The stochastic response of cross-sea bridges is susceptible to the significant effects of wind and waves. In this study, an efficient probabilistic assessment framework for cross-sea bridges was developed by combining a wind–wave bridge (WWB) model with machine learning methods. The WWB model was first proposed based on finite element analysis (FEA) where the wind and wave parameters were obtained by structural health monitoring (SHM) and then correlated using copula models. The coupling effects in the wind–bridge and the wave–bridge were solved using the Newmark-β method. Taking a cable-stayed bridge as an example to illustrate the accuracy and efficiency of the proposed method, the WWB model was established and then performed to compute the dynamic response at different positions on the bridge. To deal with the time-consuming issues, a learning machine including support vector regression (SVR) and Latin hypercube sampling (LHS) was implemented to substitute further finite element calculations. The WWB model was simplified parametrically as response surfaces for stochastic wind and wave variables, and probabilistic simulations with a large number of samples were performed. The results show that the wind load controlled the displacement response of the girder, while the wave load dominated the base shear response of the foundation. The bridge response, considering when wind and waves were correlated, was 6%–25% lower than that when wind and waves were independent. Further response contour analysis demonstrated a direct relationship between the environmental parameters and the structural response to quickly estimate the bridge's maximum response in different return periods.

This paper presents wind tunnel tests on the wake characteristics of a three-blade horizontal axis wind turbine and the wake effect on the performance of a downstream turbine. For a single turbine model, the performance was determined and this was followed by measurement of the wind characteristics including velocities, turbulence intensities, and correlation in the wake flow field. Subsequently, taking two horizontal axis wind turbines in a tandem arrangement into account, their performance was tested and the aerodynamic mechanism was discussed. The results showed that the upstream turbine with blades set at a small pitch angle provided smaller disturbance to the flow, but as the blade turned faster, larger changes in the velocity and the turbulence intensity occurred in its wake due to the more frequent disturbance of the wind turbine. The correlation of wake velocities in the turbine swept area also obviously decreased from the free-stream situation. For the downstream turbine, the output power loss largely depended on the wake characteristics of the upstream turbine, which was closely related to lower wind velocities or higher turbulence intensities. The decrease in correlation of the streamwise velocity within the blade swept area is accompanied by the increased correlation of the tangential velocity, which may be beneficial to the downstream turbine’s performance.

Uncertainties from random multiple factors bring great challenges for assessing response of long-span bridges. This study proposes a dynamic analysis framework by integrating the wind–wave–bridge system with Bayesian regularized back propagation neural network, and then investigates stochastic response of a cross-sea cable-stayed bridge under extreme wind and wave parameters. The wind–wave–bridge system involving wind–bridge and wave–bridge interactions is constructed to calculate dynamic response of the bridge by Newmark-β method, considering stationary fluctuating wind fields and multidirectional random wave fields. To reduce the calculation cost, a Bayesian regularized back propagation neural network model is introduced, and the model evaluation is carried out to illustrate its accuracy and efficiency. After performing small-scale finite element analyses, the response statistics are obtained and later used as the known samples for training the neural network. The power spectrum analyses of the deterministic results are performed to investigate the contribution mechanism of the wind and wave. Finally, the correlation between the bridge response and the single wind–wave parameter is given by uncertainty analysis of the Bayesian regularized back propagation neural network model. The results show that the proposed framework is capable of capturing the nonlinear bridge response resulting from nonlinear wind and wave loads, which, however, is significant different from that under wind alone. The bridge response receives significant contribution from wind and waves relative to the vibration characteristic of the bridge at smaller wind and wave loads. The contribution from vibration characteristic of the bridge becomes significant at larger wind and wave loads. The uncertainty analyses illustrate the significant effects of four wind and wave parameters on girder, tower, and submerged structure.