A hybrid grey generalized Verhulst model for enhanced prediction of small-sample nonlinear sequences: Development, optimization, and validation via fiber-asphalt interfacial bond-slip data

Grey prediction models are widely applied to "information-incomplete" system problems, but traditional ones like the grey Verhulst model (GVM) have inherent limitations, such as the "drift phenomenon" and inadequate adaptability to highly nonlinear scenarios. As an extended variant of GVM, the grey generalized Verhulst model (GGVM) mitigates part of these defects, yet fails to fully incorporate the "new information priority principle" into the Accumulated Generating Operator (AGO) design, which leads to underutilization of critical up-to-date information and restricts its performance for high-dynamic, high-volatility datasets. To enhance prediction accuracy, this paper proposes a hybrid grey generalized Verhulst model (Mar-NIP-FO_GGVM) that combines new information priority fractional order (NIP-FO) and Markov chain. First, the NIP-FO accumulation operator and background value adjustment coefficient are introduced to address low prediction accuracy of the GGVM model. Subsequently, the particle swarm optimization algorithm and Markov chain are employed to optimize the proposed model. Finally, it is used to predict interfacial bond-slip curves between basalt, glass, polyester fibers and asphalt matrix. Through comparisons with the Popovics model and three grey models, the model's effectiveness, applicability and robustness are verified. Results indicate that under all three scenarios, Mar-NIP-FO_GGVM's overall accuracy is significantly superior to other models, with MAPE values below 7% in both simulation and prediction intervals. It can also effectively capture characteristic differences of fibers with different moduli in viscoelastic deformation, softening debonding and debonding stages.