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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/34824

Title: 應用特徵時間展開法鑑別非線性工程問題之恢復力
A Characteristic Time Expansion Method for Restoring-Force Identification in a Nonlinear Engineering Problem
Authors: Fu-Hsuan Hsieh
謝馥亘
Contributors: NTOU:Department of Systems Engineering and Naval Architecture
國立臺灣海洋大學:系統工程暨造船學系
Keywords: 反算問題;反算振動問題;恢復力鑑別問題;多尺度特徵時間展開法;自然正則法
inverse problem;inverse vibration problems;Restoring force identification problems;Multi-Scale Characteristic Time Expansion;Natural Regularization method
Date: 2013
Issue Date: 2013-10-07T02:46:58Z
Abstract: 結構振動參數鑑別的問題,將造成數值方法在求解過程中所引發之數值不穩定的現象。為了解決此問題,本論文採用特徵時間展開法結合自然正則法,克服多項式級數展開之高階數值振盪問題。在數學上,因引入了特徵長度,在進行數值計算時,會降低因多項式展開所建立之凡德蒙矩陣(Vandermonde matrix)的條件數,同時可使多項式的級數項數大幅提高,以克服求解過程中多項式展開造成的病態情形及不穩定現象。對於克服代數方程式中,因噪音造成解的不穩定性問題,有別於傳統Tikhonov正則法,本文使用自然正則法來加以解決。經由五個標準算例,分別藉由單、多尺度特徵時間展開法加以計算,結果顯示本文所用之方法,可有效處理非線性工程問題之恢復力。
Since numerical instability phenomena always arise in the solving process for parameters identification of structural vibration, to resolve such a problem, the characteristic time expansion method in conjunction with the natural regularization method is adopted to overcome the higher order numerical oscillation problem when polynomial series expansion is necessary. Due to inclusion of the characteristic length in the scheme, the condition number of the constructed Vandermonde matrix will be reduced and will also increase the term number of polynomial series. Thus, the ill condition and numerical instability of numerical calculations can be resolved. Besides, to overcome the numerical instability problem of a noise disturbance, in contrast to the conventional Tikhonov regularization method, the natural regularization method is again adopted to resolve the problem. It is shown that single-scale and multi-scale characteristic time expansion methods with the natural regularization method can effectively those above mentioned problems through five benchmark examples.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0019951014
http://ntour.ntou.edu.tw/handle/987654321/34824
Appears in Collections:[系統工程暨造船學系] 博碩士論文

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