PSI - Issue 2_A

Pavel Skalny / Procedia Structural Integrity 2 (2016) 3727–3734 Pavel Skalny/ Structural Integrity Procedia 00 (2016) 000 – 000

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can be used. The results of the k-means are also influenced by the chosen distance for quantifying the nearest distance. Euclidean distance is used in this work. In the presented paper we will use the k-means++ variant, where the initial centres are achieved in following way:  The first center 1 is choosen uniformly from the data set .  All other centers (up to ) are one after other chosen from with the probability ( ) 2 ∑ ( ) 2 ∈ , where the ( ) denotes the shortest distance from the data point to the nearest center. So that the highest probability to choose other centre has the data point with the highest (nearest) distance from already chosen centers. K-means++ compared to k-means is faster and guarantees the lower bound to optimal solution, see Arthur and Vassilvitskii (2007). 3.2. Probability identification Another approach to the fracture identification is based on the use of conditional probability distribution. Characteristics of normal vectors are observed separately in the area with purely brittle and ductile fracture. For every type of the fracture the probability distribution is estimated. In previous work the distribution was estimated as a Gaussian mixture. In the presented paper simple multivariate normal distribution is used. For every observation (five elements vector) the probability ( ) that it belongs to the ductile fracture is calculated. ( ) = ( ) ( )+ ( ) (4) where ( ) , ( ) are distributions of the ductile and brittle fracture area. 4. Results Best result in k-means clustering can be achieved by using four clusters. Fewer clusters have proved unsatisfactory and the result with a larger number of clusters is very confusing. In Figure 2 there is presented the result of k-means clustering with four clusters. In this case the first and the second cluster (blue and light blue) represents the brittle fracture area, the third cluster (yellow) represents the ductile fracture area. The fourth cluster (red) represents mainly the notch in the DWTT specimen. Some inaccuracies are seen at the borders of the fracture surface and at the high plastic deformation area (down on the left side). The probability that the vector belongs to the ductile fracture is presented in Figure 3. As in the two cluster analysis the probability identification is loaded with an error in the area of notch and in the area of high plastic deformation.

Fig. 2. (a) first picture; (b) second picture.