A recursive polynomial grey prediction model with adaptive structure and its application

As a sparse data analysis algorithm, ensuring a reasonable model structure is an important challenge for grey models to identify the control mechanism of the uncertain system from observational data. To improve the intelligence and adaptability of the model, this study presents a synchronized optimization strategy for data prioritization and model structure for discrete polynomial grey prediction model. The proposed polynomial grey model contains two hyper-parameters: memory factor parameter and structural parameter. The memory factor is introduced into the discrete model to reconstruct the objective function of structural parameter optimization, thereby avoiding the problem of information superposition. The structural parameter is used to enhance the adaptability of grey prediction model in uncertain data analysis tasks. By employing a recursive estimation approach, an adaptive strategy for estimating model hyper-parameters is proposed, which focuses on minimizing prediction errors within the in-sample data. Additionally, a comparison is made between the proposed improved polynomial grey model and existing polynomial grey models in terms of data information mining, estimation stability, and robustness against measurement noise. The proposed model is applied to the practical engineering application of wear prediction, further validating the effectiveness of the proposed approach in non-equidistant time series prediction tasks.