Non-equidistant GM(1,1) (abbreviated as NEGM) model is widely used in building settlement prediction because of its high accuracy and outstanding adaptability. To improve the building settlement prediction accuracy of the NEGM model, the fractional-order non-equidistant GM(1,1) model (abbreviated as FNEGM) is established in this study. In the modeling process of the FNEGM model, the fractional-order accumulated generating sequence is extended based on the first-order accumulated generating sequence, and the optimal parameters that increase the prediction precision of the model are obtained by using the whale optimization algorithm. The FNEGM model and the other two grey prediction models are applied to three cases, and five prediction performance indexes are used to evaluate the prediction precision of the three models. The results show that the FNEGM model is more suitable for predicting the settlement of buildings than the other two grey prediction models.
Aiming at the problem of unstable prediction accuracy of the classic NGM (1, 1, k) model, the modeling principle and parameter estimation method of this model are deeply analyzed in this study. Taking the minimum mean absolute percentage error as the objective function, the model is improved from the two perspectives of the construction method of the background value and the fractional order accumulation generation. The fractional order accumulation NGM (1, 1, k) model based on the optimal background value (short for the FBNGM (1, 1, k) model) is proposed in the study. The particle swarm optimization algorithm is used to estimate the parameters of the proposed model. Taking two actual cases with economic significance as examples, empirical analysis of the proposed model is conducted. The simulation and prediction results show the practicality and efficiency of the FBNGM (1, 1, k) model proposed in this study, which further broadens the application scope of the grey prediction model.
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