Collaborative Proposal: Quadratic Inverse Eigenvalue Problems for Model Updating in Science and Engineering: Theory and Computation

合作提案：科学与工程模型更新的二次逆特征值问题：理论与计算

• 批准号: 0505880
• 负责人: Moody Chu
• 金额: $ 20.59万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505880&HistoricalAwards=false
• 关键词: Collaborative; Proposal; Quadratic; Inverse; Eigenvalue

This project is devoted to the study of three inverse quadraticeigenproblems with their pertinence to physical and engineeringapplications. The aim is to develop theoretic understanding andderive numerical algorithms for the quadratic model reconstructionso that the inexactness and uncertainty inherent in the model dueto the limitation of current technologies are reduced while certainspecific mathematical conditions are satisfied. The most difficulttask in the quadratic model reconstruction is to satisfy the associatedconstraints which could be inherited intrinsically from the physicalfeasibility of a certain mechanical structure or could be drivenextrinsically by the desirable property of a certain design parameter.The greatest challenge, which is also an imperative requirement inpractice, is that the reconstruction must be carried out using onlypartial eigeninformation which are available by the state-of-the-artcomputational techniques. The inverse problem of constrained modelreconstruction is essential for the understanding and management ofcomplex systems, yet many questions on the solvability, sensitivity,and computation remain unanswered. The investigators have madesignificant contributions to the quadratic model construction problemsindividually and now intend to extend their investigation and joinexpertise to these challenging inverse problems. This proposed worktherefore should be of compelling independent interest within boththe engineering and mathematical sciences communities.In mathematical modelling, techniques of inverse problems that validate,determine, or estimate the parameters of the system according to itsobserved or expected behavior are critically important. This researchconcentrates on the inverse model reconstruction problems with theirpertinence to physical and engineering applications. These problems havebeen strongly motivitated by scietific and industrial applications,including structural mechanics such as vibration control and stabilityanalysis of bridges, buildings and highways, vibro-acoustics such aspredictive coding of sound, biomedical signal and image processing,time series forecasting, information technology, and others. Thus thisproject will impact a wide variety of industries utilizing theseapplications, including aerospace, automobile, manufacturing andbiomedical engineering. The greatest challenge facing these industriesis to manufacture increasingly improved products with limited engineeringand computing resources. A great deal of money and efforts have been spentin these industries to satisactorily perform the model updating task.However, the lack of proper theory and computational tools often forcethese industries to solve their problems in an ad hoc fashion. An improvedanalytical model that can be used with confidence for future designs isan essential tool in achieving this obejective. The propsed research hasnot only strong mathematical foundation but also significant matematicalmodelling and experimental aspects using idustrial data which should beinstantly welcome by the industries. Furthermore, the students workingon this project for four years will receive a valuable interdisciplnarytraining blending mathematics and scietific computing with various areasof engineering and applied sciences. Such expertise is rare to find,but there is an increasing demand both inacademia and industries.

该项目致力于研究三个与物理和工程应用相关的逆四倍体问题。目的是为二次模型重建理论理解和数值算法，即模型二重奏中固有的不精确性和不确定性降低了当前技术的限制，而满足了某些特定的数学条件。二次模型重建中最困难的任务是满足相关的约束，这些约束可能是从某些机械结构的物理上遗传上遗传的，或可以通过特定设计参数的理想属性进行驱动的范围来实施的，这也是最重要的挑战，这是必要的，这是必不可少的，是必不可少的，是必不可少的，是构成的构造，是构成的构造，这是构成的构造，最新的计算技术。约束模型建设的反面问题对于对复杂系统的理解和管理至关重要，但是许多有关解决性，灵敏度和计算的问题仍然没有得到解答。 调查人员对二次模型构建有很大的贡献，现在打算将其调查和加入到这些具有挑战性的反问题上。因此，这项提出的工作应该在工程和数学科学社区中引起独立的兴趣。在数学建模中，根据其观察或预期行为验证，确定或估算系统参数的反问题技术至关重要。这项研究将逆向模型的重建问题与物理和工程应用的替代性有关。这些问题引起了很高的激励和工业应用的激励，包括桥梁，建筑物和高速公路的振动控制和稳定分析，氛围 - 声音，生物医学信号和图像处理，时间序列，时间序列预测，信息技术以及其他的氛围编码，氛围，建筑物和高速公路的稳定性。因此，这项项目将影响许多利用航空航天，汽车，制造业和生物医学工程在内的各种行业。这些行业面临的最大挑战是使用有限的工程和计算资源生产越来越多的改进产品。这些行业已经花费了大量的钱和努力来满足模型更新任务。但是，缺乏适当的理论和计算工具通常会宣布以临时的方式解决他们的问题。改进的分析模型，可以信心用于未来的设计ISAN基本工具，以实现这种屈服。支撑的研究不仅是强大的数学基础，而且还使用了重要的临时模型和实验方面，并使用iD工业数据应受到行业的欢迎。此外，该项目工作四年的学生将获得有价值的跨学科跨性培训，将数学和可观的计算与各个领域的工程和应用科学领域。 这种专业知识很少见，但是危险性和行业的需求都在增加。