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Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications
by Lakhmi C. Jain; N.M. Martin CRC Press, CRC Press LLC ISBN: 0849398045 Pub Date: 11/01/98 |
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The analytical approach to fault diagnosis suffers from the fact that under real conditions no accurate mathematical models of the system of interest can be obtained. The robust analytical design techniques described, e.g., in [34] can overcome this deficiency only to a certain degree and only with great effort. This consideration and the evolution of fuzzy and neural techniques led to the development of knowledge- and data-based models. In both approaches fuzzy logic can be integrated as seen in Figure 2. While in the qualitative approach a rule-based model is set up, the data-based fuzzy model consists of a fuzzy relational module whose parameters are trained by input-output data following a given performance criterion.
Fuzzy logic tools can also be applied for residual evaluation in the form of a classifier as shown in Figure 3. One possibility is the combination of this qualitative approach with a quantitative residual generating algorithm. This idea is motivated and developed in the following section.
In practice, analytical models often exist of only parts of the plant and the connections between the models are not given analytically so that the analytical model-based-methods fail to serve as useful fault diagnosis concepts for the whole plant. However, there always exists some qualitative or heuristic knowledge of the plant which may not be very detailed but is suitable to characterize in linguistic terms the connections between the existing analytical submodels. This knowledge can be expressed by fuzzy rules in order to describe the normal and faulty behavior of the system in a fuzzy manner [18].
This means that, for the submodels, quantitative model-based techniques can be used. The qualitative and heuristic knowledge of the connections can be used for the fault symptom generation of the complete system. The advantages of using such a combined quantitative/knowledge-based approach can be summarized as follows:
The fuzzy residual evaluation is a process that transforms quantitative knowledge (residuals) into qualitative knowledge (fault indications). Residuals generated by analytical submodels, as described above and depicted in Figure 4 [17], represent the inputs of the Fuzzy Filter which consists of the three basic components:
Figure 4 General structure of the Fuzzy-Filter-based diagnostic concept.
As a first step, a knowledge base has to be built which includes the definition of the faults of interest, the measurable residuals (symptoms), the relations between the residuals and the faults in terms of IF/THEN rules, and the representation of the residuals in terms of fuzzy sets, for example, normal and not normal.
The process of fuzzification includes the proper choice of the membership functions for the fuzzy sets and is defined as the assignment of a suitable number of fuzzy sets to each residual component ri with [14].
but not for the fault symptoms fi. This procedure can mathematically be described for the residuals as.
where rij describes the jth fuzzy set of the ith residual and describes the fuzzy composition operator.
This part is very important because the coupling or decoupling of the faults, respectively, will be significantly influenced by this procedure.
The task of the FDI system is now to determine, from the given rule base, indication signals for the faults with the aid of an inference mechanism [18]. The inference can be appropriately carried out by using so called Fuzzy Conditional Statements,
where fm denotes the mth fault of the system. The result of this fuzzy inference is a fault indication signal found from a corresponding combination of residuals as characterized by the rules. Note that this fault indication signal is still in a fuzzyfied format. Therefore, this signal is called Fuzzy Fault Indication Signal (FFIS) [15].
The final task of the proposed FDI concept is the proper presentation of the fault situation to the operator who has to make the final decision about the appropriate fault handling [18]. Typical for the fault detection problem is that the output consists of a number of fault indication signals, one for each fault, where these signals can take only the values one or zero (yes or no). For a fuzzy representation this means that it is not necessary to have a number of fuzzy sets to represent the output, as in control. Rather, each fuzzy fault indication signal FFIS is, by its nature, a singleton, the amplitude of which characterizes the degree of membership to only one, preassigned fuzzy set faultm. This degree is characterized by the FFIS, i. e., the signal obtained as a result of the inference. Specific for this approach is that it refrains from defuzzification and represents the fault indication signal for each fault to the operator in the fuzzy format, i.e., in terms of the FFIS, which represents the desired degree of membership to the set faultm.
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