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標題: | 考慮不確定性於斯托克斯流場域極值反應解析與量測數據降噪之連體力學研究 Continuum Mechanics of Extreme Response Analysis and Measurement Noise Reduction for Stokes flow under Uncertainty |
作者: | 林柏廷 Po-Ting Lin |
指導教授: | 王建凱 Chien-Kai Wang |
關鍵字: | 連體力學,斯托克斯流,不確定性,有限元素法,場域極值反應解析,場域量測降噪技術, Continuum mechanics,Stokes flow,Uncertainty,Finite element analysis,Extreme responses analysis,Measurement data noise reduction, |
出版年 : | 2023 |
學位: | 碩士 |
摘要: | 本論文進行連體力學研究,係針對不可壓縮斯托克斯流,提出新式場域極值反應之解析方法,和場域量測數據之降噪技術。關於極值反應解析方法,本論文基於高斯分佈統計函數描述隨機邊界條件,並結合有限元素理論推導,發展出一分析理論,可以直接且準確評估出受隨機邊界條件刺激之斯托克斯流場域極值速度與壓力場反應。為完整驗證此方法之解析能力,本論文針對不同的不確定性邊界條件,將重複執行計算流體力學所得結果之統計資料,與由本研究提出直接解析方法所得結果進行比較,除得到良好的一致性外,並進而呈現此新式分析理論之準確性;關於量測數據降噪技術,本論文結合有限元素法與拉格朗日乘數法,開發出一計算方法,將流體速度與壓力場量測數據進行降噪,且融合影像校準技術,設計一系列計算例,測試對於不同程度量測不確定性之場域降噪能力。
論文內容方面:第一章回顧斯托克斯流、場域極值反應求解方法、量測場域數據降噪技術的發展背景與相關重要研究文獻;第二章以伽遼金有限元素法(Galerkin finite element method)架構詳細推導斯托克斯流之有限元素法線性代數式,以數值解析出場域中各自由度的速度與壓力分佈;第三章提出本研究新開發流場極值反應解析之直接有限元素求解技術,推導出不可壓縮斯托克斯流在隨機刺激下之極端響應,並針對狄利克雷與諾伊曼邊界條件之不確定性,進行一系列之計算例;第四章,提出本研究新開發之不可壓縮斯托克斯流場域降噪技術,本技術主要融合有限元素理論與拉格朗日乘數法,並利用影像校準技術與參考映射技術等應用數學方法進行實作;第五章為本論文研究之結論與未來展望。 This thesis research investigates continuum mechanics on incompressible Stokes flow. This thesis proposes a novel method to analyze extreme field responses accurately and a new technique to effectively reduce the noise in measurement field data. The extreme response method combines the concepts of uncertain boundary conditions, based on the statistical model of Laplace-Gaussian distributions, with the finite element theory. By these concepts, this analytical method can directly and accurately evaluate the extreme velocity field and pressure field responses of the Stokes flow under random boundary conditions. To investigate and validate the capabilities of the proposed analytical method under different uncertain boundary conditions, the extreme responses of Stokes flow through numerous conventional computational fluid mechanics simulations are compared with the ones from the proposed method in this study. The extreme flow data obtained by repetitive simulations are in good agreement with the direct evaluation. And the accuracy of the proposed technique is thus verified. Regarding the noise reduction technique, it combines the finite element method with the Lagrange multiplier method and can reduce measurement fluid velocity and pressure field data. This thesis utilizes the image registration technique to design a series of example and test the noise reduction capability with different degrees of measurement uncertainty. The thesis is organized as follows. The research background and core concepts of Stokes flow, extreme responses analysis, and measurement noise reduction are thoroughly reviewed in Chapter 1. Chapter 2 introduces the essential concepts of the Galerkin finite element method exploiting Stokes flow mechanics and analyzes the velocity and pressure distribution over degrees of freedom on model meshes numerically. Chapter 3 presents a new direct finite element method for analyzing the extreme response of the incompressible Stokes flow under uncertainty boundary conditions. A series of computational examples considering the uncertain Dirichlet and Neumann boundary conditions are conducted for validating this method. Chapter 4 presents the newly developed measurement noise reduction technique for incompressible Stokes flow fields, which mainly combines the finite element theory and Lagrange multiplier method. In addition, the image registration approach and the reference mapping technique are utilized to implement several typical examples. Chapter 5 wraps the conclusion and future work of the thesis. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/87608 |
DOI: | 10.6342/NTU202300224 |
全文授權: | 同意授權(限校園內公開) |
電子全文公開日期: | 2024-01-01 |
顯示於系所單位: | 機械工程學系 |
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