Collaborative Research: Health Monitoring and System Identification of Complex Mechanical Systems Using Fractional-Order Calculus Modeling

检查和维护是管理和维护我国运输系统和基础设施质量的重要成本驱动因素。目前的战略是基于预防性的方法，不考虑实际的实时状态的一个特定的结构组件。在这些方法中，系统受到例行检查和部件的更换，这些部件是基于经验数据和估计寿命的数值预测的组合而预先安排的。这种方法是次优的，因为它们一方面可能导致更换功能齐全的部件，另一方面可能错过预定检查之间迅速恶化的状况。这项研究将开发新的方法来解决这两个缺点，通过调查新的建模和监测技术，特别适合和适用于现代复杂系统。 为了实现这种基于状态的监测方法，需要更好的理论和数值模型来模拟复杂机械系统的动态行为，并生成能够实时跟踪其状态的指标。该奖项支持基础研究，以开发基于分数微积分的数学和计算模型。从这项研究中产生的方法将是非常有用的应用，使用成像和遥感在结构，地质和生物介质。该项目的教育部分将包括开发一门新课程，向工程专业学生介绍分数阶微积分及其在工程系统建模中的应用。这项研究将涉及一项系统研究，以确定分数阶微分方程如何增强系统识别和监控的最新技术。分数阶模型是复杂工程系统建模的一种新的有用工具，但在工程中还不常见。它们在结构健康监测中的应用将为损伤检测和诊断提供一种新的方法，它将引入系统阶次作为系统评估的一个新参数，它将提供复杂系统动力学的高度数学结构化和简洁的描述。 更具体地说，这项工作将（1）确定结构损伤对宿主系统分数阶的影响，并开发方法来解释其对基本控制方程的影响;（2）使用分数阶方法来实现有效的降阶、子结构和反问题解决方案;（3）开发基于纯实验数据的系统识别分数阶模型;以及（4）开发实验验证的试验台。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

Inspection and maintenance are significant cost drivers to manage and preserve the quality of our nation's transportation systems and infrastructure. Current strategies are based on preventive approaches that do not consider the actual real-time status of a specific structural component. In these approaches, the systems are subject to routine inspections and replacement of components that are scheduled a priori based on a combination of empirical data and numerical predictions of the estimated life. Such approaches are sub-optimal because they may lead to replacement of fully-functional components, on the one hand, and may miss rapidly deteriorating conditions between scheduled inspections, on the other. This research will develop new methods to address both shortcomings by investigating new modeling and monitoring techniques particularly suited and applicable to modern, complex systems. To enable this condition-based monitoring approach better theoretical and numerical models are needed to simulate the dynamic behavior of complex mechanical systems as well as to produce metrics capable of tracking their status in real-time. This award supports fundamental research to develop mathematical and computational models based on fractional calculus. The methods resulting from this research will be highly useful in application that use imaging and remote sensing in structural, geological, and biological media. The educational part of this project will feature, among its different components, the development of a new course to introduce engineering students to fractional calculus and its applications to modeling of engineering systems.This research will involve a systematic study to determine how fractional-order differential equations will enhance the state-of-the-art in system identification and monitoring. Fractional-order models are a new and useful tool for modeling of complex engineering systems, however they are not yet common in engineering. Their application to structural health monitoring will provide a substantially new approach for damage detection and diagnostics, it will introduce the system order as a new parameter for system assessment, and it will provide highly mathematically structured and concise descriptions of the dynamics of complex systems. More specifically, this work will (1) determine the effect of structural damage on the fractional order of the host system and develop methodologies to account for its impact on the underlying governing equations; (2) use fractional approaches to achieve efficient order reduction, sub-structuring, and inverse problem solutions; (3) develop fractional models for system identification based on purely experimental data; and (4) develop testbeds for experimental validation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.