Forecasting of Roof Temperature in a Grey Prediction Model with Optimal Fractional Order Accumulating Operator

Abstract

Building roof temperatures mainly affected by solar radiation. With the solar radiation intensity changing, the change of roof temperature also occurs constantly. It has an uncertainty to a high degree, so the grey system can be combined with data analysis for researches. Based on the classical NDGM model, this paper introduced the fractional order \( NDGM^{{\tfrac{q}{p}}} \) model to study the important properties of the model and used the PSO particle swarm optimization algorithm to optimize the fractional order. Finally, the two representative measuring points, namely, the maximum solar radiation and the second solar radiation points, were taken as the experimental objects. The experimental results show that the mean absolute percentage error (MAPE) of the optimized fractional order \( NDGM^{{\tfrac{q}{p}}} \) model for the roof temperature is several percentage points higher than that of the classical GM, DGM and NDGM models, as well as the minimum error of the model can reach 2.4247%.