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保持我国交通系统和基础设施质量的重要成本驱动因素。目前的战略是以预防方法为基础的，没有考虑到具体结构部件的实际实时状况。在这些方法中，系统需要进行例行检查，并根据经验数据和估计寿命的数值预测预先安排更换部件。这种方法是次优的，因为一方面，它们可能导致更换功能齐全的部件，另一方面，它们可能会错过定期检查之间迅速恶化的状况。这项研究将通过研究特别适合和适用于现代复杂系统的新建模和监测技术，开发新的方法来解决这两个缺点。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，并产生能够实时跟踪其状态的指标。该奖项支持基于分数微积分的数学和计算模型的基础研究。本研究的方法将在构造、地质和生物介质中使用成像和遥感的应用中非常有用。本计画的教育部分，在其不同的组成部分中，将以开发一门新课程为特色，向工程学生介绍分数阶微积分及其在工程系统建模中的应用。这项研究将包括一个系统的研究，以确定分数阶微分方程将如何提高系统识别和监测的最新技术。分数阶模型是一种新的、有用的复杂工程系统建模工具，但在工程中还不常用。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全新的方法，它将引入系统顺序作为系统评估的新参数，并将为复杂系统的动力学提供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潜在控制方程的影响；(2)利用分数阶方法实现高效的降阶、子结构和逆问题求解；(3)建立基于纯实验数据的系统辨识分数模型；(4)建立实验验证平台。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

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.