- 學位論文
高維度動態系統之不確定參數篩選與校準方法
Enhanced Screening and Estimation of Uncertain Parameters in High-dimensional Dynamic Systems
若您是本文的作者，可授權文章由華藝線上圖書館中協助推廣。
摘要
電腦模擬模型是現代系統開發階段的重要工具，如何透過模型校準，使模擬模型的準確度提升，是複雜且重要的議題。而當要模擬的系統中，具有大量參數且輸出又為動態行為時，會大幅度增加系統分析與模型校準的難度。本研究在電腦模擬模型與真實系統間僅存在模型參數偏差、模型結構無偏差的假設下，提出一套由大量不確定參數中，篩選出重要參數，並對其進行參數校準的流程，以達到降低模擬模型與真實世界差距的最終目標。 本研究提出以時域與頻域兩個面向對系統動態輸出進行全域敏感度分析，以同時分析系統的穩態與暫態響應特性。並搭配現有的高維度系統的全域敏感度分析與參數分群策略，降低分析單一時間點或頻率輸出時的計算成本。接著從大量的參數中，選出作為待校準目標的不確定參數，本研究制定經敏感度數值假設檢定、時域參數分群結果檢查，兩階段的篩選策略。參數校準時，參考時域參數分群資訊，改良現有的基於混沌多項式之卡爾曼濾波器，進行參數校準並分析校準成果。本研究以一二分之一車模型作為簡易動態系統，再以一真實世界之車輛工程案例，使用真實的實驗與車輛數據，對一自建之車輛模型進行不確定參數篩選與校準，驗證本研究所提出之方法可降低參數校準計算時間並提升校準成效。
並列摘要
Computer simulation models play important roles in product development cycles. The ability to improve the accuracy of models is a complex and important issue. When the system to be simulated has a large number of parameters and the output is dynamic behavior, it will greatly increase the difficulty of system analysis and model calibration. In this research, we proposes a enhanced screening and estimation method of uncertain parameters in highdimensional dynamic system, by assuming only parameter deviations but no model structural problems between the model and the real system. Important uncertain parameters are first screened out and then estimated, aiming to reducing the difference between the model and the real world. This research proposes to conduct global sensitivity analysis (GSA) of the system dynamic output in both time and frequency domain, conbining with the existing GSA and factor grouping method for high-dimensional problems to reduce the computational cost. A two-stage parameter screening strategy is also proposed, basing on sensitivity hypothesis testing and time domain parameter grouping result inspection. When estimating the screened uncertain parameters, the time domain factor grouping results is used to improve the existing Polynomial Chaos-Based Kalman Filter. Finally, we uses a half-car model as a simple dynamic case, and a real-world vehicle case with real experiments and vehicle data to perform parameters screening and estimation. In these two cases, the method proposed in this research is proved to reduce parameter estimation calculation time and improve estimation results.
參考文獻
[1] L. E. Schwer, “Verification and validation in computational solid mechanics and the asme standards committee,” WIT Transactions on the Built Environment, vol. 84, 2005.
[2] L. E. Schwer, “Guide for verification and validation in computational solid mechanics,”2009.
[3] M. C. Kennedy and A. O’Hagan, “Bayesian calibration of computer models,”Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 63, no. 3, pp. 425–464, 2001.
[4] R. Oliva, “Model calibration as a testing strategy for system dynamics models,”European Journal of Operational Research, vol. 151, no. 3, pp. 552–568, 2003.
[5] M. L. Johnson and L. M. Faunt, “[1] parameter estimation by least-squares methods,”in Methods in enzymology, vol. 210, pp. 1–37, Elsevier, 1992.