On the other hand two failure mechanisms may be

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sources. On the other hand, two failure mechanisms may be indistinguishable if they result in similar acoustic emission test signatures, or one failure mechanism might result in two clusters. In pattern recognition, any clustering identifying the structure of the data is valid whereas clustering that maximizes the separability between classes might be optimum. For engineering, the 164 Acoustic Emission Testing F IGURE 18. Two-dimensional scatter plots: (a) signal intensity versus rise time; (b) energy versus amplitude. Legend = hsu nielsen event = friction = electromagnetic interference 10 7 10 6 10 5 10 4 10 3 Signal intensity (μV) Rise time (μs) 0 200 400 600 (a) 1000 500 100 50 10 5 1 Energy (counts) Amplitude (dB) 50 60 70 80 90 100 (b)
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methodology that results in partitions that represent the physical phenomena of interest is valid. In this respect, it might be sufficient to separate noise from meaningful emission no matter how many noise sources are recorded. For unsupervised pattern recognition, the results are ranked in terms of separability and compactness of the resulting classes by means of numerical indices based on the scatter matrix within each class and the overall scatter matrix. Further validation is performed by detailed evaluation of the respective cumulative hits of each class versus the applied load, 12 by means of source location of the signals of each class 38,46 or through comparison with other nondestructive test schemes 35 or stress analysis. Different clustering algorithms have been proposed for unsupervised classification of acoustic emission test data: 12 (1) cluster seeking or wish, (2) maximum and minimum distance, (3) k means or forgy and (4) isodata. All the mentioned algorithms use euclidean distance as a measure of dissimilarity between pattern classes. The first two algorithms are heuristic and are based on the selection of a representative distance threshold by which the boundary of each class is defined in the multidimensional space. The remaining two algorithms aim to minimize the square error for a given number of clusters based on an iterative procedure. The wish, forgy and isodata clustering algorithms implement heuristic procedures for creating new clusters and deleting small ones. The modified maximum and minimum distance algorithm 12 uses two starting clusters selected as the point farthest from the mass center and the point farthest from the previous one. A new cluster center is created if D m i > T m D av , where D av is the average between clusters distance, D m i is the maximum of the minimum distances between each pattern or acoustic emission hit to the existing cluster centers and T m is a user specified parameter in the range (0, 1). The algorithm identifies cluster regions farthest apart and therefore is particularly useful either for extreme noise condition identification or for the first approximation of initial cluster centers to be refined by other iterative procedures such as k means or forgy algorithms.
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