The applications of fuzzy systems in solar applications are much fewer. They concern the design of a fuzzy single-axis tracking mechanism controller (Kalogirou, 2002) and a neuro-fuzzy based model for photovoltaic power supply system (Mellit and Kalogirou, 2006b). In fact, the membership functions shown in Figures 11.24 and 11.25 and the rule basis, given previously, are from the first application, whereas the latter is a hybrid system described in the next section.
Hybrid systems are systems that combine two or more artificial intelligence techniques to perform a task. The classical hybrid system is the neuro-fuzzy control, whereas other types combine genetic algorithms and fuzzy control or artificial neural networks and genetic algorithms as part of an integrated problem solution or to perform specific, separate tasks of the same problem. Since most of these techniques are problem specific, more details are given here for the first category.
A fuzzy system possesses great power in representing linguistic and structured knowledge using fuzzy sets and performing fuzzy reasoning and fuzzy logic in a qualitative manner. Also, it usually relies on domain experts to provide the necessary knowledge for a specific problem. Neural networks, on the other hand, are particularly effective at representing nonlinear mappings in computational fashion. They are "constructed" through training procedures presented to them as samples. Additionally, although the behavior of fuzzy systems can be understood easily due to their logical structure and step by step inference procedures, a neural network generally acts as a "black-box," without providing explicit explanation facilities. The possibility of integrating the two technologies was considered quite recently into a new kind of system, called neuro-fuzzy control, where several strengths of both systems are utilized and combined appropriately.
More specifically, neuro-fuzzy control means (Nie and Linkens, 1995)
1. The controller has a structure resulting from a combination of fuzzy systems and artificial neural networks.
2. The resulting control system consists of fuzzy systems and neural networks as independent components performing different tasks.
3. The design methodologies for constructing respective controllers are hybrid ones coming from ideas in fuzzy and neural control.
In this case, a trained neural network can be viewed as a means of knowledge representation. Instead of representing knowledge using if-then localized associations as in fuzzy systems, a neural network stores knowledge through its structure and, more specifically, its connection weights and local processing units, in a distributed or localized manner. Many commercial software (such as Matlab) include routines for neuro-fuzzy modeling.
The basic structure of a fuzzy inference system is described in Section 11.6.3. This is a model that maps the input membership functions, input membership function to rules, rules to a set of output characteristics, output characteristics to output membership functions, and the output membership function to a single-valued output or decision associated with the output. Thus, the membership functions are fixed. In this way, fuzzy inference can be applied to modeling systems whose rule structure is essentially predetermined by the user's interpretation of the characteristics of the variables in the model.
In some modeling situations, the shape of the membership functions cannot be determined by just looking at the data. Instead of arbitrarily choosing the parameters associated with a given membership function, these parameters could be chosen to tailor the membership functions to the input-output data in order to account for these types of variations in the data values. If fuzzy inference is applied to a system for which a past history of input-output data is available, these can be used to determine the membership functions. Using a given input-output data set, a fuzzy inference system can be constructed, whose membership function parameters are tuned or adjusted using a neural network. This is called a neuro-fuzzy system.
The basic idea behind a neuro-fuzzy technique is to provide a method for the fuzzy modeling procedure to learn information about a data set, in order to compute the membership function parameters that best allow the associated fuzzy inference system to track the given input-output data. A neural network, which maps inputs through input membership functions and associated parameters, then through output membership functions and associated parameters to outputs, can be used to interpret the input-output map. The parameters associated with the membership functions will change through a learning process. Generally, the procedure followed is similar to any neural network technique described in Section 11.6.1.
It should be noted that this type of modeling works well if the data presented to a neuro-fuzzy system for training and estimating the membership function parameters is representative of the features of the data that the trained fuzzy inference system is intended to model. However, this is not always the case, and data are collected using noisy measurements or training data cannot be representative of all features of the data that will be presented to the model. For this purpose, model validation can be used, as in any neural network system. Model validation is the process by which the input vectors from input-output data sets that the neuro-fuzzy system has not seen before are presented to the trained system to check how well the model predicts the corresponding data set output values.
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