Comparative Study of Model Updating Methods by Considering Two Different Convergence Criteria for Iteration Procedure

在模型更新方法的疊代程序考慮兩不同收斂指標的比較

李念龍(Nien-Lung Lee)

《中國機械工程學刊》 36卷6期 (2015/12) Pp. 521-529

摘要

過去幾十年來，「敏感度」為基礎的疊代修正計算程序廣泛應用在「有限元素模型更新方法」。且多種利用模態實驗「有限量測點位」的模型更新法可修正並提高有限元素分析模型的準確性。由於相關文獻顯少探討不同的「收斂停止指標」在同一「有限元素模型更新方法」的更新修正效果。故本文「呈現」和「比較」兩個不同的收斂停止指標(theFrobenius Norm及Correlation Coefficients)在敏感度為基礎之疊代更新程序的修正效果。其目標為更新修正「有限元素分析模型」使之逼近「模態實驗」的「自然頻率」及「模態振型」。本文以平面桁架為對象，透過特徵值敏感度(eigensensitivity)的「疊代」更新計算的結果得知，不論量測值有無雜訊汙染，兩個不同收斂停止指標的模型更新程序，都可更新修正使「有限元素分析模型」的「自然頻率」逼近「模態實驗」的「自然頻率」，並提高兩者「模態振型」的MAC值。另外，有限元素分析模型，雖儘可能與實體一致，但因結構的複雜性，故先假設「截面積」和「二次慣性矩」為未確定參數。該參數需有模態實驗來驗證，其誤差需要經過有效的修正，使模型的動態特性與真實的動態特性之差異最小。結果得知，當這些模型的「未確定」參數值以模態實驗的「基準」參數值作為更新修正的目標，有雜訊汙染相較於無雜訊汙染的更新效果較差。

並列摘要

Numerous Finite Element (FE) model updating methods have been developed to improve analytical FE models that use the limited measurement coordinates of experimental models. For many decades, sensitivity-based iterative methods have been extensively used for FE model updating. However, most of the previous discussions on damage detection have described the effectiveness of model updating algorithms. There is a notable absence of attention to comparing different convergence stop criteria applied to specific model updating algorithms. In this paper, we focus on presenting and comparing the performance of sensitivity-based iterative model updating procedures that use two different convergence stop criteria (the Frobenius Norm and Correlation Coefficients). The results of this study may attract attention to the role of different convergence stop criteria implemented in the same iterative model updating algorithm. A sensitivity-based FE model updating procedure that uses incomplete coordinate measurements with and without simulated noise was applied to a rigid plane frame analyzed by consistent mass. The findings indicate that regardless of whether the measurements are polluted by noise, the relative natural frequencies change and modal assurance criterion MAC values significantly improve after a model updating procedure that uses the two convergence stop criteria. However, when the measurements are polluted by noise, the majority of FEM modification factors in 26 frame sub-elements are updated less accurately than those without noise. Noise continues to have a negative influence on the model updating accuracy of both convergence stop criteria.

並列關鍵字

iterative methods ； sensitivity-based iterative model updating procedure ； Finite Element model