13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- ( ) 11 12 1 21 22 2 1 2 n n ij m n m m mn r r r r r r R r r r r × ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ = = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ L L L L L L L , (5) among it, 1,2, i m = L ， 1,2, j n = L 。 In the factor set, for reflecting the different importance of each factor, we give each factor ic a corresponding weight. The degree of membership of proposal j[7]: ( ) ( ) 2 1 1 1 1 1 j m i ij i m i ij i u w r wr = = = ⎛ ⎞ ⎡ − ⎤ ⎜ ⎟ ⎣ ⎦ ⎜ ⎟ + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ∑ ∑ (6) We can get the fatigue life through the weighting factor method: 1 n j j j N u N = =∑ (3) Among it, j N is the fatigue life of structure when evolution level is j. 2.2 Weight vector For decreasing the affection of human factors, the method of getting the weight iwis based on its relative degree of fuzziness membership. Generally speaking, the higher degree of membership of target, the bigger attention will be pay. In other words, the bigger weight will be given. According to the fuzzy set, we can regard the degree of membership as the weight. So we transpose the array R, and get the array of relative degree of membership which is target to the “importance”, namely 11 12 1 21 22 2 1 2 ( ) m m T ji n m n n nm w w w w w w W w R w w w × ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ = = = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ L L L L L L L (7-1) From array W, we can know the vector ( ) 1 2 ( , , , )T i i i ni w w w w = r L of relative degree of membership. It is a vector of n proposals that are about factors ic to the “importance”. Because each proposal in set V completes fairly, so n proposals have the same weight to the importance of factor ic . So weight vector is[7]: 2 2 1 ( ) (1 ) i yi zi w d d − − = + ⋅ (4) Among it： 1 1 (1 ) p n p yi ji j d w = ⎧ ⎫ =⎨ − ⎬ ⎩ ⎭ ∑ ， 1 1 p n p zi ji j d w = ⎧ ⎫ = ⎨ ⎬ ⎩ ⎭ ∑ pis the index of distance, when pis one，it is Hamming distance; when pis two, it is Euclidean distance
RkJQdWJsaXNoZXIy MjM0NDE=