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It is common to assume the relationship between temperature and temperature response is instantaneous in bridge health monitoring systems. However, a time-lag effect between temperature and thermal strain response has been documented by the analysis of monitored field data of concrete box-girder s. This effect is clearly reflected by the ring feature in the temperature-strain correlation curve. Inevitably, the time-lag effect has an adverse impact on the accuracy and reliability of state assessment and real-time warning for structural health monitoring (SHM) systems. To mitigate the influence of the time-lag effect, a phase-shifting method is proposed based on the Fourier series expansion fitting method. The time-domain signal is firstly converted into the frequency domain signal to compute the phase difference between temperature data and response strain data at each decomposed order. Subsequently, the total phase difference can be obtained by weighted summation. The signal processing effectively reduces the hysteresis loop area and enhances the correlation between the structural response data and the temperature data. When processing the daily data in different seasons, it is found that after subtraction by the proposed method, the linear feature becomes dominant in the relationship between temperature and the strain during long-term observation.

Nonlinear mapping of the fuzzy relation exists between structural inputs and outputs, as well as between structural global and local response. It is difficult for the numerical simulation to introduce the nonlinear effects of the variability of loading effects and the uneven deterioration of structure. The big monitoring data make it feasible to mine these nonlinear effects, and the network of deep learning is a good tool to establish the nonlinear mapping model between the multi-source monitoring data. Based on the temperature, strain, and dynamic displacement data from the structural health monitoring (SHM) system of an in-service bridge, the deep learning regression network of long short-term memory (LSTM) is designed and trained, which is used for modeling the nonlinear mapping between the structural input-output and the structural global-local response. The digital model of the nonlinear mapping of the temperature to temperature-induced strain, dynamic displacement to vehicleinduced strain, and vehicle-induced strain to dynamic displacement is established by the deep learning of LSTM regression network. The established nonlinear mapping model can be used to recover the abnormal and missing data with multi-source data, and it digitally linked the structural input-output and the structural global-local response. Then, the utilization of SHM data analytics will be enhanced, and the digital modeling for the in-service state of the bridge structure will be fast implemented.

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Fatigue cracks in orthotropic steel decks (OSDs) have been a serious problem of steel bridges for a long time. The structural stress approach is an important approach for fatigue life evaluation of welded structures. Firstly, two parameters and the mesh sensitivity of the stress-based integration equivalent structural stress approach (stress integration approach for short) are analyzed in this paper. Then, the applicability of the master S-N curve is verified based on experimental data of the deck-rib welding details in OSDs. Finally, the multi-scale finite element model (FEM) of Jiangyin Bridge is established, and the bridge fatigue life calculation steps based on the stress integration approach are given. The influence of the slope of the master S-N curve at high cycles on the bridge fatigue life is discussed. Further, the weld parameter influences on the bridge fatigue life are analyzed, as including the following: (1) The determination of the influence of the weld size changes caused by weld manufacturing errors on the bridge fatigue life; (2) the proposal of a new grinding treatment type, and the analysis of influence of the grinding radius on fatigue life; and (3) a comparison of the fatigue life of the deck-rib welding details under 80% partial penetration and 100% full penetration. The results show that the structural stress calculated by the stress integration approach does not change significantly with the parameters of the isolation body width w and the distance δ between the crack propagation surface and the reference surface. To simplify the calculation, δ is set as 0, and w can be set as the mesh size along the weld length direction. The mesh size of the stress integration approach is recommended as 0.25 times the deck thickness. The slope of the master S-N curve at high cycles significantly affects the bridge fatigue life, and a slope of 5 is reasonable. The weld parameter studies for the deck-rib welding details in the OSD of Jiangyin Bridge show that the change of weld size caused by manufacturing errors can obviously affect the bridge fatigue life, and the fatigue life of five different weld types varies from 51 years to 113 years. The new grinding treatment type, without weakening the deck, is beneficial to improving the bridge fatigue life. The fatigue life increases by approximately 5% with an increase of the grinding radius of 2 mm. The fatigue life of 80% partial penetration is slightly higher than that of 100% full penetration.

An orthotropic steel deck (OSD) has a complicated structure, and its fatigue life is mainly determined by various welding details. Fatigue assessment of deck-to-rib welding details (DRWDs) under long-term train loads is an important concern for engineers. Properly assessing the initial residual stress and the mechanism of stress relaxation in DRWDs under long-term external loading is a prerequisite for predicting the fatigue damage and service life of OSDs. In this paper, a finite element analysis method is proposed to calculate the residual stress relaxation in DRWDs of OSDs under constant/variable amplitude cyclic loading. First, experiments on full-size OSD specimens were carried out using the hole drilling strain-gauge method, and the multi-axial distribution characteristics of residual stress on the sub-surface of the deck were obtained. On this basis, a refined residual stress analysis model of DRWDs using thermal-structural sequence coupling analysis and life and death unit technology is established, and the accuracy of the model is verified by the test data. Second, a coupling stress analysis model that considers the welding residual stress and mechanical stress using cyclic plastic constitutive model is established. The combined influence of number of cycles, stress amplitude, and stress ratio on multi-axial residual stress relaxation effect under constant/variable amplitude cyclic loading is investigated. Finally, a release formula of welding residual stress relaxation coefficient is proposed based on the external loading stress amplitude, stress ratio, and material yield stress. The results show that (1) with the increase in the number of loading cycles, the stress decreases until it is stabilized, while the global distribution of welding residual stress remains unchanged. Most of the welding residual stress release (about 95%) occurs in the first cycle; (2) the residual stress relaxation decreases with the increase in stress amplitude and increases linearly with the stress ratio; (3) the residual stress release is controlled by the maximum amplitude stress in the variable amplitude cyclic loading. After the residual stress is released, the stress will not continue to be released if the DRWDs have the same or smaller amplitude loading.

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