Mathematical methods and models for complex engineering problems

复杂工程问题的数学方法和模型

• 批准号: RGPIN-2017-05754
• 负责人: Saucier, Antoine
• 金额: $ 1.75万
• 依托单位: École Polytechnique de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=664338
• 关键词: Mathematical; methods; models; complex; engineering

Our research program focuses on the development of realistic models and computer algorithms for the solution of complex engineering problems. The applied problems that we study share the following complexity attributes: high-dimensionality, nonlinearity and modeling difficulties. We describe three parts of this program.******"ARTEFACT-FREE" NOISE REDUCTION METHODS FOR IMAGES: most noise reduction methods introduce artefacts that become visible if one looks at the residual image, which is the difference between the original noisy image and the denoised image. We propose to develop better methods that exploit a fine local analysis of the image and a global optimization strategy. This work should lead to both quantitatively and qualitatively superior noise reduction performance in signal processing, which in turn should have a major impact on the applications for which the image estimate accuracy is crucial, e.g. medical imaging.******OPTIMAL AIRCRAFT TRAJECTORIES: The cost-index is a parameter that controls flight time, which determines both fuel cost and late-arrival penalties (caused e.g. by passengers that miss their connecting flights). A precise estimation of the optimal cost-index is very important for economical and environmental reasons. We propose to develop a fast and precise cost-index estimation method. Our approach will be to use our flight trajectory optimization system with a subset of the trajectories that links departure and arrival points. A more accurate estimate of the cost-index and a better management of the fuel reserve for aircrafts should have a direct and significant impact on both fuel consumption and carbon dioxyde emissions, which have major economic and environmental consequences.******CLASSICAL AND GEOMETRICAL METHODS FOR DIFFERENTIAL EQUATIONS: Analytical solutions, even approximate, are much more useful to engineers than numerical solutions because they provide an understanding of the phenomenon as a function of its parameters. I will study a hydrogeology problem related to aquifer testing, which is a set of methods that are used to characterize groundwater. One such test is the pumping test, which consists in pumping water from a well and measuring the water level in the pumping well and observation wells as a function of time. I will study the solution of a pumping test for unconfined aquifers. No complete solution is known for unconfined aquifers, which are frequently used for drinking water supply and are the most vulnerable to contamination. Analytic solutions of their transient responses should help to achieve more reliable assessment of the resources and more effective pump-and-treat systems for contamination cases.

我们的研究计划着重于解决复杂工程问题的现实模型和计算机算法的开发。我们研究的应用问题具有以下复杂性属性：高维性，非线性和建模困难。我们描述了该程序的三个部分。******“无伪影”的图像降噪方法：大多数降低降噪方法会引入伪影，如果一个人看着残留的图像，这是原始噪声图像与分解图像之间的区别。我们建议开发更好的方法，以利用对图像的局部分析和全球优化策略的良好分析。这项工作应导致信号处理中的定量和质量降低降噪性能，这反过来又将对图像估计精度至关重要的应用产生重大影响，例如医学成像。******最佳飞机轨迹：成本指数是控制飞行时间的参数，它决定了燃油成本和后期罚款（例如，乘客错过了他们的连接飞行）。出于经济和环境原因，对最佳成本指数的精确估计非常重要。我们建议开发一种快速，精确的成本指数估计方法。我们的方法是将我们的飞行轨迹优化系统与连接出发点和到达点的轨迹的子集使用。对飞机的成本指数和更好地管理燃油储备的更准确估计应直接且重大影响，对燃料消耗和碳二氧化碳排放，这具有重大的经济和环境后果。**************的经典和几何方法的差异方程式和差异方程式：与工具的近似设置相比，他们的功能更为有用，因为他们的功能是有用的，因为他们的功能是有用的，因为他们是一种机能，因为他们是一种机能，而是一个机能，而是一种机能。 参数。我将研究与含水层测试有关的水文地质问题，该问题是用于表征地下水的一组方法。一个这样的测试就是抽水测试，它包括从井中抽水并测量泵送井中的水位和观察井随时间的影响。我将研究无限制含水层的抽水测试解决方案。没有完整的解决方案是无限制的含水层，这些含水层经常用于饮用水，并且最容易受到污染。其瞬态响应的分析解决方案应有助于对资源进行更可靠的评估，并为污染案例提供更有效的泵和治疗系统。