Estimation of the parameters of a railway vehicle suspension using model-based filters with uncertainties

Abstract

This paper presents two types of extended Kalman filter (EKF) and two types of unscented Kalman filter (UKF) based on vertical railway vehicle models for parameters estimation of secondary suspensions. Due to track irregularities, the random vertical velocity of the track can be approximated as a zero-mean Gaussian white noise and it is used to excite the dynamic model of the railway vehicle. Under this approximation, the variance of the vertical velocity of the track, which is affected by the track roughness level and vehicle velocity, can introduce uncertainty into the system. Based on the random track irregularity, two cases are proposed to determine how the track irregularities enter the system. One case uses the vertical velocity and displacement of the track as inputs of the system and assumes that the state variables are corrupted by the Gaussian noises. The other case assumes that the vertical velocity of the track is the process noise of the system. Based on these two cases, two types of EKF and UKF are developed to estimate the parameters of the secondary suspensions. In order to study the performances of the proposed EKFs and UKFs, several simulation experiments using linear and nonlinear model are carried out that consider the uncertainties of the random track.

Keywords

Railway vehicle suspension parameter estimation extended Kalman filter unscented Kalman flter uncertainty

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References

Mei

Ding

. Condition monitoring of rail vehicle suspensions based on changes in system dynamic interactions. Veh Syst Dyn 2009; 47: 1167–1181.

Sakellariou J, Petsounis K and Fassois S. On board fault detection and identification in railway vehicle suspensions via a functional model based method. In: EP Sas and B VanHal (eds) The international conference on noise and vibration engineering, Leuven, Belgium, 16--18 September 2002, pp.1323--1332. Leuven, Belgium: Katholieke University Leuven.

Ward

Goodall

Dixon

Charles

. Adhesion estimation at the wheel–rail interface using advanced model-based filtering. Veh Syst Dyn 2012; 50: 1797–1816.

Ward C, Goodall R and Dixon R. Contact force estimation in the railway vehicle wheel-rail interface. In: S Bittanti, A Cenedese and S Zampieri (eds) The 18th World congress of the international federation of automatic control, Milan, Italy, 28 August--2 September 2011, pp.4398--4403. New York: International Federation of Automatic Control.

Hussain

Mei

Ritchings

. Estimation of wheel–rail contact conditions and adhesion using the multiple model approach. Veh Syst Dyn 2012; 51: 32–53.

Charles

Goodall

Dixon

. Model-based condition monitoring at the wheel–rail interface. Veh Syst Dyn 2008; 46: 415–430.

Li P, Goodall R and Kadirkamanathan V. Parameter estimation of railway vehicle dynamic model using Rao–Blackwellised particle filter. In: The European control conference, Cambridge, UK, 1--4 September 2003, pp.1--6. UK: European Union Control Association.

Goodall

Kadirkamanathan

. Estimation of parameters in a linear state space model using a Rao–Blackwellised particle filter. IEE Proc – Control Theory Appl 2004; 151: 727–738.

Goodall

Weston

. Estimation of railway vehicle suspension parameters for condition monitoring. Control Engng Pract 2007; 15: 43–55.

10.

Zheng X. Active vibration control of flexible bodied railway vehicles via smart structures. PhD Thesis, Loughborough University, UK, 2011.

11.

Iwnicki

. Handbook of railway vehicle dynamics, New York: CRC, 2006.

12.

Suarez

Mera

Martinez

Chover

. Assessment of the influence of the elastic properties of rail vehicle suspensions on safety, ride quality and track fatigue. Veh Syst Dyn 2012; 51: 280–300.

13.

Bruni

Goodall

Mei

Tsunashima

. Control and monitoring for railway vehicle dynamics. Veh Syst Dyn 2007; 45: 743–779.

14.

Schmidt SF. Computational techniques in Kalman filtering. Technique report, 1970. London: NATO Advisory Group for Aerospace Research and Development.

15.

Julier

Uhlmann

. Unscented filtering and nonlinear estimation. Proc IEEE 2004; 92: 401–422.

16.

Julier

Uhlmann

Durrant-Whyte

. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Autom Control 2000; 45: 477–482.

17.

Wan EA and Van Der Merwe R. The unscented Kalman filter for nonlinear estimation. In: The IEEE adaptive systems for signal processing, communications, and control symposium, Alberta, Canada, 1--4 October 2000, pp.153–158. Piscataway, NJ: IEEE Press.

18.

Julier SJ and Uhlmann JK. Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations. In: The American control conference, Anchorage, Alaska, USA, 8--10 May 2002, pp.887–892. New York, USA: American Automatic Control Council.

19.

Julier SJ and Uhlmann JK. A general method for approximating nonlinear transformations of probability distributions. Technique report, 1996. Oxford, UK: Robotics Research Group, Department of Engineering Science, University of Oxford.

20.

Van Der Merwe R. Sigma-point Kalman filters for probabilistic inference in dynamic state-space models. PhD Thesis, University of Stellenbosch, South Africa, 2004.

21.

Julier SJ. The scaled unscented transformation. In: The American control conference, Anchorage, Alaska, USA, 8--10 May 2002, pp.4555–4559. New York, USA: American Automatic Control Council.

22.

Julier SJ, Uhlmann JK and Durrant-Whyte HF. A new approach for filtering nonlinear systems. In: The American control conference, Seattle, Washington USA, 21--23 June 1995, pp.1628–1632. New York, USA: American Automatic Control Council.