Purpose This paper aims to optimize the structural parameters of a newly developed coaxial electromagnetic buffer of artillery that integrates an eddy-current recoil brake and a spring-type recuperator to achieve low-recoil and stable braking performance. Design/methodology/approach The dynamic equations governing the recoil and counter-recoil processes are formulated, followed by a finite element model incorporating the nonlinear hysteresis and temperature-dependent characteristics of NdFeB permanent magnets. Multi-response grey hierarchical clustering is then proposed to identify key structural parameters. Based on the screened design variables, a Kriging surrogate model is constructed, and a hybrid multi-objective optimization strategy combining the multi-island genetic algorithm and sequential quadratic programming is developed to determine the optimal structural design. Findings The finite element model achieves high prediction accuracy, with dynamic response errors below 5% under three charge conditions. The optimized design reduces the peak recoil resistance from 39.81 kN to 34.68 kN, representing a 12.89% reduction, while satisfying the prescribed recoil displacement constraint. Practical implications The proposed electromagnetic buffer provides an effective alternative to conventional hydraulic recoil systems. The physically validated finite element model and surrogate-based optimization framework can support the structural design and performance improvement of recoil mechanisms for artillery systems. Originality/value This work proposes a multi-response grey hierarchical clustering method for design-variable sensitivity analysis, enabling comprehensive variable screening by jointly accounting for their influence across multiple performance responses.
Purpose The traffic flow system is a complex dynamic system, and the traffic flow data have complex spatiotemporal characteristics. Therefore, to deeply explore the spatiotemporal characteristics of traffic flow data, a novel spatiotemporal multivariate partial grey prediction model for multi-segment traffic flow is proposed, which is suitable for short-term traffic flow prediction. Design/methodology/approach The model adopts grey relational degree analysis to screen multi-segment traffic flow data and further selects time-series data from different periods based on the periodic patterns of traffic flow to capture the spatiotemporal characteristics of traffic datasets. Matrix analysis is then performed for parameter estimation and model construction. To enhance model applicability, particle swarm optimization is employed to optimize the background value coefficient, thereby reducing prediction errors and improving prediction accuracy. Findings The proposed model achieves mean absolute percentage error (MAPE) values below 7% across all evaluated scenarios. Short-term traffic flow prediction is examined over three time periods from three perspectives. The predicted trends closely align with the actual traffic flow sequences, confirming the model’s strong predictive performance. Originality/value The effectiveness of the new model is illustrated by three effectiveness analysis cases. The results are better than comparison models that include several multivariate grey prediction models and deep learning models, which shows the effectiveness of the proposed model. The simulation results of three effectiveness analysis cases are applied to the short-time traffic flow prediction problem.
Purpose This study aims to address the issues of overfitting and underutilization of new information in traditional grey models for multi-frequency traffic flow forecasting. It proposes the Recursive Grey Multi-frequency Fourier Model (RGMFM) to enhance the extraction of multi-frequency periodic features and enable dynamic updating, thereby improving the accuracy and stability of short-term predictions for small-sample, multi-frequency traffic flow data. Design/methodology/approach The RGMFM integrates Fast Fourier Transform (FFT) and a recursive regression algorithm into the grey modeling framework. FFT extracts primary and secondary periodic components, while recursive regression prioritizes parameter updates with new data. The model incorporates two controllable parameters—an energy threshold and a memory factor—to simultaneously optimize its structure and parameter updating mechanism. Findings Simulation and experimental results demonstrate that RGMFM significantly outperforms benchmarks (SARIMA, LSTM, Transformer), reducing average RMSE by approximately 17% on 50 subsets of the PEMS08 dataset. It accurately captures daily and peak-hour traffic patterns and maintains robust performance under varying noise levels, validating its effectiveness and stability for multi-frequency forecasting. Originality/value The main originality lies in the novel hybrid framework that embeds signal processing (FFT) and recursive learning into grey system theory. The introduction of dual controllable parameters for integrated optimization provides a new, tunable, and interpretable modeling paradigm. This work extends grey models' applicability to complex, dynamic multi-frequency forecasting tasks, offering significant practical value for intelligent transportation systems and similar domains.
Purpose Accurate and reliable energy forecasting is fundamental to strategic decision making for the global transition toward decarbonization and digitalization. This paper proposes a novel nonlinear time-varying fractional grey multivariable model to address the limitations of conventional forecasting methods. Design/methodology/approach The proposed model offers a novel methodological improvement by integrating time-varying coefficients for dynamic parameterization, logarithmic adjustment terms for enhanced nonlinear modeling and a particle swarm algorithm for systematic optimization. Findings Empirical validation across municipal, provincial, and national case studies consistently confirms the superior predictive performance of the proposed model. Comparative analyses with benchmark models show that our model achieves the lowest prediction errors across all evaluation metrics. This outperformance remains robust in both training and testing phases. Practical implications The proposed approach provides a robust methodological framework for energy consumption forecasting, offering substantial improvements in accuracy and reliability for supporting energy strategy formulation and sustainable development planning. Originality/value Its originality stems from the integration of dynamic coefficients and logarithmic adjustment terms. This integrated framework effectively addresses the limitations of static parameters and fixed structures in conventional grey models.
Purpose Aiming at the issue that traditional multivariable grey prediction models cannot fully identify nonlinear trends among sequences, this paper introduces power-exponential and time-power-logarithmic correction terms, combines intelligent algorithms to flexibly optimize the model's unstructured parameters and proposes a new logarithmic flexible discrete grey LFDGM (1, N) model to deeply mine data sequence patterns and adapt to data development trends. Design/methodology/approach Firstly, nonlinear parameters are introduced into system behavior and relevant factor sequences, and a logarithmic time-power correction term is adopted to identify system nonlinear characteristics. Secondly, four mainstream intelligent optimization algorithms are compared to select the optimal one for hyperparameter global optimization with minimum average relative error. Then, the LFDGM (1, N) model is applied to fossil energy production prediction and compared with benchmark models. Finally, model stability is verified via Monte Carlo simulation and varying sample set experiments. Findings The experimental results show that the logarithmic flexible discrete grey LFDGM (1, N) model has better accuracy than other models in the global MAPE, verifying the validity and practicability of the model and indicating that this model has the optimal modeling effect on nonlinear complex systems. In addition, this paper verifies that the LFDGM (1, N) model has good robustness through Monte Carlo simulation and experiments with different sample sets. Practical implications Scientific and accurate prediction of fossil energy output is of great reference significance for China's formulation of energy industry plans and provides solid support for the long-term stable development of its energy industry. Originality/value To tackle complex, variable and highly uncertain system data sequences, this paper develops a logarithmic flexible discrete grey LFDGM (1, N) model. Embedding nonlinear power parameters in the system feature sequence and the related factor sequence, and introducing a logarithmic time-power correction term enhances nonlinear correlation depiction, captures early system abrupt changes and restricts late prediction divergence. Hyperparameters are optimized via preferred intelligent algorithms to improve prediction accuracy.
