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It is essential to reliably predict the human-induced vibrations in serviceability design of footbridges to ensure the vibration levels to be within the acceptable comfort limits. The human-induced structural responses are dependent on the dynamic properties of structures and human-induced excitations. For concrete footbridges, the elastic modulus of concrete is a vital parameter for determining the dynamic structural properties. To this end, a two-stage machine learning (ML)-based method is first proposed for modeling the elastic modulus of concrete. At the first stage, the ensemble algorithm, i.e. the gradient boosting regression tree (GBRT), is used to predict the compressive strength by selecting eight parameters, including concrete ingredients and curing time, as the inputs. At the second stage, the elastic modulus of concrete is modeled by using the GBRT method with the compressive strength as the input. Pedestrian crowd-induced load is the most common and crucial design load for footbridges. To consider the inter- and intra-subject variability in walking parameters and induced forces among persons in a crowd, a load model is developed by associating a modified social force model with a walking force model. By integrating the two submodels of structure and excitation, an intelligent analysis method for human-induced vibration is finally developed. A concrete footbridge with typical box cross-section subjected to human-induced excitation is analysed to illustrate the application of the proposed method.

Mostly, magnetorheological (MR) dampers were optimized based on individual performance, without considering the influence of structure parameters change on vehicle performance. Therefore, a multi-objective optimization scheme of MR damper based on vehicle dynamics model was proposed. The finite element method was used to analyze magnetic flux density distribution in tapered damping channel under different structure parameters. Furthermore, the damping force expression of the tapered flow mode MR damper was derived, and the damping force was introduced into the vehicle dynamics model. In order to improve the ride comfort and operation stability of the vehicle, a collaborative optimization platform combining magnetic circuit finite element analysis and vehicle dynamics model was established. Based on this platform, the optimal design variables were determined by comfort and stability sensitivity analysis. The time domain optimization objective and frequency domain optimization objective are proposed simultaneously to overcome the lack of time domain optimization objective. The results show that compared with the time domain optimization and the initial design, the suspension dynamic deflection, tire dynamic load and vehicle body vertical acceleration are decreased after the time-frequency optimization. At the same time, in the frequency domain, the amplitude of vibration acceleration in each working condition is significantly reduced.

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