Discrete grey forecasting models based on an accumulative operator have been widely used in many practical fields. With the development of grey forecasting models, it is a problem to be solved to further analyze internal mechanisms and unify the structures. This paper aims to reconstruct the model from a perspective of sequence characteristics and simplify the modeling steps under the condition of ensuring the accuracy of the model. First, this paper analyzes dynamic sequence evolution hidden and mines relationship between the structure and original sequence features contained in discrete grey forecasting model. Then, the reconstruction is carried out to prove the equivalence and quantitative relation between reduced-order model and original model. Under order recursive estimation, new parameters are addressed. Finally, theoretical correctness is verified by large-scale numerical simulation. Moreover, the reduced-order model is applied for prediction on the peak of battery incremental capacity and capacity degradation. Results show the effectiveness and superior prediction performance of the reduced-order model, where MAPEs of grey forecasting models have controlled under 4%.

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离散灰色预测模型的降阶重构及其应用


基于累积算子的离散灰色预测模型已广泛应用于许多实际领域。随着灰色预测模型的发展，进一步分析其内部机制并统一结构是一个需要解决的问题。本文旨在从序列特征的角度重构模型，在保证模型精度的情况下简化建模步骤。首先，分析了离散灰色预测模型中隐藏的动态序列演化，挖掘了结构与原始序列特征之间的关系。然后进行重构，证明降阶模型与原模型的等价性和定量关系。在阶递归估计下，解决了新的参数。最后通过大规模数值模拟验证了理论的正确性。此外，应用降阶模型来预测电池增量容量和容量衰减的峰值。结果表明降阶模型的有效性和优越的预测性能，灰色预测模型的MAPE控制在4%以下。