使用模型校準以識別複雜系統參數數值之方法

Identifying Parameter Uncertainties in Model Calibration of Complex Systems

林岳羿(Yueh-I Lin)

指導教授 ： 詹魁元

國立臺灣大學/工學院/機械工程學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201602907

摘要

物理模型是工程師在產品開發階段重要的工具之一，本研究建立分析參數不確定因素的流程，以提升物理模型的準確度。模型校準方法是利用貝氏推論回推參數不確定因素的方法，然而在複雜系統的應用可能遇到的難處有(1)參數過多造成回推的運算成本過高，(2)回推結果信心水準不足，以及(3)回推結果難分辨各別參數不確定因素的影響。本研究藉由田口實驗設計法的直交表實驗篩選出系統的重要參數，簡化複雜系統的參數不確定因素回推問題。另外建構了模型校準中貝氏推論的更新迴圈以及使用多種測試函數，提升複雜系統模型校準的結果。最後利用兩個工程案例作為演示：一是簡支樑的穩態測試，參數不確定因素回推結果誤差約1.5%；另一是汽車的動態測試，參數不確定因素回推結果誤差約17%。本研究所提出之方法不僅可有效辨識參數不確定因素，也藉此提供參數不確定因素的一體化的分析流程。

關鍵字

複雜系統分析 ； 參數不確定因素 ； 參數數值識別 ； 模型校準 ； 貝氏推論 ； 主因素分析 ； 參數篩選

並列摘要

Effective physical models play important roles in efficient product development cycle. This research focuses on parameter uncertainty to improve precision between model predictions and measured system performances. The state-of-the-art methods use model calibration with Bayesian Inference to identify parameter uncertainties; however potential risks might exist in complex system analysis, namely (1) analyzing multiple parameters, resulting in high computational costs, (2) the predicted confidence levels are low, and (3) unable to infer each individual uncertainty in complex systems. This research adopts main effect analysis from Taguchi's framework of design of experiments to select important parameters from a complex system. The uncertainty analysis is then narrowed down to those on important parameters. Bayesian updating loop is then reinforced and joint inference of multiple testing functions are used to improve the performance of model calibration. The method is demonstrated in two engineering cases: one is a steady-state test of a simple-supported beam, and the identifying error turns out to be 1.5%; while the other vehicle dynamic test under CarSim® has 17% of identifying error.

並列關鍵字

complex system analysis ； parameter uncertainty ； parameter estimation ； model calibration ； Bayesian inference ； main effect analysis ； parameter selection

參考文獻

[1] K. Koprubasi, A. Pezzini, B. Bezaire, R. Cooley, P. Tulpule, G. Rizzoni, Y. Guezennec, and S. Midlam-Mohler, “Application of model-based design techniques for the control development and optimization of a hybrid-electric vehicle,” 2009.

[4] W. Walker, P. Harremoës, J. Rotmans, J. Sluijs, M. Asselt, P. Janssen, and M. Krauss,“Defining uncertainty: A conceptual basis for uncertainty management in model-based decision support,” Integrated Assessment, vol. 4, no. 1, pp. 5–17, 2003.

[6] P. O’Connor and A. Kleyner, Practical reliability engineering. John Wiley & Sons, 2011.

[7] R. Moore, R. Kearfott, and M. Cloud, Introduction to interval analysis. Siam, 2009.

[8] W. Kuo and M. Zuo, Optimal reliability modeling: principles and applications. John Wiley & Sons, 2003.