In this paper we present a new method of confidence interval identification for Takagi–Sugeno fuzzy models in the case of the data with regionally changeable variance. The method combines a fuzzy identification methodology with some ideas from applied statistics. The idea is to find, on a finite set of measured data, the confidence interval defined by the lower and upper bounds. The confidence interval which defines the band that contains the measurement values with certain confidence. The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. In our example the proposed method is applied to model the pH-titration curve.
COBISS.SI-ID: 8208724
This paper deals with the problem of fuzzy nonlinear model identification in the framework of a local model network (LMN). A new iterative identification approach is proposed, where supervised and unsupervised learning are combined to optimize the structure of the LMN. For the purpose of fitting the cluster-centers to the process nonlinearity, the Gustafsson–Kessel (GK) fuzzy clustering, i.e., unsupervised learning, is applied. In combination with the LMN learning procedure, a new incremental method to define the number and the initial locations of the cluster centers for the GK clustering algorithm is proposed. Each data cluster corresponds to a local region of the process and is modeled with a local linear model. Since the validity functions are calculated from the fuzzy covariance matrices of the clusters, they are highly adaptable and thus the process can be described with a very sparse amount of local models, i.e., with a parsimonious LMN model. The proposed method for constructing the LMN is finally tested on a drug-absorption-spectra process and compared to two other methods, namely, Lolimot and Hilomot. The comparison between the experimental results when using each method shows the usefulness of the proposed identification algorithm.
COBISS.SI-ID: 8730708
This paper presents a new, supervised, hierarchical clustering algorithm (SUHICLUST) for fuzzy model identification. The presented algorithm solves the problem of global model accuracy, together with the interpretability of local models as valid linearizations of the modeled nonlinear system. The algorithm combines the advantages of supervised, hierarchical algorithms, which are based on heuristic tree-construction algorithms, together with the advantages of fuzzy product space clustering. The high flexibility of the validity functions that is obtained by fuzzy clustering combined with supervised learning results in an efficient partitioning algorithm, which is independent of initialization and results in a parsimonious fuzzy model. Furthermore, the usability of SUHICLUST is very undemanding, because it delivers, in contrast with many other methods, reproducible results. In order to get reasonable results, the user only has to set either a threshold for the maximum number of local models or a value for the maximum allowed global model error as a termination criterion. For fine-tuning, the interpolation smoothness controls the degree of regularization. The performance is illustrated on both analytical examples and benchmark problems from the literature.
COBISS.SI-ID: 8730964