Summary |
Building appriopriate system models is an important aspect in the analysis and design of complex systems. Existing system models such as neural networks, polynomials, and fuzzy systems have been widely used to model system mechanisms. Compared with other schemes, fuzzy systems have the advantages of incorporating human knowledge, being able to be explained in natural language and easy-to-understand. They have been successfully used in control, communications, data processing and time series prediction. A serious problem of the current methods to build fuzzy systems is 'the curse of dimensionality', which says that the complexity of a system increases exponentially with the number of input variables involved. To solve this problem, we propose a new scheme 'Principal Component Fuzzy Systems' to build fuzzy models. With this scheme, two kinds of algorithms are proposed in this thesis: the off-line algorithm and the on-line algorithm, stated as follows: (a) Off-line algorithm: Given a batch of input-output pairs with the number of input variables being too large, we first convert these inputs into a reduced number of inputs, and then apply this new inputs to build a fuzzy system model. (b) Online algorithm: When new input-output pairs are presented, the parameters of the fuzzy system need to be updated to follow the changes of the environment. Instead of rerun the off-line algorithm each time a new set of input-output pair is presented, a totally new online algorithm is proposed. In this research, we present the details of the algorithms and apply each algorithm to build fuzzy models for several systems. The training errors and the testing errors are calculated and compared with those obtained from traditional fuzzy models, and the results show that our proposed modeling methods perform satisfactorily in terms of these modeling errors. |