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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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These phrases must be modified to make the fuzzy switching functions fuzzy-consistent. The complete design algorithm can be summarized as follows [16]:
If Res1 is normal and Res2 is negative or If Res1 is positive and Res2 is negative then f1
The corresponding fuzzy switching function is given as
The definition is based on the assumption that the first index indicates the residual and the second index indicates the fuzzy set of this residual.
In this formula to check for faultk, just the terms for k to p are considered, because the previous steps checked that fault k is fuzzy consistent with respect to fault1, . . . , faultk-1.
This algorithm ensures that all faults are detectable and distinguishable. If a perfect distinction of the residuals is not possible, the algorithm indicates these inconsistencies. This helps the operating personnel to evaluate signals giving consideration to the inconsistency. To prove the algorithm it was applied to a part of a wastewater plant.
The anaerobic digestion process is a self-regulating biological process that converts organic matter into gas. The metabolic pathway of the process is shown in Figure 5 [15]. The output of the process is carbon-dioxide (CO2) and methane (CH4). To run such a biological process under optimal conditions, which means to reduce the waste concentration in the effluence and yield a maximum methane rate, some requirements have to be met. To include all effects, the model of the process has to be highly nonlinear and of high order. Because of these facts some researchers have tried to simplify the model [1], [28] by reducing the number of acids in the process. The complete model contains three kinds of acids:
Because acetic acid is the most significant part some models contain just this kind of acid, see, e.g., [36]. The next step is the integration of the propionic acid [24], [27]. If, on the other hand, the model contains all the acids, the used kinetics and the transformation of the gas from the liquid to the gas-phase are quite simple [30]. In addition most of the models consider only the acids as the source of methane. It has been shown in [8] that approximately 30% of the methane derives from the synthesis of hydrogen (H2) and carbon dioxide (CO2). To include this synthesis, the hydrogen and carbon-dioxide balance equations have to be adequately modeled. Finally, most of the models consider an acid as an input, rather than considering a component which is one or two steps above in the metabolic pathway, see Figure 5.
Figure 5 Metabolic pathway of the process
To include all the effects and leave out the above mentioned disadvantages, the model presented in this paper includes the following effects [18]:
The design of the fuzzy filter for the qualitative residual evaluation is based on the following assumptions [15]:
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