Since most of the research about grey forecasting models is focused on developing novel models and improving accuracy, relatively limited attention has been paid to the modelling mechanism and relationships among diverse kinds of models. This paper aims to unify and reconstruct continuous-time grey models, highlighting the differences and similarities among different models. First, the unified form of grey forecasting models is proposed and simplified into a reduced-order ordinary differential equation. Then, the integral matching that consists of integral operator and least squares, is proposed to estimate the structural parameter and initial value simultaneously. The cumulative sum operator, an essential element in grey modelling, proves to be the discrete approximation of the integral operator. Next, grey models are reconstructed by the integral matching-based ordinary differential equations. Finally, the existing grey models are compared with the reconstructed models through extensive simulations, and a real-world example shows how to apply and further verify the reconstructed model.

由于灰色预测模型的研究大多集中在开发新模型和提高准确性上，对建模机制和各种模型之间的关系的关注相对较少。本文旨在统一和重构连续时间灰色模型，突出不同模型之间的异同。首先，提出了灰色预测模型的统一形式，并将其简化为降阶常微分方程。然后，提出了由积分算子和最小二乘法组成的积分匹配，同时估计结构参数和初始值。累积和算子是灰色建模中的一个基本元素，被证明是积分算子的离散近似。下一个，灰度模型由基于积分匹配的常微分方程重构。最后，通过广泛的模拟将现有的灰色模型与重建模型进行比较，并通过一个真实世界的例子展示了如何应用和进一步验证重建模型。