The effect of different pedestrian densities (0.2, 0.5, 1, 1.5 and 4.6 persons/m²) on a pedestrian bridge is studied, the comfort level is evaluated according to the acceleration peak, and the most sensitive part of the acceleration response employs tuned mass dampers (TMDs) for vibration control. The study shows that the bearing capacity level of the pedestrian bridge with articulated piers meets the standard. Compared with a pier rigid connection system, the structural dynamic characteristics of pier articulation do not change much, and the vertical frequency and peak acceleration in the span are slightly smaller. The comfort evaluation results of the bridge with articulated piers are the same as those of the bridge with a rigid pier. The TMD setting can effectively reduce the human-induced vibration time response, the vibration reduction efficiency can reach 52%, and the comfort level changes from CL2 to CL1 after vibration reduction.

To study the standardized evaluation method of vibration comfort of pedestrian bridges, the effect of the transient response term is ignored based on the generalized single degree of freedom (SDOF) method with reference to the American Institution of Steel Construction inc (AISC 11) specification. The resonance conditions between the crowd and the bridge structure are also considered, and the pedestrian bridge structure is simplified to an SDOF system. Then, the peak acceleration of the structure under crowd excitation is directly calculated using the generalized crowd load, and the comfort evaluation is carried out according to the German EN03 code and the Chinese code. For a new pedestrian bridge with hinged piers, human-induced vibration tests were carried out to obtain the structural acceleration time response data under various crowd load excitation conditions, and the acceleration values calculated with the numerical simulation method, the frequency response function method, the generalized SDOF method, and the proposed method were compared with field measurements. The results show that for the normal excitation condition with a crowd density less than or equal to 0.2 person/m², the acceleration maximum error for the proposed method is between 4.22% and 13.28%. The error is only 6.35% compared with the finite element simulation results. The method can derive peak acceleration by performing only modal tests, eliminating errors caused by different testers and errors due to deflection measurements. It saves considerable time cost and economic cost, and improves the speed of pedestrian bridge comfort evaluation. Therefore, the method proposed for the first time in this study can accurately assess the human-caused vibration comfort of pedestrian bridges with articulated piers. Although the hinged-pier and column steel pedestrian bridge meets the code requirement of a vertical first-order frequency greater than 3 Hz, it is recommended to add TMD vibration damping measures to the bridge in order to improve pedestrian comfort.

Dynamical systems with a distributed yet interconnected structure, like multi-rigid-body robots or large-scale multi-agent systems, introduce valuable sparsity into the system dynamics that can be exploited in an optimal control setting for speeding up computation and improving numerical conditioning. Conventional approaches for solving the Optimal Control Problem (OCP) rarely capitalize on such structural sparsity, and hence suffer from a cubic computational complexity growth as the dimensionality of the system scales. In this paper, we present an OCP formulation that relies on graphical models to capture the sparsely-interconnected nature of the system dynamics. Such a representational choice allows the use of contemporary graphical inference algorithms that enable our solver to achieve a linear time complexity in the state and control dimensions as well as the time horizon. We demonstrate the numerical and computational advantages of our approach on a canonical dynamical system in simulation.

Spatially-variant morphological operators are studied extensively in the literature for image processing. In this paper, first, we model a reasonable spatially-variant morphological regularization method based on nonlocal amoeba kernel for general inverse problems in imaging (e.g., denoising, deblurring and super resolution). The novel regularization term which provides spatially adaptive prior information, resulting in a powerful overall setting for blurred image with seriously noises. And second, the inverse problems in imaging are formulated as to minimize the TV cost function which consists of data-fidelity term and proposed morphological regularization term. For optimization problem, Bregman iteration algorithm and operator splitting technique are effectively used in this stage in order to minimize the TV functional. Finally, numerical results on inverse problems show that the proposed method gives better performance than state-of-the-art algorithms in terms of both PSNR and visual perception, which demonstrates the efficiency of our proposed algorithm.

The effect of different pedestrian densities (0.2, 0.5, 1, 1.5 and 4.6 persons/m²) is studied, and the comfort level is evaluated according to the acceleration peak, and the most sensitive part of the acceleration response is set up with tuned mass dampers (TMD) for vibration control. The study shows that the bearing capacity level of the pedestrian bridge with articulated piers and columns meets the standard. Compared with the pier-column rigid connection, the structural dynamic characteristics of pier-column articulation do not change much, and the vertical frequency and peak acceleration in the span are slightly smaller. The comfort evaluation results are the same as those of the pier-column rigid pedestrian bridge. The setting of TMD can effectively reduce the human-induced vibration time response, and the vibration reduction efficiency can reach 52%, and the comfort level changes from CL2 to CL1 after vibration reduction.