An adaptive Grey-Markov model based on parameters Self-optimization with application to passenger flow volume prediction

Abstract

It has been demonstrated that local prediction approaches show better prediction performance compared with global ones. The paper proposes a novel local prediction model named as the adaptive grey-Markov prediction model for incomplete and complex dynamic systems. This model displays favorable adaptability, flexibility and universality because of four advantages. Firstly, because of the randomness and non-repeatability of time series, the paper proposes adaptive exponential accumulated generating operators to describe different contribution degrees of historical information to future change trends of system characteristics. Secondly, this paper proposes a new paradigm of adaptive grey background value, which can automatically adjust parameters based on historical information to optimize this model and reduce prediction errors. Thirdly, the optimization model based on average absolute percentage error is constructed, and the corresponding adaptive parameters are searched by Ant Lion Optimizer algorithm. Fourthly, this model consists of a quadratic polynomial function describing nonlinearity and a periodic function generated by a Fourier series characterizing noise and period. Thereupon, the adaptive odd-period grey model is proposed. Its residual modified model, named as adaptive grey-Markov modified model, is given based on Markov chain (MC) and virtual linguistic trust degree (VLTD) to further improve prediction accuracy. The modified values of absolute errors are determined by the score functions produced from trust degrees of absolute errors to states on MC calculated by VLTD method. This modified way retains the influence degrees of absolute errors on the modified values and improves the prediction accuracy. Finally, the paper further demonstrates performance and practicability of the proposed prediction model through predicting passenger flow of Chengdu Metro Line1 and comparative analysis.