Improvement of background value and its application in non-equidistance GM (1, 1) modeling

Based on the geometric explanation of integral, a new construction method of GM(1,1)´s background value for non-equidistance sequence is put forward by using approach that actual area is substituted by summation of small rectangle area and small echelon area. Because the method is able to optimize the result of modeling, so the GM(1,1)´s fitting precision and prediction precision are advanced greatly The method is applied in building model of relation between titanium alloy fatigue strength and temperature change, the result proves its validity and enlarges the scope of GM(1,1) ´s application wildly.