In this paper, we investigate changes in the mechanical properties of complex structures using a combination of the discrete model, Fast Fourier Transform (FFT) analysis and deep learning. The first idea from this research utilizes the discrete model from a perspective that is different from the finite element method (FEM) of previous works. As the method in this paper only models the mechanical properties of structures with finite degrees of freedom instead of dividing them into smaller elements, it reduces error in evaluation and produces more realistic results compared to the FEM model. Another advantage is how it allows the research to survey both parameters that affect the mechanical properties of structures—the overall stiffness (K) and the damping coefficient (c)—during vibration, while previous researches focus only on one of these two parameters. The second idea is to use FFT analysis to increase the sensitivity of the signal received during vibration. FFT analysis simplifies calculations, thereby reducing the effect of noise or errors. The sensitivity achieved in FFT analysis increases by 25% compared to traditional Fourier Transform (FT) analysis; moreover, the error in FFT analysis compared to experimental results is quite small, less than 2%. This shows that FFT is a suitable method to identify sensitive characteristics in evaluating changes in the mechanical properties. When FFT is combined with the discrete model, results are much better than those of several existing approaches. For the last idea, the manuscript applies deep learning (FFT-deep learning) in the noise reduction process for the original data. This makes the results much more accurate than in previous studies. The results of this research are shown through the monitoring of spans of the Saigon Bridge—the biggest and most important bridge in Ho Chi Minh City, Vietnam—during the past 11 years. The correspondence between the theoretically obtained result and the experimental one at the Saigon Bridge suggests a new area for development in evaluating and forecasting structural changes in the future.

在本文中，我们结合使用离散模型、快速傅立叶变换 (FFT) 分析和深度学习来研究复杂结构的力学性能变化。本研究的第一个想法是从不同于以往工作的有限元方法 (FEM) 的角度利用离散模型。由于本文中的方法仅对具有有限自由度的结构的力学特性进行建模，而不是将它们划分为更小的单元，因此与 FEM 模型相比，它减少了评估误差并产生了更真实的结果。另一个优点是它允许研究调查影响结构力学性能的两个参数——整体刚度 ( K ) 和阻尼系数 ( c)——在振动过程中，以前的研究只关注这两个参数之一。第二个想法是使用FFT分析来增加振动过程中接收到的信号的灵敏度。FFT 分析简化了计算，从而减少了噪声或错误的影响。与传统傅立叶变换 (FT) 分析相比，FFT 分析的灵敏度提高了 25%；此外，与实验结果相比，FFT 分析的误差非常小，小于 2%。这表明 FFT 是一种在评估机械性能变化时识别敏感特性的合适方法。当 FFT 与离散模型相结合时，结果比现有的几种方法要好得多。对于最后一个想法，手稿在原始数据的降噪过程中应用了深度学习（FFT-深度学习）。这使得结果比以前的研究更准确。这项研究的结果通过对越南胡志明市最大和最重要的桥梁西贡大桥在过去 11 年中的跨度监测显示出来。理论获得的结果与西贡大桥的实验结果之间的对应关系为评估和预测未来结构变化提供了一个新的发展领域。