A generalization of the GM(1,1) direct modeling method with a step by step optimizing grey derivative's whiten values and its applications

This paper generalises the GM(1,1) direct modeling method with a step by step majorizing grey derivative's whiten values to unequal time interval sequence modeling, and proves that the new method still has linear transformation consistency of the old method. The example indicates that the new method still has gradual approaching white exponential law coincidence property. With this new method, we then model the high precision soft foundation settlement.