Novel grey dynamic trend relational analysis models with different types of accumulation delay effects for time-delay systems

Abstract

In order to analyze the unknown accumulation delay relationship between the given inputs and outputs, one basic model and four extended models are proposed to simulate the different accumulation delay processes. The basic model called grey dynamic trend relational analysis model calculates the similarity between two sequences based on their trends. On the basis of the basic model, four extended models are developed to simulate the different accumulation delay effects. Two types of the accumulation delay effects, called driven-type and yielded-type accumulation delay effects, are put forward for different time-delay relationships. Each type of the accumulation delay effects designs two weight distributions for analyzing the different time-delay processes. Two optimization models based on grid-search are given to determine the lag parameters in the four extended models. The pseudo-codes of intelligent algorithms are provided for the optimization problems. To explain how it can be employed in practice, the new approaches for the time-delay systems are applied to analyze the relationships between the air pollution and its driven factors and results in the Yangtze River Economic Belt. The comparing results show that the novel models can handle the time-delay systems with accumulation delay effects and can determine the delay processes.