Structural health monitoring systems continuously monitor the operational state of structures, generating a large amount of monitoring data during the process. The structural responses of extreme events, such as earthquakes, ship collisions, or typhoons, could be captured and further analyzed. However, it is challenging to identify these extreme events due to the interference of faulty data. Real-world monitoring systems suffer from frequent misidentification and false alarms. Unfortunately, it is difficult to improve the system’s built-in algorithms, especially the deep neural networks, partly because the current neural networks only output results and do not provide an interpretable decision-making basis. In this study, a deep learning-based method with visual interpretability is proposed to identify seismic data under sensor faults interference. The transfer learning technique is employed to learn the features of seismic data and faulty data with efficiency. A post hoc interpretation algorithm, termed Gradient-weighted Class Activation Mapping (Grad-CAM), is embedded into the neural networks to uncover the interest regions that support the output decision. The in situ seismic responses of a cable-stayed long-span bridge are used for method verification. The results show that the proposed method can effectively identify seismic data mixed with various types of faulty data while providing good interpretability.
Carbon nanotubes (CNTs) have wide-ranging applications due to their excellent mechanical and electrical properties. However, there is little research on the nonlinear mechanical properties of thermal-electro-mechanical coupling. In this paper, we study the nonlinear vibrations of CNTs by a thermal-electro-mechanical coupling beam theory. The Galerkin method is used to discretize the partial differential equation and obtain two nonlinear ordinary differential equations that describe the first- and second-order mode vibrations. Then, we obtain the approximate analytical solutions of the two equations for the primary resonance and the subharmonic resonance using the multi-scale method. The results indicate the following three points. Firstly, the temperature and electric fields have a significant influence on the first-mode vibration, while they have little influence on the second-mode vibration. Under the primary resonance, when the load amplitude of the second mode is 20 times that of the first mode, the maximal vibrational amplitude of the second is only one-fifth of the first. Under the subharmonic resonance, it is more difficult to excite the subharmonic vibration at the second-order mode than that of the first mode for the same parameters. Secondly, because the coefficient of electrical expansion (CEE) is much bigger than the coefficient of thermal expansion (CTE), CNTs are more sensitive to changes in the electric field than the temperature field. Finally, under the primary resonance, there are two bifurcation points in the frequency response curves and the load-amplitude curves. As a result, they will induce the jump phenomenon of vibrational amplitude. When the subharmonic vibration is excited, the free vibration term does not disappear, and the steady-state vibration includes two compositions.
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