Sensitivity Analysis And Robust Optimal Control For Pedestrian-induced Vibration In Footbridges

The vibration serviceability problems of footbridges under pedestrian-induced excitation have been paid more and more attention,even regarded as a new type of disaster.If the vibration serviceability cannot satisfy the requirements,vibration control measures should be taken,among which TMD is the most widely used control measure.There are inherent uncertainties in bridge and human body dynamics as well as dynamic force generated by humans.Therefore,it is more reasonable to adopt the stochastic analysis and robust optimal control for pedestrianinduced vibration of footbridges.To reduce the computational effort and experimental cost of stochastic analysis for pedestrian-induced vibration,the Sobol’-based global sensitivity analysis method is utilized in this thesis to select important uncertain parameters.To improve the performance and design efficiency of TMD,a robust optimal design method for TMD based on the intrusive polynomial chaos expansion method is developed.The main contents are as follows:(1)The approaches for estimating the vertical vibration response of a footbridge induced by a single pedestrian and a crowd are introduced,in which two pedestrian-induced load models are considered,i.e.a moving force model and mass-spring-damping model conjunction with a moving force.The statistical characteristics of bridge modal parameters,pedestrian-induced dynamic force parameters and human body dynamics parameters are summarized.After that,the Monte-Carlo simulation method is adopted to quantify the uncertainty in pedestrian-induced vibration of a footbridge.(2)The Sobol’-based global sensitivity analysis method and OATbased local sensitivity method are briefly introduced.The influence of uncertainties in bridge and human body dynamics as well as dynamic force on the pedestrian-induced vibration of footbridges is investigated using these two methods.Parametric analysis is carried out to investigate the influence of the variation of the mean values of bridge modal parameters on the results of global and local sensitivity analysis.Systematic comparison of the results of global and local sensitivity analysis is performed to identify their similarities and differences.The possible reasons for the inconsistency in sensitivity analysis of pedestrian-induced vibration of footbridges in existing literature are discussed.The results show that the pedestrian-induced vibration only insensitive to the damping ratio and natural frequency of the human body for different footbridges or pedestrian crossing scenarios.(3)A robust optimal design method for TMD based on the intrusive polynomial chaos expansion method is developed.To verify the proposed method,a footbridge is taken as an example and the human-structure interaction are considered.The performance of TMD designed by the proposed method and deterministic method is compared by numerical analysis.The results show that the proposed method is characterized by extremely high computational efficiency(three orders of magnitude higher than the robust optimization method based on Monte-Carlo simulation),and the TMD designed by the proposed method has better performance when there are uncertainties in structural parameters.(13.7% better than the deterministic method).