Abstract
Belief rule-based (BRB) systems are an extension of traditional IF-THEN rule based systems and capable of capturing complicated nonlinear causal relationships between antecedent attributes and consequents. In a BRB system, various types of information and knowledge with uncertainties can be represented using belief structures, and a belief rule is designed with belief degrees embedded in its possible consequents. In this paper, we first review the scheme of belief rules for representing and inferring uncertain knowledge. Then we present two BRB system identification methods in which different training objectives are used. Finally, numerical studies are conducted to demonstrate the capability of BRB systems on uncertain nonlinear system modeling and identification.
This work was partially supported by the UK Engineering and Physical Science Research Council under Grant No.: EP/F024606/1 and the EC REFERENCE project.
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
Preview
Unable to display preview. Download preview PDF.
References
Ackermann, J.: Robust Control: Systems with Uncertain Physical Parameters. Springer, Heidelberg (1993)
Nelles, O.: Nonlinear System Identification. From Classical Approaches to Neural networks and Fuzzy Models. Springer, Heidelberg (2001)
Reinelt, W., Ljung, L.: Robust control of identified models with mixed parametric and non-parametric uncertainties. European Journal of Control 9(4), 373–380 (2003)
Isermann, R., Münchhof, M.: Identification of Dynamical Systems: An Introduction with Applications. Springer, Heidelberg (2011)
Sjöberg, J., Zhang, Q., Ljung, L., Berveniste, A., Delyon, B., Glorennec, P., Hjalmarsson, H., Juditsky, A.: Nonlinear black-box modeling in system identification: a unified overview. Automatica 31, 1691–1724 (1995)
González-Olvera, M.A., Tang, Y.: Black-Box Identification of a Class of Nonlinear Systems by a Recurrent Neurofuzzy Network. IEEE Transactions on Neural Networks 21(4), 672–679 (2010)
Škrjanc, I., Blažič, S., Agamennoni, O.: Interval Fuzzy Model Identification Usingl ∞ -Norm. IEEE Transactions on Fuzzy Systems 13(5), 561–567 (2005)
Senthilkumar, D., Mahanta, C.: Identification of uncertain nonlinear systems for robust fuzzy control. ISA Transactions 49, 27–38 (2010)
Yang, J.B.: Rule and utility based evidential reasoning approach for multiple attribute decision analysis under uncertainty. European Journal of Operational Research 131(1), 31–61 (2001)
Yang, J.B., Liu, J., Wang, J., Sii, H.S., Wang, H.W.: A belief rule-base inference methodology using the evidential reasoning approach – RIMER. IEEE Transactions on Systems, Man, and Cybernetics – Part A 36(2), 266–285 (2006)
Yang, J.B., Liu, J., Xu, D.L., Wang, J., Wang, H.W.: Optimization models for training belief rule based systems. IEEE Transactions on Systems, Man, and Cybernetics – Part A 37(4), 569–585 (2007)
Wang, Y.M., Yang, J.B., Xu, D.L.: Environmental Impact Assessment Using the Evidential Reasoning Approach. European Journal of Operational Research 174(3), 1885–1913 (2006)
Cheney, E.W.: Introduction to Approximation Theory. AMS Chelsea Publishing (1998)
Zhou, Z.J., Hu, C.H., Xu, D.L., Yang, J.B., Zhou, D.H.: New model for system behaviour prediction based on belief-rule-based systems. Information Sciences 180, 4834–4864 (2010)
Chen, Y.W., Yang, J.B., Xu, D.L., Zhou, Z.J., Tang, D.W.: Inference analysis and adaptive training for belief rule based systems. Expert Systems with Applications 36(10), 12845–12860 (2011)
Chen, Y.W., Yang, J.B., Xu, D.L., Yang, S.L.: On the inference and approximation properties of belief rule based systems. Information Sciences 234, 121–135 (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, YW., Yang, JB., Xu, DL. (2013). Uncertain Nonlinear System Modeling and Identification Using Belief Rule-Based Systems. In: Qin, Z., Huynh, VN. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2013. Lecture Notes in Computer Science(), vol 8032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39515-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-39515-4_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39514-7
Online ISBN: 978-3-642-39515-4
eBook Packages: Computer ScienceComputer Science (R0)