In this paper, the recently developed analytical mode decomposition with a constant or time-varying cutoff frequency is extended into the decomposition of a non-stationary discrete time sequence. The discretization of the signal and the selection of the cutoff frequency may cause the failure of low frequency component extraction. In this study, to eliminate the effects of the signal discretization, the one-step, two-step, and four-step low-pass filters with cutoff frequencies are proposed. Based on the theoretical derivation, the previous one-step low-pass filter is effective only when the cutoff frequency is not greater than a quarter of the sampling frequency and the maximum frequency of the signal not greater than a half of the sampling frequency. In this study, if the cutoff frequency is less than or equal to a quarter of the sampling frequency, a two-step low-pass filter is proposed to extract the low frequency component. If the cutoff frequency is greater than a quarter of the sampling frequency, a four-step low-pass filter with frequency shifting process is proposed. When the time-varying cutoff frequency is not always larger than or less than a quarter of the sampling frequency, a sufficient condition, which is the sampling frequency is greater than four times of the maximum frequency of the signal component, is provided in this study. Two numerical examples are used to validate the effectiveness of the proposed low-pass filters. Both the theoretic derivation and numerical simulations show that the proposed filters can analytical extract the discrete low frequency component with an appropriate cutoff frequency.

Dynamic displacement is an important indicator for bridge safety estimation but is difficult to measure due to economic or technological limitations. Dynamic responses of a passing vehicle include the bridge dynamic response information. This study proposes a framework utilizing artificial neural networks to efficiently and accurately predict bridge displacements from the dynamic response of a passing vehicle. The input and the output of the networks are the vehicle acceleration responses and the bridge dynamic displacement responses, respectively. The implemented framework consists of convolutional neural network (CNN) and gated recurrent units (GRU). CNN is adept at feature extraction in the microcosm of short‐term time series, revealing intricate nuances. As a complement, GRU plays a crucial role in extracting features of macroscopic long‐term time series. The CNN‐GRU network can efficiently extract higher‐order features contained in the input data. Numerical experiments are conducted using the developed vehicle‐bridge interaction (VBI) system model to obtain requisite data for training the deep neural network. The impact of the presence or absence of roadway irregularities and the number of vehicles are discussed, indicating the accuracy of the framework. Furthermore, a laboratory experiment is conducted to further assess the performance of the CNN‐GRU network. Results indicate that the CNN‐GRU network offers an effective alternative for bridge displacement measurements.

Traditional pavement materials used in the orthotropic steel bridge deck suffer from various pavement distresses and thus reduce the service life of the steel bridge. Therefore, this study proposed a novel engineered material named polyester polyurethane concrete (PPUC) for the steel bridge deck pavement. Indoor laboratory experiments and numerical comparison analysis were conducted to comprehensively assess the feasibility of PPUC as the steel bridge deck pavement and ordinary Portland cement (OPC), guss asphalt concrete (GAC), asphalt mastic concrete (SMAC) and epoxy asphalt concrete (EAC) were used as references compared with PPUC. After the specimens of PPUC were prepared by mixing polyester polyurethane binder (PPUB) and aggregate with the binder-aggregate ratio of 15%, the specimens were subjected to compressive test, splitting tensile test, flexural tensile strength test, wheel tracking test, low-temperature cracking test, freeze-thaw splitting test, shear test and pull-out test. The mechanical performance comparison of different pavement structures with different materials was also analyzed using finite element analysis method. Results show that PPUC presents higher mechanical properties (compressive, tensile and flexural strength) compared to OPC, and it has good durability properties compared to SMAC, GAC, and EAC, such as high temperature stability, low temperature cracking resistance and water stability. In addition, PPUC has strong adhesive property with steel deck and does not change significantly with temperature changes. The finite element simulation results show that the maximum tensile strength and maximum compressive strength of PPUC in the single-layer structure are 0.51 MPa and 3.52 MPa respectively, which are much smaller than the experimental values and those of other materials. The maximum tensile strength and maximum shear strength of PPUC in the PPUC + SMAC composite structure are 0.232 MPa and 0.148 MPa respectively, which are also much smaller than the experimental values and those of other structures. The mechanical performance comparison results indicate that PPUC pavement structure can improve the overall stiffness of the steel bridge deck and protect the wear layer. These results support that the PPUC has a promising application for the steel bridge deck pavement.

This paper proposes the use of Gaussian Bayesian networks (GBNs) for damage detection of steel truss bridges by using the strain monitoring data. Based on the proposed damage detection procedure, a three-layer GBN model is first constructed based on the load factors, structural deflections, and the stress measurements of steel truss bridges. More specifically, the load factors of the structures are defined as the first-layer network nodes, structural deflections are considered as the second-layer network nodes, and the third-layer nodes of the GBN model are built based on the stress data of the truss elements. To achieve the training for the constructed GBN model, the finite element analysis of the bridge structures under the different load factors is performed. Then, the training of the network is performing by using the maximum likelihood estimation approach, and the optimized network parameters are obtained. Based on the trained network model, the measured load factors and the corresponding stress monitoring data of a limited number of truss elements are considered as input, and the stress measurements of all truss elements of bridges can be accurately estimated by searching the optimized topological information among network nodes. For a steel truss bridge, when the truss elements are damaged, the stress states of the damaged elements will be changed. Therefore, a damage index is further constructed for damage detection of steel truss bridges based on the changed stress states of those damaged elements. To verify the feasible and effective use of the proposed damage detection approach, an 80 m steel truss bridge with various damage cases was conducted as numerical simulations, and the investigation results show that the trained GBN can be accurately used for stress prediction of steel truss bridges, and the proposed damage index with the estimated stress data can be further applied for structural damage localization and quantification with a better accuracy. Furthermore, the results also suggest that the proposed damage detection procedure is accurate and reliable for steel truss bridges under vehicle loads.