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研究生： 林彬儀
Lin, Pin-Yi
論文名稱： 針對非充裕不確定資料設計之最佳取樣與資源配置
Optimal Sampling Augmentation and Resource Allocation for Design with Inadequate Uncertainty Data
指導教授： 詹魁元
Chan, Kuei-Yuan
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2012
畢業學年度： 100
語文別： 英文
論文頁數： 89
中文關鍵詞： 可靠度設計 、不確定性因素 、樣本量測 、貝氏二項式推估 、資源配置 、馬可夫鏈蒙地卡羅法
外文關鍵詞： Uncertainty, reliability-based design optimization, Bayesian binomial inference, sample measurement, resource allocation, Markov chain Monte Carlo
相關次數： 點閱：126  下載：1 
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    • 可靠度設計需有大量的樣本量測以建立不確定因素的模型，但在實際工程運用上，樣本的量測費時且昂貴。雖然，大量的量測可以提供一較為適用的設計，但設計者經常必須在有限時間內根據有限的資訊做出設計判斷。文獻中，多採用貝氏二項式推估法來進行具有樣本型態的不確定性因素的可靠度評估。然而，文獻中均假設一組不確定性參數為一個樣本，事實上，每一次量測均代表一個樣本。因此，在增加額外的樣本時，不同不確定性參數的對最終設計的貢獻差異需被納入考量。本文透過樣本組合的概念來使不確定性因素的相對重要性在增加樣本時得以被顯現。本文建立一藉由在最佳化中逐漸增加樣本來協助有效的資源分配與進行非充裕不確性資料可靠度設計的方法。為了避免量測品質不佳的樣本影響可靠度評估的準確度，因此，本研究發展一以馬可夫鏈蒙地卡羅法為基礎的樣本過濾機制來避免偏頗樣本。本研究可以在滿足可靠度目標與使用者定義的信賴區域中，透過逐漸增加少許的新樣本，並有效的配置樣本進而提供較準確的可靠度評估，獲得可接受的可靠度最佳化設計。由於信賴區域受限於樣本數量，本文定義在此樣本數量下的信賴區域的上限為信賴邊界，並將其納入可靠度最佳化的拘束條件中。額外的樣本量測在關鍵的拘束條件相關的不確定性因素上來幫助可靠度最佳化的進行。設計與額外的樣本量測會持續進行直到滿足設計者要求的目標。透過此研究方法 ，可藉由較少且較有效率的樣本量測配置進行可靠度最佳化設計。本論文以一個數學範例與一汽車懸吊系統設計演示此方法並討論結果，最後，並將汽車懸吊系統設計延伸至複雜系統來示範此設計方法。

    Uncertainty models in reliability-based design optimization problems require a large amount of measurement data that are generally unavailable in engineering practice. Each measurement requires resources, sometimes costly. Although a comprehensive set of measurements could lead to design that is more applicable, engineers are constantly challenged to make timely design decisions with only limited information at hand. In the literature, Bayesian binomial inference techniques have been used to estimate the reliability value of a function of uncertainties with limited samples. However, existing methods assume data set as one sample for each uncertain quantity, while in reality we consider one sample as one measurement on a specific quantity. The relative contributions of uncertainties on the final optimum should be considered when adding samples.

    In this thesis, we use the concept of sample combinations to reveal the relative contributions of uncertainties when adding samples. We propose a sampling augmentation process to add measurements of uncertain quantities only when they are `important' by allocating resource more efficiently. To alleviate the impact of bad samples, biased samples that would affect the evaluation of reliability inference will be filtered via a mechanism through Markov chain Monte Carlo method. Once a desired reliability target and a user-specified confidence range are provided by the designer, a confidence bound limit that predicts the upper bound of no-failure confidence is then calculated. This confidence bound limit is then considered in a reliability-based design optimization framework as constraints. Additional measurements on critical constraints with respect to uncertainties in the form of discrete samples are necessary. Design then iterates until the desired targets are reached. In this work our method could minimize the efforts and resources without assuming distributions for uncertainties. Several examples are used to demonstrate the validity of the method in product development.

    書名頁 i 論文口試委員審定書 ii Copyright iii 中文摘要 iv Abstract v 誌謝 vi Table of Contents vii List of Tables xi List of Figures xiii List of Symbols xv 1 Introduction and Motivation 1 1.1 Introduction 1 1.2 Motivation and Objective 4 1.3 Organization of the Thesis 5 2 Bayesian Reliability Inference with Sample Data 6 2.1 Data Inference using Bayesian Theory 6 2.1.1 Bayes Theorem 6 2.1.2 Binomial Distribution 9 2.1.3 Bayesian Binomial Inference 10 2.2 Reliability Estimation with Sample Data 13 2.2.1 Bayesian Inference of Constraint Reliability Values 13 2.2.2 Con_dence Range and Con_dence Bound 15 2.2.3 Clari_cation of “Sample” 16 2.2.4 Reliability Estimation Example 17 2.3 Sample Data Filter via Markov Chair Monte Carlo 19 2.3.1 Backgrounds on Markov Chain 19 2.3.2 Markov Chain Monte Carlo by Metropolis-Hasting Algorithm 22 2.3.3 MCMC Modi_cation with Bootstrap 24 3 Optimal Sampling Augmentation and Resource Allocation 29 3.1 RBDO with Inadequate Uncertainty Data 29 3.1.1 Introduction of RBDO 29 3.1.2 Activity of Bayesian Reliability Constraints 30 3.1.3 Generalized Optimization Model of RBDO with Inadequate Uncertainty Data 33 3.2 Optimal Sampling Augmentation for Design 35 3.2.1 Purpose of Sampling Augmentation 35 3.2.2 Sampling Augmentation Process 36 3.3 Resource Allocation Process 41 3.3.1 Sensitivity Analysis 41 3.3.2 Scheme of Resource Allocation 42 4 Case Studies in Single Level Systems 44 4.1 A Mathematical Example 44 4.1.1 Optimization Model of Mathematical Example 45 4.1.2 Optimal Results and Discussions 47 4.1.3 Comparison of Sampling Augmentation with Different Sample Size 50 4.2 Passive Vehicle Suspension Design 51 4.2.1 Optimization Model of Passive Vehicle Suspension Design 51 4.2.2 Optimization Result and Discussions 54 4.2.3 Comparison of MCMC and without MCMC in Passive Vehicle Suspension Design with different sample size 57 4.3 Summary 59 5 Case Studies in Complex Multilevel System 60 5.1 Introduction to Analytical Target Cascading 60 5.1.1 ATC Problem Decomposition 61 5.1.2 Augmented Lagrangian Method for ATC 63 5.2 Passive Vehicle Suspension Design in Complex System 63 5.2.1 All in One System of Passive Vehicle Suspension Design 64 5.2.2 Multilevel Passive Vehicle Suspension Design 70 5.2.3 Optimal Results and Discussion 73 5.3 Summary 80 6 Conclusions and Future Work 81 6.1 Conclusions 81 6.2 Future Work 82 References 83 Personal Communication 89

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