Modelling Dependence between Traffic Noise and Traffic Flow through An Entropy-Copula Method

In this study, an entropy-copula method is proposed for modelling dependence between traffic volume and traffic noise on the Trans-Canada Highway (#1 highway of Canada) in the City of Regina based on a series of field experiment measurements. The proposed entropy-copula method combines the maximum entropy and copula methods into a general framework. The marginal distributions of traffic volume and traffic noise are estimated through the principle of maximum entropy (POME) theory, and the joint probabilities are derived through the Gaussian and Student t copulas. The underlying assumptions of the coupled entropy-copula method are that: i) the entropy variables are mutually independent from each other, and ii) the marginal distributions of traffic flow and traffic noise are continuous. The proposed method is applied to two field experiment sites on the Trans-Canada Highway. Based on the K-S and A-D tests and RMSE value, the entropy method shows well performance in quantifying the probability distributions of traffic volume and traffic noise. Meanwhile, both the Gaussian and Student t copulas can well model the joint probability distributions of the traffic volume and traffic noise at the both experiment sites, which is demonstrated by the Cramer von Mises statistics and the RMSE value. Furthermore, the conditional CDFs of the traffic noise at the two experiment sites are derived based on the established copulas with respect to different traffic volume scenarios. These conditional CDFs indicate positive structures between traffic volume and traffic noise at the both experiment sites. The conditional PDFs of the traffic noise under different traffic flow scenarios are also generated, indicating the potential reduction effect of traffic noise due to the decrease of the traffic volume. This proposed approach can quantify the dependence between traffic flow and traffic noise, and reveal the inherent uncertain relationship between these two variables. Moreover, the obtained results can provide useful information for traffic noise reduction through traffic flow management.