn. Wiley, Blackwell, New York (1994)
Acknowledgements
The authors would like to express their gratitude to reviewers for their valuable and constructive comments to improve this paper. This research has been supported by the Serbian Ministry of Education, Science and Technological Development under Grant 451-03-68/2020-14/200108.
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Stojanovic, V., Prsic, D. Robust identification for fault detection in the presence of non-Gaussian noises: application to hydraulic servo drives. Nonlinear Dyn 100, 2299–2313 (2020). https://doi.org/10.1007/s11071-020-05616-4
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DOI: https://doi.org/10.1007/s11071-020-05616-4