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The tensile force on the hanger cables of a suspension bridge is an important indicator of the structural health of the bridge. Tensile force estimation methods based on the measured frequency of the hanger cable have been widely used. These methods empirically pre-determinate the corresponding model order of the measured frequency. However, because of the uncertain flexural rigidity, this empirical order determination method not only plays a limited role in high-order frequencies, but also hinders the online cable force estimation. Therefore, we propose a new method to automatically identify the corresponding model order of the measured frequency, which is based on a Markov chain Monte Carlo (MCMC)-based Bayesian approach. It solves the limitation of empirical determination in the case of large flexural rigidity. The tensile force and the flexural rigidity of cables can be calculated simultaneously using the proposed method. The feasibility of the proposed method is validated via a numerical study involving a finite element model that considers the flexural rigidity and via field application to a suspension bridge.

In order to deeply study the influence of the coal bedding structure on coal gas adsorption, low nuclear magnetic resonance (LNMR) and a confining pressure loading system were used to carry out the LNMR experiment of gas adsorption of high-rank coals with different beddings under different confining pressures. The results showed that the amount of gas adsorption of high-rank coals with different beddings increases with time and decreases with the increase of confining pressure. In the process from low confining pressure to high confining pressure, the coal sample with oblique bedding (bedding angles 30°, 45°, and 60°) has the largest average increment of gas adsorption, followed by the coal sample with vertical bedding (bedding angle 90°), and the coal sample with parallel bedding has the smallest increment of gas adsorption (bedding angle 0°). The linear function relation between the different-bedding high-rank coal gas adsorption state and the confining pressure is y = a – bx . The relation between the free peak area and the confining pressure conforms to the exponential function y = a + b exp( cx ). Different-bedding high-rank coal adsorption peaks and the peak area decrease with the increase of confining pressure, and the free peak continues to move to the left; that is, the large pores gradually shrink. With the increase of angle and bedding, the area of the adsorption peak increases first and then decreases, presenting an “inverted V” shape on the whole. The area of the free peak decreases first and then increases, presenting a “V” shape on the whole.

In order to study the pore structure characteristics of high-rank coals with different bedding, NMR experiments were carried out for high-rank coals with different bedding angles (0°, 30°, 45°, 60°, and 90°). The results show that the distribution of T2 map of high-rank coal with different bedding is similar to some extent, showing a double peak or triple peak distribution, and the first peak accounts for more than 97% of the total, indicating that small holes are developed in high-rank coal with different bedding, while macropores are not developed. The influence of bedding angle on the fracture proportion is less than 0.3%. Compared with the fracture proportion, the effect of bedding angle on the proportion of microhole, medium hole, and large hole is greater and presents a certain rule. There are certain differences in T2 cutoff value (T2C) of high-rank coal with different bedding. The relationship between bedding angle and T2C conforms to exponential function, and the correlation degree R2 is 0.839. The research results provide a theoretical basis for gas extraction and utilization and prevention of gas disaster in coal mines in China.

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