27b the m m m 1 2 3 1 p m m m b β β β β 1 1 2 2 3

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distribution histogram of Fig. 27b. The M M M 1 2 3 1 + + = P M M M b = + + + β β β β 0 1 1 2 2 3 3 173 Acoustic Emission Signal Processing F IGURE 26. Failure mechanism bands in the acoustic emission amplitude distribution. 56 Events (relative scale) Amplitude (dB) 0 20 40 60 80 100 1 2 3 Legend 1. Matrix cracking (50 to 72 dB). 2. Fiber breaks (62 to 82 dB). 3. Delaminations (78 to 97 dB).
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resolution in Fig. 27a is three times that in Fig. 27b: the smallest discernible increment in Fig. 27a is two events on the vertical scale whereas in Fig. 27b it is six events. It was thought that this decreased resolution or noise in the input data of the set 3 bottles might reduce the prediction capability of the neural network trained on all three bottle sets. There was also some question as to how well the network would handle the amplitude data for the bottles that experienced polar boss blowouts. Network Architecture The backpropagation neural network consisted of an input layer, a single hidden layer and an output layer as shown in Fig. 28. In each case, the input was a 48 × 1 dimensional vector with the following entries: (1) a categorical variable defining the resin type and (2) the 47 integer variables ( 0) representing the event frequencies at each amplitude from 50 to 96 dB during the acoustic emission test. Variations in the number of neurons in the hidden layer and the learning parameters were made to find a network with a prediction error of ±5 percent. The number of neurons in the hidden layer determines the closeness of fit to the training data. If too many neurons are used, the network will fit the training data extremely well but will not predict well on the test data. On the other hand, if too few neurons are used, the network will fit neither the training set nor the test data well, so there is a tradeoff. A good fit is generally obtained when the errors in fitting the test set, though slightly higher, are of the same order of magnitude as those from the training set. At this point, the network is properly trained. The output vector was the burst pressure of the composite pressure vessel. During the training phase, the target output was the actual burst pressure; for the test phase, it was the predicted burst pressure. Hence, the output layer consisted of a single neuron representing this continuous variable. Training and Testing of Network The backpropagation neural network was trained on a total of nine bottles, three from each of the three sets of bottles. The remaining eight bottles were then used as the test set to evaluate the accuracy of the network’s burst pressure prediction. Details of the training and test data for all three sets of bottles are published elsewhere. 55 The training sets in each case were chosen to include the highest and lowest burst pressures from each bottle set, plus one bottle with an intermediate burst pressure. It was also necessary to train on one of the bottles that experienced a polar boss blowout.
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