To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) ...To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.展开更多
The mixed model of improved exponential and power function and unequal interval gray GM(1,1)model have poor accuracy in predicting the maximum pull-out load of anchor bolts.An optimal combination model was derived usi...The mixed model of improved exponential and power function and unequal interval gray GM(1,1)model have poor accuracy in predicting the maximum pull-out load of anchor bolts.An optimal combination model was derived using the optimally weighted combination theory and the minimum sum of logarithmic squared errors as the objective function.Two typical anchor bolt pull-out engineering cases were selected to compare the performance of the proposed model with those of existing ones.Results showed that the optimal combination model was suitable not only for the slow P-s curve but also for the steep P-s curve.Its accuracy and stable reliability,as well as its prediction capability classification,were better than those of the other prediction models.Therefore,the optimal combination model is an effective processing method for predicting the maximum pull-out load of anchor bolts according to measured data.展开更多
基金The 11th Five-Year Plan for Key Constructing Academic Subject of Hunan Province(No.XJT2006180)Natural Science Foundation of Hunan Province (No.07JJ3093)Hunan Province Foundation Research Program (No.2007FJ3030,2007GK3058)
文摘To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.
基金The National Natural Science Foundation of China(No.51778485).
文摘The mixed model of improved exponential and power function and unequal interval gray GM(1,1)model have poor accuracy in predicting the maximum pull-out load of anchor bolts.An optimal combination model was derived using the optimally weighted combination theory and the minimum sum of logarithmic squared errors as the objective function.Two typical anchor bolt pull-out engineering cases were selected to compare the performance of the proposed model with those of existing ones.Results showed that the optimal combination model was suitable not only for the slow P-s curve but also for the steep P-s curve.Its accuracy and stable reliability,as well as its prediction capability classification,were better than those of the other prediction models.Therefore,the optimal combination model is an effective processing method for predicting the maximum pull-out load of anchor bolts according to measured data.
