使用吻合與雷同指標以驗證工程系統之動態行為

Model Validation on Engineering System with Dynamic Performances Using Statistical Similarity and Fitness Metrics

朱盈樺(Ying-Hua Chu)

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(2017年)

https://doi.org/10.6342/NTU201704219

摘要

模擬模型與實驗模型的驗證是模型建構的初期任務之一，在動態模型的動態行為驗證上，常遇到的困難有(1)動態系統性能輸出缺乏可評估的單一量化方式(2)現行模型驗證指標過度強調模型吻合而非一致性。(3)動態系統輸出與參數的耦合關係複雜。本研究著重在模型動態行為驗證上，使用Karhunen-Loeve轉換及重組動態資訊，藉以有效比對重要資訊，並運用無母數檢定方式建立驗證指標，再以檢定之p值建構指標座標圖，如此一來能夠完整說明模擬模型與實驗模型的雷同程度與吻合程度，提供修正模型的方向。本研究使用三個案例作為演示:一為複製文獻中數學案例，說明本研究方法的延伸性，二為使用簡易常見工程系統(彈簧阻尼系統)，說明研究方法的有效性，三為真實工程車輛案例，說明研究方法的運用性。本研究不只探討動態模型結果之資訊擷取，同時完整提供動態模型驗證手法及程序上的輔助。

關鍵字

模型驗證 ； 無母數檢定 ； K-L轉換 ； 雷同度 ； 吻合度 ； 模型驗證指標 ； 動態模型分析

並列摘要

Validation is a vital step in the early stages of modelling. However,challenges in dynamic model validation include: (1) Dynamic performances need to be properly quantified. (2) Current studies emphasize on more model fitness rather than similarity.(3) Dynamic performances and systematic parameters are highly coupled.This thesis focuses on the validation of dynamic models. By using Karhunen–Loève transform (K-L transform) and rearranging of dynamic data, important information can be compared effectively. Together with nonparametric tests, where by using p-value in statistical hypothesis testing to construct a reference coordinate system, it is capable to describe the similarity and the fitness between a computational model and an experimental model, and at the same time, calibrate the model. This method is demonstrated using three cases: a mathematical case from literature to show its extensibility, a simple engineering case – a mass-spring-damper system to show its effectiveness, and a real case of vehicle to show its adaptivity. This thesis not only explores into the acquirement of dynamic modelling output data, but also provides a complete method of dynamic modelling validation and facilitation of the process.

並列關鍵字

Model validation ； Nonparametric test ； K-L transform ； Fitness metric ； Similarity metric ； Dynamic simulation analysis

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