Rational Models and Dynamical Characterization of Fatigue using Phase Space Warping and Smooth Orthogonal Decomposition

疲劳失效和裂纹扩展的准确预测超出了目前的最先进水平。目前的研究几乎完全集中在寻找？对吗？物理损伤变量 与此相反，这项工作的目的是将重点转移到抽象的，缓慢发展的，动态疲劳损伤变量？广义疲劳损伤坐标服从控制微分方程的简单数学形式。 精心设计的实验将显示这些可观察的坐标是什么，以及它们如何使用新的多变量和非线性时间序列分析（即，平滑正交分解和相空间弯曲）。 基于这一证据，合理的疲劳模型，管理这些抽象的损伤变量，并需要数学结构，以提供实验观察到的动态特性，将开发。 疲劳和相应的模型识别的实验表征将进行使用一种新的实验装置，允许疲劳损伤累积在各种加载环境中，与自然的动态耦合之间的损伤演化和结构动力学。 从基本的角度来看，这项工作将导致更好地了解疲劳损伤累积动力学，其与结构动力学和负载的相互作用，它将提供工具的开发和/或验证预测损伤演化模型。 这些工具将有助于发展真正的预测能力的结构健康监测（SHM）和基于状态的维护（CBM）technology.The实验数据分析工具和模型，在这项研究中开发的将有一个重大的影响，各种各样的SHM和CBM的应用。同样的方法也可以适用于表征其他缓慢发展的隐藏过程，如生理疲劳，驾驶非平稳的力量在地球物理和海洋学过程中，疾病的进展等，这项工作也支持与国际研究小组以及与一个国家实验室的合作。一个博士一级研究生和几名本科生将直接受益于拟议的活动。拟议的努力的跨学科性质将丰富学生的学习经验，让他们接触到现代非线性和多元数据分析技术及其在机械工程和其他领域的应用。由于计划将研究纳入教育活动，更广泛的学生也将更好地了解这些工具在分层系统的动态特性中的使用。一个新的本科生课程SHM的发展，预计将提高本科机械工程计划在罗得岛大学的学生接触到一个新的职业领域。

An accurate prognosis of fatigue failure and crack growth is beyond current state of the art. Current research is almost exclusively focused on finding the ?correct? physical damage variable. In contrast, the aim of this work is to shift this focus to abstract, slowly evolving, dynamical fatigue damage variables?generalized fatigue damage coordinates?that obey some simple mathematical form of a governing differential equation. Carefully designed experiments will show what these observable coordinates are and how they evolve in time using new multivariate and nonlinear time series analyses (i.e., smooth orthogonal decomposition and phase space warping). Based on this evidence, rational fatigue models, which govern these abstract damage variables and have needed mathematical structure to provide experimentally observed dynamical characteristics, will be developed. Experimental characterization of fatigue and corresponding model identification will be carried out using a new experimental apparatus allowing fatigue damage accumulation in various loading environments, with natural dynamic coupling between the damage evolution and structural dynamics. From the fundamental standpoint, this work will lead to improved understanding of fatigue damage accumulation dynamics, its interaction with structural dynamics and loads, and it will provide tools for the development and/or verification predictive damage evolution models. These tools will be instrumental in developing true prognostic ability for structural health monitoring (SHM) and condition based maintenance (CBM) technologies.The experimental data analysis tools and models developed in this study will have a major impact on a wide variety of SHM and CBM applications. The same methodology can also be applied to characterize other slowly evolving hidden processes, such as physiologic fatigue, driving nonstationary forces in geophysical and oceanographical processes, disease progression, etc. This work also supports collaborations with international research groups as well as with one national laboratory. One Ph.D. level graduate and several undergraduate students will directly benefit from the proposed activities. The interdisciplinary nature of the proposed effort will enrich the learning experience of students by exposing them to modern nonlinear and multivariate data analysis techniques and their applications in mechanical engineering and other fields. A wider set of students will also acquire a better appreciation for the use of these tools in the dynamical characterization of hierarchical systems due to the planned integration of research into education activities. The development of a new undergraduate course on SHM is expected to enhance the undergraduate mechanical engineering program at the University of Rhode Island by exposing students to a new career field.