This study addresses a key issue that prevents the wide application of the novel predominant natural frequency (PNF)-based method for bridge scour monitoring, which is also applicable to the frequency-based health monitoring of other structures with soil–structure interaction. This issue is that no theory or method is currently available to guide the prediction of scour depths based on measured PNFs. The most feasible way is to first measure a few scour depths and their corresponding PNFs for obtaining the PNF–scour depth relationship, which is termed the bridge scour characteristic curve (BSCC) in this study, and then use this BSCC to predict future scour depths with measured PNFs. This study provides a comprehensive investigation into the BSCC and proposes a simulation-based optimization approach, in which the whole BSCC, that is, from light to severe scour conditions, can be predicted with a few measured scour depth–PNF data points (e.g., 2–4) within a small scour depth range (e.g., 0.2–0.5 m). The proposed approach integrates the Winkler-based numerical model into a global optimization technique to predict the whole BSCC to avoid the use of a closed-form BSCC function, which may not exist. Additionally, the approach can be used to estimate the modulus of subgrade reaction, which is very hard to obtain at real bridges. The performance of the proposed approach was evaluated using several practical scenarios with realistic multilayered soil conditions. We found that the proposed approach is accurate for predicting the whole BSCC with four measured points or even less, regardless of the scour severity for the measurements and the number of the soil layer. For applications, the influence of random errors in the measurements of PNFs and scour depths was investigated and concluded to be negligible. This study sets a solid cornerstone for the maturation of the PNF-based scour monitoring method and other frequency-based structural health monitoring methods with soil–structure interaction.

中文翻译：

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基于仿真优化的基于固有频率的桥梁冲刷监测的桥梁冲刷特性曲线

本研究解决了一个关键问题，该问题阻止了基于新的主固有频率 (PNF) 的桥梁冲刷监测方法的广泛应用，该方法也适用于其他具有土壤-结构相互作用的结构的基于频率的健康监测。这个问题是目前没有理论或方法可用于指导基于测量的 PNF 预测冲刷深度。最可行的方法是首先测量几个冲刷深度及其对应的 PNF 以获得 PNF-冲刷深度关系，在本研究中称为桥梁冲刷特征曲线（BSCC），然后使用该 BSCC 预测未来的冲刷深度与测量的 PNF。本研究对 BSCC 进行了全面调查，并提出了一种基于模拟的优化方法，其中整个 BSCC，即，从轻微到严重的冲刷条件，可以通过在小冲刷深度范围（例如，0.2-0.5 m）内的几个测量的冲刷深度-PNF 数据点（例如，2-4）进行预测。所提出的方法将基于 Winkler 的数值模型集成到全局优化技术中来预测整个 BSCC，以避免使用可能不存在的封闭形式的 BSCC 函数。此外，该方法可用于估计路基反应的模量，这在实际桥梁中很难获得。使用具有真实多层土壤条件的几个实际场景评估了所提出方法的性能。我们发现，无论测量的冲刷严重程度和土壤层的数量如何，所提出的方法都可以准确地预测具有四个测量点甚至更少的整个 BSCC。对于应用程序，研究了随机误差对 PNF 和冲刷深度测量的影响，并得出结论认为可以忽略不计。该研究为基于 PNF 的冲刷监测方法和其他具有土壤-结构相互作用的基于频率的结构健康监测方法的成熟奠定了坚实的基石。