Model Updating of Structural Systems with Incomplete Information: Global Identifiability, Optimal Instrumentation and Uncertainty Quantification

民用基础设施系统是任何国家经济福祉和进步的支柱。结构健康监测(SHM)领域涉及此类系统的适当维护和及时修复，从而确保其持续运行。在结构抗震设计中，拥有可靠的结构模型是必不可少的。通常，有限元模型用于预测实际系统(例如桥梁和建筑物)在各种条件下的行为，从日常服务条件(例如交通)到极端事件(例如地震、飓风)。然而，例如，工程师使用的建模假设存在一定程度的固有不确定性。此外，由于老化和季节性影响以及/或突发极端事件，系统的特性会随时间发生变化。模型修正的目的是利用从实际结构中获得的信息对结构模型的物理参数进行修正，以得到准确描述系统当前状态的修正模型。这一更新后的模型可用于预测、健康监测和可靠性分析。这个项目的重要性在于它处理了与实际执行有关的限制，例如没有足够数量的传感器，这可能会产生严重的影响，从而可能使整个模型表示的结果无效。在项目中，将按照以下步骤进行模型更新策略。首先，将制定全球确定和随后对仪器要求的限制的测试，提供最小的仪器设置以确保唯一识别。接下来，将开发一种振型归一化方案来估计完整的归一化模态信息，然后将其用于估计系统的物理参数。为了模式匹配的目的，将使用有效的模态参数比较措施，并且还将研究如何解释未观察到的模式。考虑到系统的不确定信息、环境波动和不可避免的测量噪声的存在带来的不确定性，该算法将扩展到一个随机框架中，使用贝叶斯推理和另一种基于敏感度的方法来表征不同步骤的不确定性传播。该项目的目标是表示结构在其当前状态下的分析。

Civil infrastructure systems form the backbone of the economic well-being and progress of any nation. The field of Structural Health Monitoring (SHM) addresses the proper maintenance and timely rehabilitation of such systems, thereby ensuring their continued functionality. In SHM, having a reliable model of the structure is essential. Usually, Finite Element models are used to predict how actual systems, e.g. bridges and buildings, behave under various conditions, from day-to-day service conditions (e.g. traffic) to extreme events (e.g. earthquakes, hurricanes). However, there is a certain level of uncertainty inherent, for example, to the modeling assumptions used by the engineer. In addition, a system changes its characteristics with time due to aging and seasonal effects, and/or sudden extreme events. The aim of model updating is to correct the physical parameters of a model of a structure using information obtained from the real structure so as to get an updated model accurately describing the current condition of the system. This updated model can then be used for predictive, health monitoring and reliability analyses purposes. The importance of this project is in its treatment of constraints related to practical implementation, e.g. not having a sufficient number of sensors, which could have serious implications and could consequently invalidate the results of the entire representation of the model. In the project, a model updating strategy will be conducted according to the following steps. First, tests for global ascertaining and consequent constraints on instrumentation requirements will be formulated, providing minimal instrumentation set-ups to guarantee unique identification. Next, a mode shape normalization scheme will be developed to estimate the complete normalized modal information, which will then be used to estimate the system's physical parameters. Efficient modal parameter comparative measures will be used for mode matching purposes and ways to account for unobserved modes will also is investigated. To account for the uncertainties introduced by uncertain information about the system, environmental fluctuations and the inevitable presence of measurement noise, the algorithm will be extended into a stochastic framework using Bayesian inference as well as an alternative sensitivity based approach to characterize the uncertainty propagation at different steps. The goal of the project is to represent the structure in its present condition for analysis.