Nonlinear dynamic systems identification and nonlinear dynamic behavior prediction are important tasks in several areas of industrial applications. Multiple works proposed multimodel-based approaches to model nonlinear systems. Multimodeling permits to blend different model types together to form hybrid models. It advocates the use of existing, well known model types within the same model structure. Recently, a multi modeling strategy based on belief functions theory was developed based on a fuzzy rule based system. We propose a different approach of this latter taking advantage of new efficient evidential clustering algorithms for the determination of the local models and the assessment of the global model. In particular, we propose an online procedure based on the Evidential Evolv- ing Gustafsson-Kessel (E2GK) algorithm that ensures an evolving partitioning of the data into clusters that correspond to operating regions of the global system. Thus the estimation of the local models is dynamically performed by upgrading and modifying their parameters while the data arrive. Each local model is weighted by a belief mass provided by E2GK, and the global model (multimodel) is a combination of all the local models.
How to Cite
Belief functions, Evolving systems, Multi-modelling
Angelov, P. P., & Filev, D. P. (2004). An approach to online identification of Takagi-Sugeno fuzzy models. IEEE Trans Syst Man Cybern B Cybern, 34, 484-98.
Cobb, B. R., & Shenoy, P. P. (2006). On the plausibility transformation method for translating belief function models to probability models. International Journal of Approximate Reasoning, 41, 314-330.
Denoeux, T. (2000). A Neural network classifier based on Dempster-Shafer theory. IEEE Trans. Syst., Man, Cybern, 30, 131-150.
El-Koujok, M., Gouriveau, R., & Zerhouni, N. (2011). Re- ducing arbitrary choices in model building for prog- nostics: An approach by applying parsimony princi- ple on an evolving neuro-fuzzy system. Microelec- tronics Reliability, 51, 310-330.
Georgieva, O., & Filev, D. (2009). Gustafson-Kessel Algorithm for Evolving Data Stream Clustering. In International Conference on Computer Systems and Technologies - CompSysTech 09.
Gustafson, E., & Kessel, W. (1978). Fuzzy clustering with a fuzzy covariance matrix. In IEEE Conference on Decision and Control.
Madani, K., Rybnik, M., & Chebira, A. (2003). Non Linear Process Identification Using a Neural Network Based Multiple Models Generator. LNCS series, 647-654.
Masson, M.-H., & Denoeux, T. (2008). ECM: An evidential version of the fuzzy c-means algorithm. Pattern Recognition, 41(4), 1384 - 1397.
Petit-Renaud, S., & Denoeux, T. (1999). Regression analysis using fuzzy evidence theory. Proceedings of FUZZ-IEEE, 3, 1229-1234.
Ramdani, M., Mourot, G., & Ragot, J. (2005). A Multi- Modeling Strategy based on Belief Function Theory. In CDC-ECC ’05.
Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage Propagation Modeling for Aircraft Engine Run-to-Failure Simulation. In IEEE Int. Conf. on Prognostics and Health Management.
Serir, L., Ramasso, E., & Zerhouni, N. (2011). E2GK: Evidential Evolving Gustafsson-Kessel Algorithm For Data Streams Partitioning Using Belief Functions. In 11th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty.
Smets, P., & Kennes, R. (1994). The Transferable Belief Model. Artificial Intelligence, 66, 191-234.
Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control. IEEE Trans. On Systems Man and Cyberneticc, 15, 116-132.
Yager, R. R., & Filev, D. P. . (1995). Including probabilistic uncertainty in fuzzy logic controller modeling us-
ing Dempster-Shafer theory. IEEE Trans. Syst., Man, Cybern., 25, 1221-1230.
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