Fuzzy System Identification And Its Application To Locomotive Adhesion

Fuzzy systems have demonstrated their ability for modeling or control in a huge number of applications. The keys for their success and interest are the ability to incorporate human knowledge, so the information mostly provided for many real-world systems could be discovered or described by fuzzy statements. In this way, the existing information in objective world could be comprehended as linguistic rules. To develop and establish fuzzy systems is fuzzy system identification, which considers model structures in the form of fuzzy rule-based systems and constructs them by means of different parametric system identification techniques.This paper mainly focuses on data-driven approaches to fuzzy system identification. The aim is to utilize existing or modified data analysis techniques and try to establish an interpretable fuzzy model which usually has a transparency rule base; simultaneously the model possesses excellent approximation and generalization performance. In general, the data measured is usually endowed with various types of uncertainties, such as randomness, non-specificity and fuzziness. Hence, it is vital for selecting the form of fuzzy model in order to deal with different circumstances in real world. Here, two kinds of fuzzy models are under consideration: type-1 fuzzy model and type-2 fuzzy model. With regard to them, some important issues have been discussed in this paper as follows.In the framework of traditional fuzzy clustering, in order to reconstruct fuzzy relation in fuzzy partition matrix using unimodal and convex fuzzy set, a modified fuzzy learning vector quantization (M-FLVQ) algorithm is proposed. It abandons the descending mechanism, and employs the cooling schedule. In the iteration process, the weighting exponent is automatically adjusted so that the resulting memberships are more interpretable than those derived by traditional fuzzy clustering. At the same time, this algorithm is also used as a tool to identify the type-1 fuzzy basis function model.When one uses support vector learning mechanism to type-1 fuzzy modeling, too many support vectors will lead to a complicated fuzzy model. Therefore, a reduced-set vector-based Takagi-Sugeno fuzzy model (RV-TSFM) which alternatively extracts reduced-set vectors for generating fuzzy rules is presented. The product type multidimensional fuzzy membership functions in antecedents of rules can be directly created by Mercer kernels, and the nonlinear functions represent the consequents. The model structure and parameters can be effectively identified by utilizing bottom-up simplification algorithm combinedε-insensitive learning or experience-oriented hybrid learning.Utilizing type-2 fuzzy theory, this paper also presents alternating iteration architecture for clustering called robust interval type-2 possibilistic c-means (IT2PCM) clustering algorithm. It is actually alternating cluster estimation, but membership functions are selected directly with interval type-2 fuzzy sets by the users. In proposed algorithm, the cluster prototype update equation is calculated by type reduction combined with defuzzification, and it is robust to uncertain inliers and outliers on the basis of itsφfunction analysis in the framework of robust statistics.Consequently, with robust IT2PCM clustering algorithm as main tool, a rapid-prototyping approach to interval type-2 fuzzy modeling is proposed. Firstly, the IT2PCM clustering is carried out in input and output space, and then cluster prototypes are extracted to generate interval type-2 fuzzy rules that can be used to obtain a first approximation to the interval type-2 fuzzy logic system (IT2FLS). This first approximation model is an initial fuzzy model, so it can be introduced as a good initial structure of IT2FLS for further tuning in a subsequent process.Finally, the dynamics of locomotive traction are analyzed, and a disturbance observer is used to estimate adhesion coefficient. According to the simulation data of slip velocity and adhesion coefficient, a fuzzy model, RV-TS model, is built to describe the adhesion characteristic curve.