Prediction and Analysis of Abalone Aquaculture Production in China Based on an Improved Grey System Model

This study employs an improved fractional-order grey multivariable convolution model (FGMC(1,N,2r)) to predict abalone aquaculture output in Fujian, Shandong, and Guangdong. By integrating fractional-order accumulation ( r 1 , r 2 ) with a particle-swarm-optimization (PSO) algorithm, the model addresses limitations of handling multivariable interactions and sequence heterogeneity within small-sample regional datasets. Grey relational analysis (GRA) first identified key factors exhibiting the strongest associations with production: abalone production in Fujian and Shandong is predominantly influenced by funding for aquatic-technology extension (GRA degrees of 0.9156 and 0.8357, respectively), while in Guangdong, production was most strongly associated with import volume (GRA degree of 0.9312). Validation confirms that FGMC(1,N,2r) achieves superior predictive accuracy, with mean absolute percentage errors (MAPE) of 0.51% in Fujian, 3.51% in Shandong, and 2.12% in Guangdong, significantly outperforming benchmark models. Prediction of abalone production for 2024–2028 project sustained growth across Fujian, Shandong, and Guangdong. However, risks associated with typhoon disasters ( X 6 and import dependency ( X 5 ) require attention. The study demonstrates that the FGMC(1,N,2r) model achieves high predictive accuracy for regional aquaculture output. It identifies the primary drivers of abalone production: technology-extension funding in Fujian and Shandong, and import volume in Guangdong. These findings support the formulation of region-specific strategies, such as enhancing technological investment in Fujian and Shandong, and strengthening seed supply chains while reducing import dependency in Guangdong. Furthermore, by identifying vulnerabilities such as typhoon disasters and import reliance, the study underscores the need for resilient infrastructure and diversified seed sources, thereby providing a robust scientific basis for production optimization and policy guidance towards sustainable and environmentally sound aquaculture development.