A grey incidence model with cumulative time-delay effects and its applications

To identify the time-delay relationship between sequences more accurately, we propose a grey incidence model for time-delay systems. Before constructing the new model, we first clarify several time-delay relationships, including instantaneous form and cumulative form. Subsequently, the Weibull distribution is initially used to represent multiple types of time-delay effects. To reduce the computational load, the minimum cumulative step size is designed to simplify convolution, which is used to aggregate cumulative time delay effects in our research. This facilitates us to extract discrepancy information using relative angles and distances. To streamline the process of obtaining results, we utilize particle swarm optimization to optimize the self-adaptive parameters of the Weibull distribution and obtain cumulative time-delay information. The proposed model is validated through numerical experiments to analyze the time-delay effects of key influencing factors on air pollution. Finally, a comparative analysis with ten prevailing models demonstrates that our model not only integrates the functionalities of traditional models but also exhibits significant advantages in the detection of continuous time delay.