Issue 45

X.Z. Wang, Frattura ed Integrità Strutturale, 45 (2018) 100-107; DOI: 10.3221/IGF-ESIS.45.08 101 search. This theory has been broadly used in many engineering fields. Grey prediction is based on the processing of raw data and the establishment of grey model, find and master the devel- opment law of the system, and make a scientific and quantitative prediction of the future state of the system [4-7]. Grey prediction model generally refers to GM (1,1) model. GM (1,1) model Make x (0) is the modeling sequence of GM(1,1) : (0) (0) (0) (0) ( (1), (2), , ( )) X x x x n   , and make x (1) is the AGO sequence of x (0) : (1) (1) (1) (1) ( (1), (2), , ( )) X x x x n   , (1) (0) (1) (1) x x  , (1) (0) 1 ( ) ( ) k m x k x m    (1) Make z (1) (k) is the mean sequence of x (1) (k) (1) (1) (1) ( ) 0.5 ( ) 0.5 ( 1) z k x k x k    (2) (1) (1) (1) (1) ( ) ( (2), (3), , ( )) Z k Zx Zx Zx n   (3) The definition type of GM (1,1) , that is, the grey differential equation model of GM (1,1) is: (0) (1) ( ) ( ) x k az k b   , 1, 2, , k n   (4) In the formula: a and b are constants, among them, a is development coefficient, b is grey influencing coefficients. The GM (1,1) definition equation can be transformed into matrix equations. N Y BP  (5) T (0) (0) (0) N (2), (3), , ( ) Y x x x n       (6) (1) (1) (1) (2) 1 (3) 1 ( ) 1 z z B z n                   (7) . a P b        (8) Under the least square criterion, the solution of Y N =BP is: 1 . ( ) T T N a P B B B Y b          (9) Substitute B and Y N into the formula, it can calculate the value of a and b . The detailed formula of (1,1) GM grey predic- tion model is obtained. When k=0, 1, 2, …, n , the original sequence fitting value is obtained, for k=n+1 , a prediction val- ue of the original sequence is obtained, and a multi-step prediction can be obtained at one time.