13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- The addition scale function and the multiplication scale function do not make the full use of the high precise numerical results in the whole optimization process. They use only the high precise analysis results of a point. The previous high precise analysis result is difficult to reflect in the subsequent scale function. This paper introduces the two point scale function which combines the multiplication factor and the additive factor. At the initial point 0x , the two-point scale function displays for the formula (5); similarly, the scale function is formula (6) at 1x ∗. 1α and 1β is solved from the formula (5) and formula (6) simultaneous as formula (7). 0 1 0 1 ( ) ( ) h l f x f x β α = + （5） 1 1 1 1 ( ) ( ) h l f x f x β α ∗ ∗ = + （6） 1 0 1 1 0 1 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) h h l l h l f x f x f x f x f x f x β α β ∗ ∗ ∗ ∗ − = − = − （7） Accordingly, when the i th approximation function achieves convergence in inner loop, the ( ) h i f x ∗ and ( ) l i f x ∗ is obtained by calling the high and medium accuracy analysis at the design point ix ∗. The optimal solution 1 ix ∗ − , the corresponding 1 ( ) h i f x ∗ − and 1 ( ) l i f x ∗ − could be also gain in the 1 i − th inner loop. Therefore the iα and iβ could be list in the formula (8) and (9) : 1 1 ( ) ( ) ( ) ( ) h i i l i i h i i l i i f x f x f x f x β α β α ∗ ∗ − − ∗ ∗ = + = + （8） 1 1 ( ) ( ) ( ) ( ) ( ) ( ) h i h i i l i l i i h i l i f x f x f x f x f x f x β α β ∗ ∗ − ∗ ∗ − ∗ ∗ − = − = − （9） Where iα is the additive correct term, and iβ the multiplicative correct term. The two-point scale function inherits the former and later value of the high precise results, and need not calculate the additional derivative information. Thus the computational efficiency and precision are ensured simultaneously. Therefore, before the start of the 1 i + th inner loop, the original data will be corrected in accordance with the formula (10). ( ) ( ) j j h i i l i i f x f x β α = + （10） Where i stands for the number of inner loop executed; 1 j n = , n is the total number of sampling point. Then the value of ( )j h i f x 1 j n = could construct the approximate function 1 ( ) R i f x+ of objects and constraints in the 1 i + th inner loop by the least-squares regression method. 3.4. Multiple-Precision Optimization Strategy The collaborative optimization (CO) strategy [13, 14] need usually call a large number of discipline analyses. That means very expensive cost. Because the extra compatible constraint is optimization target in subsystem layer, the cost further increases. The CO efficiency has been improved by the approximation method [15], which is a good solution for the interdisciplinary relatively independent. However the inherent couple of the turbine blade does not reflected in a previous study. The discipline coupled analysis stands for the development of the high precise numerical method. Compared with the single discipline analysis, the closely coupled analysis need consume more cost.
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