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Fault diagnosis is one of the most important tasks assigned to intelligent supervisory control systems. Recently, artificial neural networks have been applied to this area more or less successfully with simple networks based on the Multi-Layer Perceptron (MLP). In this report, we will show a different approach to fault diagnosis through the use of...
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... fact, ρ enables the cluster to react just like a fuzzy number, the closer we are from the centroid, the more likely the fault can be considered as that very fault. For instance, the Figure 10 ...
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... assume that we arrange the hyperspheres in such a way that each centre is never included in any other hypersphere. The best arrangement possible is what could be called the "wine rack arrangement" as shown in Figure 11 in a 2-dimensional Euclidean space. Given this, there will be then a maximum of α ρ-radius hyperspheres that can be ...
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... fact, if there are n hyperspheres that are very close but without contact (cf. Figure 12) ; if a n+1 th hypersphere covers a part of each n hypersphere (cf. Figure 14), then all of them, according to the algorithm will belong to the same cluster. ...
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... fact, if there are n hyperspheres that are very close but without contact (cf. Figure 12) ; if a n+1 th hypersphere covers a part of each n hypersphere (cf. Figure 14), then all of them, according to the algorithm will belong to the same cluster. ...
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... in term of neurons, there are n hidden neurons of different colour linked with n output neurons paired with one hidden neuron (cf. Figure 13). When the extra sample is analysed, a new hidden neuron is added; and then, each of the n hidden neuron become of the same colour, and n-1 output neurons are removed 6 (cf. Figure 15). ...
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... the extra sample is analysed, a new hidden neuron is added; and then, each of the n hidden neuron become of the same colour, and n-1 output neurons are removed 6 (cf. Figure 15). Then, provided that n is greater than 2, the overall number of neurons decreases at each step. ...
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... because of the clustering phenomenon, the complexity is not quite polynomial, but rather in θ(1). It seems that in fact the complexity should look rather like the sigmoid shown in Figure 16. ...
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... the cluster of samples does not represent the same fault according to its position in the cluster while there is no visible border (cf. Figure 17), then any system based on the clustering method will not work. ...
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... a large set of colours can be allocated. The Figure 18 shows the different structures used in the implementation of the RBFN module. In this figure, only the data are shown. ...
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... to the fuzzyMode variable, it is used to have either a genuine classifier network, or a network which output give an idea of the fault with values ranging from 0 to 1. Figure 18 : Structure chosen for the module To make the network computing samples make a call to Process() with the sample (an array of double) given in parametre, and then, the calculation is run. When it's over, the result is accessible via the functions FirstOutput(), NextOutput() and GetOutput(). ...
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