Real-time dynamic displacement and acceleration responses of the main span section of the Tianjin Fumin Bridge in China under ambient excitation were tested using a Global Navigation Satellite System (GNSS) dynamic deformation monitoring system and an acceleration sensor vibration test system. Considering the close relationship between the GNSS multipath errors and measurement environment in combination with the noise reduction characteristics of different filtering algorithms, the researchers proposed an AFEC mixed filtering algorithm, which is an combination of autocorrelation function-based empirical mode decomposition (EMD) and Chebyshev mixed filtering to extract the real vibration displacement of the bridge structure after system error correction and filtering de-noising of signals collected by the GNSS. The proposed AFEC mixed filtering algorithm had high accuracy (1 mm) of real displacement at the elevation direction. Next, the traditional random decrement technique (used mainly for stationary random processes) was expanded to non-stationary random processes. Combining the expanded random decrement technique (RDT) and autoregressive moving average model (ARMA), the modal frequency of the bridge structural system was extracted using an expanded ARMA_RDT modal identification method, which was compared with the power spectrum analysis results of the acceleration signal and finite element analysis results. Identification results demonstrated that the proposed algorithm is applicable to analyze the dynamic displacement monitoring data of real bridge structures under ambient excitation and could identify the first five orders of the inherent frequencies of the structural system accurately. The identification error of the inherent frequency was smaller than 6%, indicating the high identification accuracy of the proposed algorithm. Furthermore, the GNSS dynamic deformation monitoring method can be used to monitor dynamic displacement and identify the modal parameters of bridge structures. The GNSS can monitor the working state of bridges effectively and accurately. Research results can provide references to evaluate the bearing capacity, safety performance, and durability of bridge structures during operation.

To investigate the dynamic characteristics of a self-anchored suspension bridge (i.e. Tianjin Fumin Bridge), a real time kinematic-global navigation satellite system (RTK-GNSS) is used to achieve the displacement responses of the structure. Seeing the defect in the positioning accuracy of RTK-GNSS, a combined method (EEMDWP) of ensemble empirical mode decomposition (EEMD) and wavelet packet (WP) analysis is firstly put forward to improve the precision of the vibration signals. Subsequently, fast Fourier transform and the random decrement technique are applied to estimate the natural frequency and the corresponding damping ratio of the structure. Meanwhile, to contrast the field measurement results, the finite element model (FEM) of the structure is established. Finally, the analysis results indicate that: (1) the RTK-GNSS technique is a powerful tool for monitoring the deformation of long-span bridges; (2) the proposed EEMDWP method is demonstrated to be better than the single EEMD or WP method; (3) the structural dynamic parameters are successfully obtained (i.e. the first natural frequency: 0.5873 Hz, the corresponding damping ratio: 2.12%); (4) the results from the field measurement are in agreement with the FEM with a difference of about 5% from each other.

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With the increasing number of long span bridges, real-time, accurate and continuous monitoring of their safety is important at present. This study investigates the combination of a global navigation satellite system (GNSS) and accelerometer for monitoring dynamic and semi-static characteristics of bridge structures. A field experiment was conducted with the integration of a GNSS and accelerometer. Considering the noise interference of GNSS monitoring, performance tests were first conducted in different environments to investigate the noise characteristics. Next, complete ensemble empirical mode decomposition with adaptive noise-wavelet packet (CEEMDAN-WP) algorithm was chosen for denoising, among which a double criterion based on the correlation coefficient and effective coefficient was proposed to sift the intrinsic mode functions. After the noise reduction process, structural dynamic displacements and modal frequencies were successfully extracted from the 50 Hz GNSS real-time kinematic (GNSS-RTK) and accelerometer data, in which the displacements presented a consistent trend and the first natural frequency was the same (i.e. 0.369 Hz). Structural semi-static characteristics were evaluated by using 1 Hz (RTK), post-processed kinematic, and precise point positioning data. With reference to relevant specifications, the structural failure probability of the bridge in the vertical direction was calculated to be 0.4319. The results indicate that GNSS-RTK is reliable in monitoring structural dynamic and semi-static displacements of the bridge. Additionally, the proposed improved CEEMDAN-WP with double criterion is effective for background noise reduction. In addition, there may be some non-adequate behaviors, such as heavy traffic and vehicle overload, leading to the critical operation of the bridge.

A one-dimensional generalized magnetothermoelastic problem of a thermoelastic rod with finite length is investigated in the context of the fractional order thermoelasticity. The rod with variable properties, which are temperature-dependent, is fixed at both ends and placed in an initial magnetic field, and the rod is subjected to a moving heat source along the axial direction. The governing equations of the problem in the fractional order thermoelasticity are formulated and solved by means of Laplace transform in tandem with its numerical inversion. The distributions of the nondimensional temperature, displacement, and stress in the rod are obtained and illustrated graphically. The effects of the temperature-dependent properties, the velocity of the moving heat source, the fractional order parameter, and so forth on the considered variables are concerned and discussed in detail, and the results show that they significantly influence the variations of the considered variables.