Analytical Mode Decomposition of Dynamic Structural Response for The Detection of Damage

损伤检测是识别对结构系统性能产生不利影响的材料和/或几何特性变化发生的过程。目标是将主观和不一致的视觉检查转变为客观可靠的退化结构条件筛选，特别是在地震和爆炸等极端事件中。目前可用的大多数技术都依赖于建立一个没有随时间变化的损伤的结构模型，这在极端事件中通常是不现实的。该奖项支持开发无模型和自适应数据分析技术的基础研究。这项新技术将能够对随时间变化的结构条件进行准确而有力的评估，这种评估越来越多地应用于灾难事件发生后的民用基础设施。因此，本研究的结果将极大地有利于事后响应和恢复，从而增强弹性和稳定经济。这项技术将通过维基百科页面提供，可能适用于科学、工程、医疗保健和金融行业的多个学科。这些多学科的应用将有助于扩大代表性不足的群体在研究中的参与，并对工程教育产生积极影响。经验模态分解是一种非参数的自适应损伤检测技术，自1996年以来已被证明在处理非平稳和非线性动态响应方面具有强大的功能。然而，它从未在数学上被证明能够在各种应用中保证成功，因此在分析噪声数据、弱间歇性波动、紧密间隔的振动模式和振动模式的时间变化方面面临挑战。本研究旨在为结构动力响应分解提供数学基础，探索时变结构损伤检测的解析模态分解方法。研究小组将建立一个采样率和有限数据长度标准，以保证离散时间序列的准确分解，开发一种新的自适应小波变换，用于确定与时间相关的分频的最佳选择，为最近发现的非线性结构的新系统响应特性关系推导出计算效率高的解决方案，并通过实验验证该方法的鲁棒性、准确性、分析分解在不同非线性复杂结构的系统识别和损伤检测中的有效性。

Damage detection is the process of identifying the occurrence of changes to the material and/or geometric properties of a structural system that adversely affect performance. The goal is to transform subjective and inconsistent visual inspections into objective and reliable condition screening of degrading structures, in particular during extreme events such as earthquakes and blasts. Most techniques currently available depend on the establishment of a structural model with no damage progression over time, which is often unrealistic during extreme events. This award supports fundamental research for the development of a model-free and adaptive data analysis technique. The new technique will enable an accurate and robust evaluation of time-dependent structural conditions, which has been increasingly sought for applications in civil infrastructure immediately after a disastrous event. Therefore, results from this study will greatly benefit post-event response and recovery, leading to enhanced resiliency and stable economy. The technique will be made available through a Wikipedia page and may be applicable to multiple disciplines in science, engineering, healthcare and finance industries. These multi-disciplinary applications will help broaden the participation of underrepresented groups in research and positively impact engineering education.Empirical mode decomposition is a non-parametric and adaptive damage detection technique that has since 1996 been demonstrated powerful to deal with nonstationary and nonlinear dynamic responses. However, it has never been mathematically proven for guaranteed success in various applications and thus faced challenges in analyzing noisy data, weak intermittent fluctuations, closely-spaced modes of vibration, and temporal changes in vibration mode. This research is to provide a mathematical foundation to the decomposition of structural dynamic response and explore analytical mode decomposition for damage detection of time-varying structures. The research team will establish a sampling rate and finite data length criterion that guarantees an accurate decomposition of a discrete time sequence, develop a new adaptive wavelet transform for the optimal determination of time-dependent bisecting frequencies, derive a computationally efficient solution to a new system-response characteristics relationship recently discovered for nonlinear structures, and experimentally validate the robustness, accuracy, and efficiency of the analytical decomposition in system identification and damage detection of complex structures with different nonlinearities.