13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- accuracy analysis results; r ( ) f x is the result of the response surface method belong to the low precise model. First of all, the medium accuracy analysis l ( ) f x computes design points picked out by DOE, and the initial correction factor corrects them as h( ) f x . This group of data could construct the initial optimization object and constraints, r ( ) f x , which would be used in optimization cycle; a correction factor is get by contrasting the high precise analysis h( ) f x with the medium precise analysis l ( ) f x , and the correction factor could be updated in the optimization process. 3.2. Periodic Updating Method The correction factor in the traditional VCM could be updated once in several times cycle on the interval method. This method reduces the calling number of the high precise model on the optimization, so it does not only ensure the accuracy and also the efficiency. However, the interval method is often lack of rationality in the search space. For example, the difference between high and low precise analysis could not be constant in design space. When the difference tends to perhaps stable, the interval should be adopted large. When the difference has great fluctuation in the certain design space, the interval may be small. Therefore, the constant interval could not meet the fact. Therefore, it is worth studying problem how to properly use the high precise model to reasonable correct the low precise model. This paper shows a new method called the periodic updating method. When the initial approximate function achieves convergence, the variable records as 1x ∗. Meanwhile, the correct factor could be computed, when h 1 ( ) f x ∗ and l 1 ( ) f x ∗ is obtained by two kinds of precise analysis. New h 1 ( ) f x ∗ would be get by correct factor and added to the previous database. Then the approximation function would be reframed by the least square method from the updated database. The correct function and the approximate function reframed synchronously after the inner convergence provides a relative better time calling the high precise model in the periodic updating method. 3.3. Two-Point Scale Function The correct method of ( ) lf x is called the scale function. Presently, the kinds of the correct factor have the additive factor and the multiplication factor, as well as their high order form, so the scale function are often divided into the addition scale function and the multiplication scale function. The value of 0 ( ) hf x and 0 ( ) lf x is obtained at the initial point 0x . The formula (1) could get a constant addition factor. The subscript "0" means the initial. The multiplication factor is as formula (2): 0 0 0 ( ) ( ) ( ) h l x f x f x α = − （1） 0 0 0 ( ) ( ) ( ) h l f x x f x β = （2） The result of the approximate function will be corrected as ( ) hf x in the loop. The approximation of the ( ) hf x is expressed as the formula (3) and (4) at its design point x. The ( ) hf x obviously contains the information of the high accurate analysis and simplifies calculation process by the approximation model. ( ) hf x represents the data to construct the approximation function. 0 ( ) ( ) ( ) ( ) h h l f x f x f x xα ≈ = + （3） 0 ( ) ( ) ( ) ( ) h h l f x f x f x xβ ≈ = （4）
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