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
基本信息
- 批准号:0505880
- 负责人:
- 金额:$ 20.59万
- 依托单位:
- 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:
- 关键词:
项目摘要
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.
本课题致力于研究与物理和工程应用相关的三个反二次特征问题。其目的是加深对二次模型重构的理论理解和推导数值算法,从而在满足某些特定的数学条件的同时,减少由于现有技术的限制而导致的模型的不精确性和不确定性。二次模型重建中最困难的任务是满足关联约束,这些约束可以内在地继承于某种机械结构的物理可行性,或者可以外在地受到某种设计参数的期望性质的驱动。最大的挑战,也是实践中的迫切要求,就是必须仅使用最新的计算技术获得的部分特征信息来进行重建。约束模型重构反问题对于理解和管理复杂系统是必不可少的,但在可解性、灵敏度和计算量等方面仍有许多问题没有得到解答。研究者们各自对二次模型构造问题做出了重大贡献,现在打算将他们的研究和联合专业知识扩展到这些具有挑战性的逆问题上。因此,这项拟议的工作在工程界和数学科学界都应该具有令人信服的独立兴趣。在数学建模中,根据系统的服务或预期行为来验证、确定或估计系统参数的反问题技术至关重要。本文主要研究与物理和工程应用无关的逆模型重建问题。这些问题受到科学和工业应用的强烈刺激,包括结构力学,如桥梁、建筑物和高速公路的振动控制和稳定性分析,振动声学,如声音的预测编码,生物医学信号和图像处理,时间序列预测,信息技术等。因此,该项目将影响使用这些应用的各种行业,包括航空航天、汽车、制造和生物医学工程。这些工业面临的最大挑战是用有限的工程和计算资源制造日益改进的产品。为了令人满意地完成模型修正任务,这些行业投入了大量的资金和精力,但由于缺乏适当的理论和计算工具,往往迫使这些行业以临时方式解决自己的问题。一个改进的分析模型可以自信地用于未来的设计,是实现这一目标的必要工具。所提出的研究不仅有坚实的数学基础,而且在利用工业数据进行建模和实验方面具有重要的数学意义,应立即受到业界的欢迎。此外,在这个项目上工作了四年的学生将接受将数学和科学计算与工程和应用科学的各个领域相结合的宝贵的跨学科培训。这样的专业知识很少找到,但学术界和工业界的需求都在不断增加。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Moody Chu其他文献
On the Refinement of Cartan Decomposition: An Implicit Commutative Substructure in $$\mathfrak {su}(2^{n})$$
- DOI:
10.1007/s00025-025-02478-3 - 发表时间:
2025-07-19 - 期刊:
- 影响因子:1.200
- 作者:
Moody Chu - 通讯作者:
Moody Chu
Moody Chu的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Moody Chu', 18)}}的其他基金
Preparing Hamiltonians for Quantum Simulation: A Computational Framework for Cartan Decomposition via Lax Dynamics
为量子模拟准备哈密顿量:通过 Lax 动力学进行嘉当分解的计算框架
- 批准号:
2309376 - 财政年份:2023
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
From Quantum Entanglement to Tensor Decomposition by Global Optimization
从量子纠缠到全局优化的张量分解
- 批准号:
1912816 - 财政年份:2019
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
Numerical Algorithms as Dynamcal Systems - Structure Preservation, Convergence Theory, and Rediscretization
作为动态系统的数值算法 - 结构保持、收敛理论和重新离散化
- 批准号:
1316779 - 财政年份:2013
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
Automated Structure Generation, Error Correction, and Semi-Definite Programming Techniques for Structured Quadratic Inverse Eigenvale Problems: Theory, Algorithms and Applications
结构化二次反特征值问题的自动结构生成、纠错和半定编程技术:理论、算法和应用
- 批准号:
1014666 - 财政年份:2010
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
MSPA-MCS: Collaborative Research: Fast Nonnegative Matrix Factorizations: Theory, Algorithms, and Applications
MSPA-MCS:协作研究:快速非负矩阵分解:理论、算法和应用
- 批准号:
0732299 - 财政年份:2007
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
The Centroid Decomposition and Other Approximations to the SVD
SVD 的质心分解和其他近似
- 批准号:
0204157 - 财政年份:2002
- 资助金额:
$ 20.59万 - 项目类别:
Continuing Grant
Algorithms for the Inverse Problem of Matrix Construction
矩阵构造反问题的算法
- 批准号:
0073056 - 财政年份:2000
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
Adaptive Control Algorithms for Adaptive Optics Applications
用于自适应光学应用的自适应控制算法
- 批准号:
9803759 - 财政年份:1998
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
Mathematical Sciences: Inverse Eigenvalue Problems
数学科学:反特征值问题
- 批准号:
9422280 - 财政年份:1995
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
Mathematical Sciences: Matrix Differential Equations and Their Applications
数学科学:矩阵微分方程及其应用
- 批准号:
9123448 - 财政年份:1992
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
相似海外基金
RESEARCH PROPOSAL What is your project title? Development of additive manufactured polymeric seals for low molecular weight gases
研究计划 您的项目名称是什么?
- 批准号:
2908868 - 财政年份:2024
- 资助金额:
$ 20.59万 - 项目类别:
Studentship
Development of a low-pressure loss air purification device using rotating porous media and a proposal for its use in ventilation systems
使用旋转多孔介质的低压损失空气净化装置的开发及其在通风系统中的使用建议
- 批准号:
24K17404 - 财政年份:2024
- 资助金额:
$ 20.59万 - 项目类别:
Grant-in-Aid for Early-Career Scientists
Conference: Supporting Mentoring in STEM Graduate Education: A Proposal for Virtual Workshops and Supporting Activities
会议:支持 STEM 研究生教育辅导:虚拟研讨会和支持活动的提案
- 批准号:
2413980 - 财政年份:2024
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
Proposal Title : NemeSys - Smart Multiphasic Nanoreactors Based On Tailored Foams for Direct H2O2 Synthesis
提案标题:NemeSys - 基于定制泡沫的智能多相纳米反应器,用于直接合成 H2O2
- 批准号:
EP/Y034392/1 - 财政年份:2024
- 资助金额:
$ 20.59万 - 项目类别:
Research Grant
Collaborative Research: Time-Sharing Experiments for the Social Sciences (TESS): Proposal for Renewed Support, 2020-2023
合作研究:社会科学分时实验(TESS):2020-2023 年更新支持提案
- 批准号:
2424057 - 财政年份:2024
- 资助金额:
$ 20.59万 - 项目类别:
Continuing Grant
CRCNS US-German Collaborative Research Proposal: Neural and computational mechanisms of flexible goal-directed decision making
CRCNS 美德合作研究提案:灵活目标导向决策的神经和计算机制
- 批准号:
2309022 - 财政年份:2024
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
Travel: Texas Power and Energy Conference (TPEC) 2024 Travel Proposal
旅行:德克萨斯州电力与能源会议 (TPEC) 2024 年旅行提案
- 批准号:
2341300 - 财政年份:2024
- 资助金额:
$ 20.59万 - 项目类别:
Standard Grant
Business and Local Government Data Research Centre Legacy Status Proposal
企业和地方政府数据研究中心遗留状态提案
- 批准号:
ES/Y003411/1 - 财政年份:2024
- 资助金额:
$ 20.59万 - 项目类别:
Research Grant
Lite(House) - A Financially Flexible, Adaptive and Efficient Live/Work Housing Proposal
Lite(House) - 财务灵活、适应性强且高效的生活/工作住房提案
- 批准号:
10071140 - 财政年份:2023
- 资助金额:
$ 20.59万 - 项目类别:
Collaborative R&D
Proposal of effective utilization of polyphenols as functional food ingredients for realization of a healthy longevity society
有效利用多酚作为功能性食品成分以实现健康长寿社会的提案
- 批准号:
23K10889 - 财政年份:2023
- 资助金额:
$ 20.59万 - 项目类别:
Grant-in-Aid for Scientific Research (C)