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This paper presents a new perception in evaluating fretting fatigue damage nucleation and propagation lifetime under periodically forced circulation. A new approach, which is proposed in this paper, is to measure the change of the central point of power spectral density (CP-PSD) in different structural stiffness degradation stages. A notable aspect of this study lies in the combination between vibration amplitude and forced frequency of the fatigue-causing factors in beam structures. Additionally, it is found that randomization of the first phase from 0 to 2π yields more accurate modelling of the fatigue phenomenon. Results show that the CP-PSD parameter is significantly more sensitive compared to the regularly damage-evaluating parameters such as natural frequency, eigenvalues, or stress value. This reflects different levels of fatigue cycle effect on the structure in the experiment. At the same time, CP-PSD also categorizes the degradation level on different points on the structure under the periodically forced circulation. In addition, this paper also quantifies the relation between the changes of CP-PSD and each fatigue state. Results of this research will be a reference source to evaluate the lifespan of the structure by experimental methods.

Summary The bridge structures must work under random and complex excitation conditions. The vibration response of these structures includes two main components as a determining component and a stochastic component. Thus, using vibration data, the structural health monitoring (SHM) process for these structures requires eliminating random parts impact. The random decrement (RD) signature, a known technique to serve this requirement, is applied to analyze the bridge's vibrations under the ambient load (random excitation) in this study. The nonlinear viscoelastic model is used to evaluate the energy dissipation of material. Then, a new damage index, called the loss factor function (LF), determined from the power spectral density (PSD) of vibration modes, is used to assess material deterioration. In fact, only some vibration modes of structures that occur with large amplitude are considered to be determined. Therefore, the article evaluates some of the first vibration modes' energy dissipation to monitor the change of material's mechanical properties. The vibration of the Saigon bridge under actual traffic loadings over 9 years is used as an illustrative example. One single beam with the same modes of the bridge span is modeled and used to extract numerical data to train convolutional neural network (CNN). CNN is widely known at the current time with outstanding capabilities in the typical image classification. The distribution of these LF values is overall evaluated by using a featured image built from their contour plot images. With the supervised learning algorithm, the proposed network is trained to assess the deterioration level of materials. The output is the label corresponding to the deterioration level, and the inputs are featured images about energy dissipation.