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We propose a novel representative power spectrum density as a specific characteristic for showing responses of spans during a long operational period. The idea behind this method is to use the representative power spectrum density as a powerful tool to evaluate the stiffness decline of spans during their operation period. In addition, a new measurement method has been introduced to replace the traditional method of monitoring the health conditions of bridges through a periodic measurement technique. This helps to reduce costs when carrying out testing bridges. Besides, the proposed approach can be widely applied not only in Vietnam but also in many other underprivileged countries around the world. Obtained results show that, during the operational process of spans, there is not only a pure vibration evaluation such as bending vibration and torsion vibration tests but also a combination of various vibration types including bending-torsion vibration or high-level vibrations like first-mode bending and first-mode torsion. Depending on each type of structure and material properties, different types of vibrations will appear more or less during the operational process of spans under a random moving load. Furthermore, the representative power spectrum density is also suitable for evaluating and determining many different fundamental vibrations through the same measurement time as well as various measurement times.

This study proposes two parameters, including the appearance frequency of harmonics (AFH) and the change in shape of the power spectral density (PSD), which are examined to assess the decline in stiffness of a bridge span. PSDs are obtained from the real vibration signals of the randomized traffic load model based on accelerometer multi-sensors that indicate the change in mechanical behavior of the structure over time. In addition, AFHs evaluate the workability of the structure. With these parameters in mind, actual vibrations in real beam structures are studied with the aim of using structural health monitoring to assess the bearing capacity reduction on Saigon Bridge’s spans. The results show that AFHs and the high-frequency regions relate to the decreased stiffness of the bridge’s spans over a given period of time. In the future, this research can be used to monitor structural health for various types of structure materials and many different bridge spans.

Power spectral density (PSD) is used for evaluating a structure’s vibration process. Moreover, PSD not only shows a discrete form of vibration but also presents various components in a vibration structure. The superposition of multiple vibration patterns on the same spectrum poses difficulty in analyzing the spectral information in the way needed to find the structure’s discrete vibration. This paper proposes a method for separating the synthetic vibration signal into a structure’s discrete vibration and other extraneous vibrations using the maximal overlap discrete wavelet transform (MODWT) method combined with the method of fast Fourier transform (FFT). With the combination of these two algorithms, MODWT and FFT, the signals of the synthesized vibration have been separated into component signals with different frequency ranges. This means that PSD will be formed, which is based on the combination of the single power spectra of the component signals. Thus, the single spectrum of each of these constructed components can be used to evaluate the types of discrete vibrations coexisting in a structure’s vibration process. The survey results in this paper show the sensitivity and suitability of select types of discrete vibrations to be separated out during the assessment of the structural change, so as to achieve the best possible plan for eliminating the unwanted and unexpected noise and vibration components.

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Through the combination of two approaches to evaluating structure change, a structural model and an unstructured model, a constructed model has been proposed in this article that evaluates structural change through the expansion of a linear model following the Hooke’s Law principle. The study has relied on the pure compression model of a structure’s concrete beam with elastic modulus ( E) and has added the coefficient of viscosity resistance ( C) to suggest a new evaluation method. By defining the aggregation of values of both coefficients C and E through the experimental model, the input parameters are the amplitude values of the vibration spectra and the values of frequencies based on machine learning, through which Z EC values are generated. The Z EC values determine a regression plane accumulated from the aggregation of values for both C and E. The article has introduced the Z EC concept as a useful parameter for the assessment of the quality of concrete structures by the nonlinear model with the appearance of the coefficient C. The results show that the Z EC values have expressed the distribution validity according to the structure’s differing degrees of change. Depending on the texture type and the structure status, these Z EC values will form different shapes. By implementing the actual surveys from many bridges with two types of beam structures, prestressed concrete and conjugated concrete, the Z EC values show the same development trend. On the contrary, in the case of a change in mechanical structure, the Z EC values tend to increase. This evidence proves, in regard to the process of structural change, that the larger the changes in the structure, the more pronounced the distribution of Z EC values, and the wider the distribution range. This shows that the ratio of the damping coefficient C to the elastic modulus E will become increasingly unstable as the structure becomes weaker and weaker. In the future, the results from this study can be applied in the assessment of many types of actual structures.