Copula-based JPDF of wind speed, wind direction, wind angle, and temperature with SHM data

Abstract

Structural health monitoring (SHM) systems installed on long-span bridges can obtain environmental data around them. To deeply mine the correlation between types of data, this paper proposes a multivariant joint probability density distribution function (JPDF) based on copula theory. Specifically, the univariate probability density function (PDF) is characterized by the finite mixture (FM) method, that is, the 1D model. In addition, the parameters in the FM distribution are estimated by the genetic algorithm (GA). Then, the bivariate JPDF based on copula theory is established, i.e., the 2D model; next, the trivariate JPDF is derived, i.e., the 3D model. Furthermore, the quaternary JPDF of wind speed, wind direction, wind angle, and temperature is derived, i.e., the 4D model. The feasibility of the proposed model is verified by a case study of a specific bridge in China, on which the SHM system is installed to collect SHM data including wind speed, wind direction, wind angle, and temperature. The trivariate JPDF of wind speed, wind direction, and wind angle, and the trivariate JPDF of wind speed, wind direction, and temperature based on FM are established.