A novel self-adaptive nonlinear discrete grey model and its application

Purpose To overcome the structural limitations arising from subjectively preset adjustable parameters in the NGBM(1,1) model family and significantly enhance its predictive capability for complex nonlinear systems, this study develops a novel self-adaptive nonlinear discrete grey model (SANDGMO(1,1)). Design/methodology/approach The proposed SANDGMO(1,1) model is developed by integrating non-homogeneous discrete grey modeling principles into the traditional NGBM(1,1) model to eliminate jumping errors. Parameterization functions are introduced to optimize all adjustable parameters, and a multi-parameter collaborative optimization strategy based on the firefly algorithm is designed to solve for the optimal hyperparameters, thereby overcoming the limitations of subjectively preset adjustable parameters used as fixed values in the existing NGBM(1,1) model family. Finally, the Sobol method analyzes the global sensitivity of hyperparameters to elucidate their mechanism and provides a theoretical foundation for multi-parameter simultaneous optimization. Findings The validity of the SANDGMO(1,1) model was verified using two classical fluctuating time series and a real-world case of predicting China's marine transportation industry output value. Results demonstrate its effectiveness in predicting complex nonlinear systems. Projections indicate China's marine transportation output value will reach 958.6436 billion CNY by 2027. Practical implications This study reveals the evolutionary trajectory of China's marine transportation industry and provides empirical evidence for policy formulation, facilitating the green, high-quality development of the industry. Originality/value This study constructs a novel SANDGMO(1,1) model by integrating the non-homogeneous discrete grey model with the NGBM(1,1) model. The proposed model employs parameterization functions to optimize all adjustable parameters and establishes a unified optimization framework based on the firefly algorithm, resolving the limitations of subjectively preset adjustable parameters used as fixed values in the existing NGBM(1,1) model family. The Sobol method quantifies the interactions among hyperparameters, establishing a theoretical foundation for multi-parameter simultaneous optimization algorithms and addressing limitations in existing research.