不確定參數之最佳激發與校準：以車輛模型開發為例

Abstract

模擬模型是系統開發階段重要的工具之一，如何透過模型驗證以優化模型，建立高度可靠之模型更是重要的議題。本研究在模型與真實系統僅存在參數的偏差之假設下，以校準模型參數為設計出發點，提出一套系統化的參數校準流程，用以解決普遍的驗證程序中，參數校準無法有效診斷模型與真實系統的誤差來源、且缺乏系統化的建立參數驗證操作之處境。 本研究在考量模型的複雜程度導致模擬成本過高的情況下，以電腦實驗設計與分析(Design and Analysis of Computer Experiment, DACE) 之概念結合替代模型，設計一套可用於複雜系統分析的模型驗證流程，透過對系統輸出進行全域敏感度分析，進一步使用最佳化方法設計於激發觀測參數的操作方法，並以基於混沌多項式之卡爾曼濾波器進行參數校準，最後驗證結果。本研究以單一輸出及動態輸出之數學模型確認所提出之方法的可行性，同時驗證了此方法的一般性。再以一自建之線控操作三輪車做為分析對象之車輛工程案例，透過所提出之方法，對車輛動力學模型中的不確定參數進行校準，得到於95%信心水準下被認定為準確之模型參數。透過多個案例，也強調了所提出之方法的重要性。

Simulation models play important roles in efficient product development cycles. The ability to improve the confidence level of models during the validation stage is also an important topic. In this research, we proposed a systematic procedure on model validation by assuming all the output errors between simulation models and real model experiments are contributed from deviations of model parameters. This procedure aims to counter the inability to create a proper and logical operation when validating dynamic models. In this research, considering the expensive costs associated with model simulation used in complex systems, a Design and Analysis of Computer Simulation (DACE) based procedure including an optimization method for generating a proper operation which maximizes the sensitivity of uncertain parameters based on global sensitivity analysis (GSA), estimation of parameters with polynomial chaos-based Kalman filter, and model validation based on hypothesis testing, is introduced. Furthermore, two illustrative math models with scalar and dynamic output are demonstrated to verify the method, consequently proving its generality. Finally, an application on validating vehicle dynamic models is shown as an engineering case, which successfully estimates the unknown model parameters with 95% confidence. The significance of this research is also emphasized through multiple cases.