Abstract
The paper compares two approaches to measurement fault estimation for linear discrete-time stochastic systems. The first fault estimator utilizes the parity-space approach. It assumes that at most a limited number of components of the measurement fault can be non-zero. A fault is detected using the \(\chi ^2\) test applied to the parity-space based residuals and then the indices of non-zero components and fault itself are estimated. The second fault estimator is based on the multiple-model approach. The space of measurement faults is quantized to construct a set of models and a variable structure interacting multiple-model estimator is employed to estimate the state and the measurement fault. Both approaches are compared in a numerical example.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Note that a time-varying model and a known input to the monitored system can also be considered at the expense of more complicated notation.
- 2.
Note that a particular fault estimator might not necessarily use the whole sequence of past measurements to generate the fault estimate.
- 3.
Although the condition (6) can be omitted, a more computationally demanding expression for the statistic \(S_{k}=\textbf{r}_{k}^{\text {T}}(\textbf{W}\textbf{H}\textbf{H}^{\text {T}}\textbf{W}^{\text {T}})^{-1}\textbf{r}_{k}\) must be evaluated on-line.
- 4.
Note that there are no undetectable faults if \(\textbf{M}\) has the full column rank, i.e., \(m=n_f\).
- 5.
Notation \([\textbf{M}]_{:,i}\) denotes the i-th column of the matrix \(\textbf{M}\).
References
Bar-Shalom, Y., Li, X.R., Kirubarajan, T.: Estimation with Applications to Tracking and Navigation. Wiley, New York, NY, USA (2001)
Blom, H.A.P., Bar-Shalom, Y.: The interacting multiple model algorithm for systems with Markovian switching coefficients. IEEE Trans. Autom. Control 33(8), 780–783 (1988)
Chiang, L.H., Russell, E.L., Braatz, R.D.: Fault Detection and Diagnosis in Industrial Systems, 1st edn. Springer, London, UK (2001)
Gao, Z., Ding, S.X., Ma, Y.: Robust fault estimation approach and its application in vehicle lateral dynamic systems. Optim. Control Appl. Methods 28(3), 143–456 (2007)
Isermann, R.: Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance. Springer, Berlin, Germany (2006)
Isermann, R.: Fault-Diagnosis Applications. Springer, Heidelberg, Germany (2011)
Li, X.R.: Multitarget/Multisensor Tracking: Applications and Advances, chap. Engineer’s Guide to Variable-Structure Multiple-Model Estimation for Tracking, Artech House (2000)
Patton, R.J., Frank, P.M., Clark, R.N.: Issues of Fault Diagnosis for Dynamic Systems, 1st edn. Springer, London, UK (2000)
Punčochář, I., Straka, O., Šimandl, M.: Confidence regions for multi-sensor state estimation under faulty measurements. In: Proceedings of 2013 Conference on Control and Fault-Tolerant Systems, pp. 202–207. Nice, France (2013)
Sun, X., Patton, R.J.: Robust actuator multiplicative fault estimation with unknown input decoupling for a wind turbine system. In: 2013 Conference on Control and Fault-Tolerant Systems (2013)
Wang, Z., Rodrigues, M., Theilliol, D., Shen, Y.: Sensor fault estimation filter design for discrete-time linear time-varying systems. Acta Automatica Sinica 40(10), 2364–2369 (2014)
Zhong, M., Ding, S.X., Han, Q.L., Ding, Q.: Parity space-based fault estimation for linear discrete time-varying systems. IEEE Trans. Autom. Control 55(7), 1726–1731 (2010)
Acknowledgements
The work was supported by the Czech Science Foundation under grant 22-11101S.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Punčochář, I., Straka, O. (2023). Parity-Space and Multiple-Model Based Approaches to Measurement Fault Estimation. In: Theilliol, D., Korbicz, J., Kacprzyk, J. (eds) Recent Developments in Model-Based and Data-Driven Methods for Advanced Control and Diagnosis. ACD 2022. Studies in Systems, Decision and Control, vol 467. Springer, Cham. https://doi.org/10.1007/978-3-031-27540-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-031-27540-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-27539-5
Online ISBN: 978-3-031-27540-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)