A New Interval Finite Element Approach for Structural System Identification and Damage Detection under Uncertainty

识别现有结构系统的材料特性对于监测其性能和确保其安全至关重要。关于这些属性的知识允许确定系统中发生的任何劣化的幅度和位置。这些知识将允许采取适当的必要措施，以避免任何故障。识别程序需要大量的测量数据，这些数据通常与不确定性有关。考虑各种因素引起的不确定性是结构系统识别和损伤检测中最具挑战性的任务之一。在本项目中，由于设备公差和现场条件导致的测量不确定性将以可能的值（表示为间隔）进行处理，而无需对其性质进行任何事先假设。 在系统辨识中对不确定性的严格考虑将导致对其行为的更可靠和可靠的预测。这种可靠的预测对民用基础设施系统的安全至关重要，并将有助于减少危及生命的故障和灾害。研究小组将通过夏令营为高中生提供研究机会。虽然基于区间的方法和系统识别都是非常强大的和发达的技术在各自的领域，到目前为止，他们很少一起使用的背景下的反问题的不确定性。通过研究分析，数值和计算处理这两种方法相互结合的最佳方式，我们将开发一个强大的技术，不仅为手头的问题，但大量的其他反问题与偏微分方程（PDE）的约束。在这项研究中，重点将放在使用区间有限元方法（IFEM）的优化解决逆问题，出现在结构系统识别和损伤检测下的不确定性，没有事先假设其性质。因此，预计这将是一个长期研究计划的第一步，该计划将在许多领域的应用范围广泛，同时保持其基础计算和数学方法的一致性。

Identifying material properties of existing structural systems is crucial for monitoring their performance and ensuring their safety. Knowledge about these properties allows the determination of the magnitudes and the locations of any deterioration occurring in the system. Such knowledge will allow the proper required actions to avoid any failures. The identification procedures require a significant amount of measured data that typically are associated with uncertainty. Accounting for uncertainty due to different factors is one of the most challenging tasks in structural system identification and damage detection. In this project, uncertainty in measurements due to device tolerances and field conditions will be treated in terms of possible values expressed as intervals, without any prior assumptions on their nature. The rigorous consideration of uncertainty in system identification will lead to a more reliable and dependable predictions of their behavior. Such reliable and dependable predictions are crucial for the safety of civil infrastructure systems, and will contribute to the reduction of life endangering failures and disasters. The research team will offer research opportunities to high school students through summer camps. While interval-based methods and system identification are both very powerful and well-developed techniques within their respective fields, thus far they have scarcely been used together in the context of inverse problems under uncertainty. By investigating the best ways of analytically, numerically and computationally handling these two methodologies in conjunction with each other, we shall develop a powerful class of techniques not only for the problem at hand, but for a vast number of other inverse problems with partial differential equation (PDE) constraints. In this research an emphasis will be placed on the use of Interval Finite Element Methods (IFEM) in the context of optimization to solve for inverse problems that arise in structural system identification and damage detection under uncertainty without prior assumptions on its nature. This is therefore expected to be the first step of a long lasting research program which will be both broad in its scope of applications across many fields and at the same time remain coherently focused in its underlying computational and mathematical methodologies.