Neural - fuzzy approach for system identification

Most real-world processes have nonlinear and complex dynamics. Conventional methods of constructing nonlinear models from first principles are time consuming and require a level of knowledge about the internal functioning of the system that is often not available. Consequently, in such cases a nonlinear system identification procedure from observational data is a more attractive alternative. If the model structures to be investigated are purely chosen from a set of mathematically convenient structures, without incorporation of knowledge about the internal functioning, this is called black-box modeling. In case that some qualitative a priori information can be used in the above modeling procedure, it is sometimes referred to as gray-box modeling. Artificial neural network models and fuzzy models are typical examples of black-box and gray-box modeling, respectively. They have the same property of parallel processing and both serve as universal function approximators to perform nonlinear mapping. Each of them has its own weak and strong points. The fuzzy model has a transparent knowledge representation but has restricted learning ability. A neural network model can easily learn from new data, but it is difficult to interpret the information contained in its internal configuration. This thesis investigates how to construct an integrated neural-fuzzy model that can perform approximation of an unknown system via a set of given input-output observations. The result is the integrated neural-fuzzy model NUFZY, which combines the advantages of the above two paradigms, and concurrently compensates for their weaknesses. Thus, it has a transparent network structure and a self-explanatory representation of fuzzy rules. The NUFZY system is a special type of neural network, which is characterized by partial connections in its first and second layers. Through its network connections the NUFZY system carries out a particular type of fuzzy reasoning. Also, the NUFZY system is functionally equivalent to a zero th -order Takagi-Sugeno fuzzy model, so that it is an universal function approximator as well. Two existing learning methods, i.e., the orthogonal least squares and the prediction error algorithms, can be applied directly to the developed NUFZY model. The former method, referred to as batch learning, can be used to detect redundant fuzzy rules from the prototype rule base and to find the weight parameters of the NUFZY model by one-pass estimation. The latter, referred to as recursive learning, allows a fast adaptation of parameters of the NUFZY model. Several practical examples with real data of agricultural problems, which address the tomatoes growth and the greenhouse temperature, have been presented in this thesis, showing the capability of the NUFZY system for modeling nonlinear dynamic systems. Two questions concerning the integrated neural-fuzzy model are addressed by studying the equivalent T-S fuzzy model: how to obtain a linguistic interpretation of fuzzy rules deduced by learning from training examples, and how to incorporate a priori knowledge into the T-S fuzzy model. It is found out that it is possible to have linguistic interpretations of the crisp consequent of the T-S fuzzy rules by transforming them into Mamdani - like fuzzy rules. A new parameter set, the consequent significance level, is associated to the consequent of each Mamdani fuzzy rule to form an extended Mamdani fuzzy model. This model has a more flexible modeling ability than the ordinary Mamdani fuzzy model and has a comparable model accuracy as that of the T-S fuzzy model. Regarding the second question, an optimization approach is employed to systematically incorporate the a priori knowledge into the T-S fuzzy model. If the knowledge about the system behavior outside the identification data range is expressed in the form of a qualitative Mamdani fuzzy model, then this model can be incorporated in the objective function of the parameter estimation problem as an additional penalty term. Thus, the estimation of the parameters of the T-S fuzzy model from the identification data is constrained by the involvement of a priori knowledge. As a consequence, the resultant fuzzy model becomes more robust in the extrapolation domain. This approach can be extended to neural -fuzzy modeling without difficulty. To conclude, the beauty of the integrated neural-fuzzy model, NUFZY, developed in this thesis is that it is a neural network, enabling the implementation of efficient learning algorithms in an easy way, and that it is a fuzzy model at the same time, allowing incorporation of priori knowledge and transparent interpretation of its internal network structure. So, among the various methods of nonlinear system identification, the NUFZY model can serve as an attractive alternative. See also http://www.math.utwente.nl/disc/dissertations/tien.html