冲压模具设计挖掘规则英文文献和中文翻译(2)
12 11 {, ,..., } f aa a where attributes 111 ~ aa are BT(Bend Type), ASBM(Anti-Spring Back Property of Material), T(Thickness), BR(Bend Radius), BA(Bend Angle), SD(Symmetry Degree), DLH(Distance between Bend Line and Hole), CH(Cliff Height), LDA(Linear Dimension Accuracy), ADA(Angular Dimension Accuracy Degree) and SQD(Surface Quality Degree). The meaning of some attributes is shown in Fig. 1. Fig. 1 Some attribute of a U type bend feature A stamping design case base E can be represented as: { | ( , ), 1,..., } ii iiE ee fd i n , where if is a bend feature and id is a related die design implementing the bend process. 3. Fuzzy-classification of cases Among all of examples, there are some similar stamping parts. Before mining rules from the case base, similar parts and their die designs should be partitioned into one cluster. Fuzzy classification approach is adopted in this paper to do the partition[7]. The procedure of fuzzy classification is pided into three stages: 1) Calculate a similarity matrix SM based on the similarity of every two cases. 2) Transfer the similarity matrix SM into an equivalent matrix. 3) Partition the cases into several clusters. 3.1 constructing a similarity matrix The similarity degree of every two cases can be represented by an N×N matrix SM (spq), where N is the case number of a case base and spq denotes the similarity between two cases ep and eq. Let ep=(ap1,ap2, ,ap11) and eq=(ap1,ap2, ,ap11) as described in section 2. The similarity degree of the two cases is defined as: 11() ()1(,) ( , )WWpq p q j pj qjjs see wsmfaa ¦ , (1) where smf() is the function to evaluate the similarity of two attributes and is defined as: . , (2) Where W=(w1,w2, w11) is the weight vector for attributes. Some techniques like gradient decent can be used to automatically get optimized weights[8]. In this paper, we determine the weights manually as each attribute has its special importance and determining the weight manually brings a better accuracy of partition. The resulting similarity matrix for the cases in table 1 is: 1 0.42 0.44 0.4 0.82 0.31 0.33 0.350.42 1 0.31 0.3 0.35 0.38 0.34 0.350.44 0.31 1 0.93 0.33 0.25 0.25 0.280.4 0.3 0.93 1 0.33 0.22 0.23 0.240.82 0.35 0.33 0.33 1 0.32 0.36 0.380.31 0.38 0.25 0.22 0.32 1 00.33 0.34 0.25 0.230.35 0.35 0.28 0.24!#%#" .46 0.450.36 0.46 1 0.970.38 0.45 0.97 1§•¨¸¨¸¨¸¨¸¨¸¨¸¨¸¨¸¨¸¨¸¨¸¨¸©¹ 3.2 Fuzzy classification The technique of fuzzy classification is applied in this method to partition the cases into several clusters. This approach first transforms the similarity matrix to an equivalent matrix. According to Eq. 1 and Eq. 2, the similarity matrix is symmetric and reflexive because, for any spq, sii=1 and sij=sji (ij). To become an equivalent matrix, the similarity matrix should be transformed to be transitive by computing the transitive closure[7]. After the transformation, a Ȝ-matrix of the equivalent matrix is calculated and cases are partitioned into several clusters. Cases that are approximately equivalent to each other are considered within the same cluster. The clustering algorithm is described as follows. step 1. Let 1() pq SM SM SM s D , where max (min( , )) pq k pk kq s ss . 1111 1 j=1 and ( , ) 0 j=1 and 2*min( , ) j 1pqpj qj p qpj qjpj qjaasmf a a a aaaaa° °° z ®°° z°