Wind speed and wind direction are two important factors to describe the wind properties. The statistical probability model of wind speed and wind direction is widely used to characterize the uncertainty of wind field around the structures. Considering the correlation between the wind speed and wind direction, they should be modeled simultaneously, which highlights the importance of using joint probability density function (JPDF) to describe the wind properties. An angular–linear (AL) model is employed to construct the JPDF of wind speed and wind direction based on long-term monitoring data. The finite mixture (FM) Gumbel distribution, which models the wind speed, and the FM von Mises distribution, which models the wind direction, are proposed to formulate the AL model. Expectation–maximization (EM) and genetic algorithm (GA) are adopted to estimate the AL model parameters. For the EM method, the analytical expressions for calculating the AL model parameters are derived. For the GA method, the analytical fitness functions are derived. These derived analytical expressions facilitate the implementation of the EM and GA methods. One-year wind monitoring data collected by structural health monitoring (SHM) system installed on Jiubao Bridge is employed to demonstrate the feasibility of the AL model-based method in evaluating the wind properties. The results show that the AL model formulated by the FM Gumbel distribution and FM Von Mises distribution is effective for establishing JPDF for joint modeling of the wind speed and wind direction. In the AL model, the EM method is more effective for estimating the parameters of the FM von Mises distribution, whereas the GA methods is more powerful for estimating the parameters of the FM Gumbel distribution.
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The work described in this paper was jointly supported by the National Natural Science Foundation of China (Grant nos. 51822810, 51878235, and 51778574), the Zhejiang Provincial Natural Science Foundation of China (Grant no. LR19E080002), and the Fundamental Research Funds for the Central Universities of China (Grant nos. 2019XZZX004-01, and 2020QNA4015).
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Ye, XW., Ding, Y. & Wan, HP. Statistical evaluation of wind properties based on long-term monitoring data. J Civil Struct Health Monit 10, 987–1000 (2020). https://doi.org/10.1007/s13349-020-00430-3
- Structural health monitoring
- Wind properties
- Angular–linear model
- Finite mixture distribution
- Genetic algorithm
- Joint probability density function