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An efficient algorithm is proposed for the stochastic responses of vehicle–bridge systems. The pseudo-excitation method is combined with the self-adaptive Gauss integration to handle the stochastic responses of vehicle–bridge systems, for which the statistic characteristics are calculated. The applicability and accuracy of the proposed hybrid numerical method are demonstrated by comparing the results with those from Monte Carlo simulation. Besides, nondimensional time is introduced to evaluate the stochastic responses of vehicles. [ABSTRACT FROM AUTHOR]

Abstract: To meet the application of nonlinear FEM analysis to the real bridge structure, a general and versatile nonlinear analysis program for concrete bridge structures is presented in this paper. The structural effects such as material nonlinear behavior, prestress effect, construction process, temperature, creep of concrete and so on, which are concerned in practical engineering, are covered. To simulate the nonlinear behaviors, an efficient 3D degenerated beam element is adopted. The step-by-step analysis method allows one to comprehend the structural behaviors of the bridges during the construction, service, and failure periods, respectively. Finally, two examples are studied to verify the accuracy of the program and demonstrate its application in practical bridge engineering. [Copyright &y& Elsevier]

The dynamic response of a vehicle-bridge system (VBS) has been a key problem in assessments of train-running safety on bridges, ultimately requiring reliability analyses owing to uncertain parameters and random rail irregularities. To improve the computational efficiency and promote the development of a reliability analysis for VBS, this paper proposes a novel approach incorporating a stochastic pseudo-excitation method (SPEM) to optimize a deep learning approach. This approach can more efficiently calculate the dynamic responses of a VBS than the traditional methods. In this study, the dynamic responses of the uncertain system produced by the SPEM were utilized as the training datasets for the deep learning approach. Based on the training datasets, a neural network was established to construct a numerical model consisting of two functional modules: a full convolutional network (FCN) training for the input rail irregularities and gated recurrent unit (GRU) layer for the VBS response prediction, i.e., a SPEM–FCN–GRU (SFG). The GRU cell was simulated by introducing the randomness of the excitation and uncertain parameters of the system into a portion of the cell, thereby enabling the numerical model to convey the randomness of the VBS and to obtain its stochastic response. Addition, long-time-domain samples of the VBS responses were predicted based on the short-time-domain samples. To verify the accuracy and applicability of the proposed method, a train running through a multi-span simply supported railway bridge was investigated. The dynamic responses of the train were analyzed using the training set data and Monte Carlo method (MCM) and the results showed good agreement with each other. Next, by introducing an algorithm combining a convolutional neural network (CNN) with the MCM and GRU (an MCM–CNN–GRU) and comparing it with the method proposed herein, it was verified that the proposed method has better predictions and higher efficiency than those of a traditional neural network. The prediction efficiency of the SFG was analyzed. Based on the shortcomings of the SFG, we proposed an optimized SFG algorithm. The short-time-domain results predicted by the proposed method were input into the training datasets for the deep learning architecture to enhance the number of training data for the prediction of long-time-domain responses. The efficiency and accuracy of the proposed method were verified by comparing them with those of traditional neural networks. As an example, the dynamic responses of a train running through a three-span bridge were computed by the SPEM; these could be adopted to predict those of a train running through a 10-span bridge. Finally, based on the simulated and predicted results, the reliability of the VBS was studied using a first-order reliability method. [ABSTRACT FROM AUTHOR]

A hybrid method combining the stochastic pseudo excitation method (SPEM) and the response surface method (RSM) was presented to handle the effect of both random characteristics of power spectral density of excitation and uncertain parameters. Based on basic principle of pseudo excitation method (PEM), an optimized algorithm was proposed to be SPEM. The effects of the uncertainties of structure and excitations could be considered through SPEM, thus directly acquiring the whole sampling results of random vibration of uncertain structural system. To reduce the cost of computing the total number of required finite element analysis simulations, RSM was adopted to hold calculated sampling results to gain the probability density function (PDF) of random vibration. The proposed method can consider both the effects of random characteristics of power spectrum of random excitations and the uncertainties of target system. Neverthless, Since the proposed method is based on the pseudo excitation method, the SPEM-RSM can handle the stochastic vibration analysis of determine and uncertain structure. In order to verify the accuracy and efficiency of proposed method, taking a single degree of freedom linear uncertain oscillator and a pier construction as two verification cases, the PDF of responses computed by the hybrid method was verified by Monte Carlo method (MCM), and the efficiency of the proposed method was presented. Then, stochastic responses of the railway continuous bridge subjected to earthquake were calculated, several uncertainties are involved in the computation. In addition, sensitivity analysis was solved for uncertain parameters. • A named as stochastic pseudo excitation method (SPEM) is proposed. • A hybrid method combing the SPEM and the response surface method (RSM) was presented. • The hybrid method handle the stochastic vibration of linear structure with various excitation. • The structural uncertainties can increase predictive uncertainty and discreteness for the stochastic response in this case study. • The most significant uncertain parameter in sensitivity of all the random variable is damping ratio. [ABSTRACT FROM AUTHOR]