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属性对于监控其性能和确保其安全性至关重要。对这些性质的了解可以确定系统中发生的任何恶化的大小和位置。这样的知识将允许采取适当的所需行动，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识别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引起的测量不确定度将根据以间隔表示的可能值来处理，而不会事先对其性质做出任何假设。在系统辨识中严格考虑不确定性将导致对其行为的更可靠和可靠的预测。这种可靠和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难。研究团队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辨识在各自的领域中都是非常强大和成熟的技术，但到目前为止，它们很少被一起用于不确定情况下的反问题。通过研究分析、数值和计算相结合处理这两种方法的最佳方法，我们将发展出一类强大的技术，不仅用于手头的问题，而且用于大量其他具有偏微分方程(PDE)约束的反问题。在这项研究中，将重点使用区间有限元方法(IFEM)在优化的背景下，解决结构系统识别和损伤识别中出现的不确定情况下的反问题，而不需要对其性质进行事先假设。因此，预计这将是一个长期研究方案的第一步，该方案将在许多领域广泛应用，同时继续一致地专注于其基本的计算和数学方法。

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.